Semiclassical electron and phonon transport from first principles: application to layered thermoelectrics
Tóm tắt
Thermoelectrics are a promising class of materials for renewable energy owing to their capability to generate electricity from waste heat, with their performance being governed by a competition between charge and thermal transport. A detailed understanding of energy transport at the nanoscale is thus of paramount importance for developing efficient thermoelectrics. Here, we provide a comprehensive overview of the methodologies adopted for the computational design and optimization of thermoelectric materials from first-principles calculations. First, we introduce density-functional theory, the fundamental tool to describe the electronic and vibrational properties of solids. Next, we review charge and thermal transport in the semiclassical framework of the Boltzmann transport equation, with a particular emphasis on the various scattering mechanisms between phonons, electrons, and impurities. Finally, we illustrate how these approaches can be deployed in determining the figure of merit of tin and germanium selenides, an emerging family of layered thermoelectrics that exhibits a promising figure of merit. Overall, this review article offers practical guidelines to achieve an accurate assessment of the thermoelectric properties of materials by means of computer simulations.
Tài liệu tham khảo
Yang, L., Chen, Z.-G., Dargusch, M.S., Zou, J.: High performance thermoelectric materials: progress and their applications. Adv. Energy Mater. 8, 1701797 (2018). https://doi.org/10.1002/aenm.201701797
Hasan, M.N., Wahid, H., Nayan, N., Mohamed Ali, M.S.: Inorganic thermoelectric materials: a review. Int. J. Energy Res. 44, 6170 (2020). https://doi.org/10.1002/er.5313
Zoui, M.A., Bentouba, S., Stocholm, J.G., Bourouis, M.: A review on thermoelectric generators: progress and applications. Energies 13, 3606 (2020). https://doi.org/10.3390/en13143606
Gutiérrez Moreno, J.J., Cao, J., Fronzi, M., Assadi, M.H.N.: A review of recent progress in thermoelectric materials through computational methods. Mater. Renew. Sustain. Energy (2020). https://doi.org/10.1007/s40243-020-00175-5
Giustino, F.: Materials Modelling Using Density Functional Theory: Properties and Predictions. Oxford University Press (2014)
Szabo, A., Ostlund, N.S.: Modern Quantum Chemistry. Introduction to Advanced Electronic Structure Theory. Dover (1996)
Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964). https://doi.org/10.1103/PhysRev.136.B864
Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133 (1965). https://doi.org/10.1103/PhysRev.140.A1133
Sholl, D., Steckel, J.A.: Density Functional Theory: A Practical Introduction. Wiley (2009)
Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford University Press (1994)
Ceperley, D.M., Alder, B.J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566 (1980). https://doi.org/10.1103/PhysRevLett.45.566
Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996). https://doi.org/10.1103/PhysRevLett.77.3865
Perdew, J.P., Wang, Y.: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244 (1992). https://doi.org/10.1103/PhysRevB.45.13244
Perdew, J.P., Ruzsinszky, A., Csonka, G.I., Vydrov, O.A., Scuseria, G.E., Constantin, L.A., Zhou, X., Burke, K.: Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008). https://doi.org/10.1103/PhysRevLett.100.136406
Zhang, Y., Yang, W.: Comment on Generalized gradient approximation made simple. Phys. Rev. Lett. 80, 890 (1998). https://doi.org/10.1103/PhysRevLett.80.890
Sun, J., Marsman, M., Csonka, G.I., Ruzsinszky, A., Hao, P., Kim, Y.-S., Kresse, G., Perdew, J.P.: Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method. Phys. Rev. B 84, 035117 (2011). https://doi.org/10.1103/PhysRevB.84.035117
Sun, J., Ruzsinszky, A., Perdew, J.P.: Strongly constrained and appropriately normed semilocal density functional. Phys. Rev. Lett. 115, 036402 (2015). https://doi.org/10.1103/PhysRevLett.115.036402
Perdew, J.P., Ernzerhof, M., Burke, K.: Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 105, 9982 (1996). https://doi.org/10.1063/1.472933
Heyd, J., Scuseria, G.E., Ernzerhof, M.: Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207 (2003). https://doi.org/10.1063/1.1564060
Krukau, A.V., Vydrov, O.A., Izmaylov, A.F., Scuseria, G.E.: Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 125, 224106 (2006). https://doi.org/10.1063/1.2404663
Görling, A.: Density-functional theory for excited states. Phys. Rev. A 54, 3912 (1996)
Cohen, A.J., Mori-Sánchez, P., Yang, W.: Insights into current limitations of density functional theory. Science 321, 792 (2008)
Gonze, X., Amadon, B., Anglade, P.-M., Beuken, J.-M., Bottin, F., Boulanger, P., Bruneval, F., Caliste, D., Caracas, R., Côté, M., Deutsch, T., Genovese, L., Ghosez, P., Giantomassi, M., Goedecker, S., Hamann, D., Hermet, P., Jollet, F., Jomard, G., Leroux, S., Mancini, M., Mazevet, S., Oliveira, M., Onida, G., Pouillon, Y., Rangel, T., Rignanese, G.-M., Sangalli, D., Shaltaf, R., Torrent, M., Verstraete, M., Zerah, G., Zwanziger, J.: Abinit: first-principles approach to material and nanosystem properties. Comput. Phys. Commun. 180, 2582 (2009). https://doi.org/10.1016/j.cpc.2009.07.007
Clark, S.J., Segall, M.D., Pickard, C.J., Hasnip, P.J., Probert, M.I.J., Refson, K., Payne, M.C.: First principles methods using castep. Z. Krist. Cryst. Mater. 220, 567 (2005). https://doi.org/10.1524/zkri.220.5.567.65075
Hutter, J., Iannuzzi, M., Schiffmann, F., VandeVondele, J.: cp2k: atomistic simulations of condensed matter systems. WIREs Comput. Mol. Sci. 4, 15 (2014). https://doi.org/10.1002/wcms.1159
Enkovaara, J., Rostgaard, C., Mortensen, J.J., Chen, J., Dułak, M., Ferrighi, L., Gavnholt, J., Glinsvad, C., Haikola, V., Hansen, H.A., Kristoffersen, H.H., Kuisma, M., Larsen, A.H., Lehtovaara, L., Ljungberg, M., Lopez-Acevedo, O., Moses, P.G., Ojanen, J., Olsen, T., Petzold, V., Romero, N.A., Stausholm-Møller, J., Strange, M., Tritsaris, G.A., Vanin, M., Walter, M., Hammer, B., Häkkinen, H., Madsen, G.K.H., Nieminen, R.M., Nørskov, J.K., Puska, M., Rantala, T.T., Schiøtz, J., Thygesen, K.S., Jacobsen, K.W.: Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method. J. Phys. Condens. Matter 22, 253202 (2010). https://doi.org/10.1088/0953-8984/22/25/253202
Prentice, J.C., Aarons, J., Womack, J.C., Allen, A.E., Andrinopoulos, L., Anton, L., Bell, R.A., Bhandari, A., Bramley, G.A., Charlton, R.J., et al.: The onetep linear-scaling density functional theory program. J. Chem. Phys. 152, 174111 (2020). https://doi.org/10.1063/5.0004445
Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., Corso, A.D., de Gironcoli, S., Fabris, S., Fratesi, G., Gebauer, R., Gerstmann, U., Gougoussis, C., Kokalj, A., Lazzeri, M., Martin-Samos, L., Marzari, N., Mauri, F., Mazzarello, R., Paolini, S., Pasquarello, A., Paulatto, L., Sbraccia, C., Scandolo, S., Sclauzero, G., Seitsonen, A.P., Smogunov, A., Umari, P., Wentzcovitch, R.M.: QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009). https://doi.org/10.1088/0953-8984/21/39/395502
Kresse, G., Furthmüller, J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996). https://doi.org/10.1103/PhysRevB.54.11169
Kresse, G., Furthmüller, J.: Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15 (1996). https://doi.org/10.1016/0927-0256(96)00008-0
Marzari, N., Vanderbilt, D.: Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847 (1997). https://doi.org/10.1103/PhysRevB.56.12847
Marzari, N., Mostofi, A.A., Yates, J.R., Souza, I., Vanderbilt, D.: Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419 (2012). https://doi.org/10.1103/RevModPhys.84.1419
Mostofi, A.A., Yates, J.R., Lee, Y.-S., Souza, I., Vanderbilt, D., Marzari, N.: wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685 (2008). https://doi.org/10.1016/j.cpc.2007.11.016
Mostofi, A.A., Yates, J.R., Pizzi, G., Lee, Y.-S., Souza, I., Vanderbilt, D., Marzari, N.: An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185, 2309 (2014). https://doi.org/10.1016/j.cpc.2014.05.003
Born, M., Huang, K.: Dynamical Theory of Crystal Lattices. Clarendon Press (1966)
Hellmann, H.: Einfuhrung in Die Quantenchemie. F. Deuticke, Leipzig (1937)
Feynman, R.P.: Forces in molecules. Phys. Rev. 56, 340 (1939). https://doi.org/10.1103/PhysRev.56.340
DeCicco, P., Johnson, F.: The quantum theory of lattice dynamics. IV. Proc. Lond. A R. Soc. Math. Phys. Sci. 310, 111 (1969). https://doi.org/10.1098/rspa.1969.0066
Pick, R.M., Cohen, M.H., Martin, R.M.: Microscopic theory of force constants in the adiabatic approximation. Phys. Rev. B 1, 910 (1970). https://doi.org/10.1103/PhysRevB.1.910
Maradudin, A.A., Vosko, S.H.: Symmetry properties of the normal vibrations of a crystal. Rev. Mod. Phys. 40, 1 (1968). https://doi.org/10.1103/RevModPhys.40.1
Baroni, S., Giannozzi, P., Testa, A.: Elastic constants of crystals from linear-response theory. Phys. Rev. Lett. 59, 2662 (1987). https://doi.org/10.1103/PhysRevLett.59.2662
Levine, Z.H., Allan, D.C.: Linear optical response in silicon and germanium including self-energy effects. Phys. Rev. Lett. 63, 1719 (1989). https://doi.org/10.1103/PhysRevLett.63.1719
Giannozzi, P., De Gironcoli, S., Pavone, P., Baroni, S.: Ab initio calculation of phonon dispersions in semiconductors. Phys. Rev. B 43, 7231 (1991). https://doi.org/10.1103/PhysRevB.43.7231
de Gironcoli, S., Baroni, S., Resta, R.: Piezoelectric properties of III–V semiconductors from first-principles linear-response theory. Phys. Rev. Lett. 62, 2853 (1989). https://doi.org/10.1103/PhysRevLett.62.2853
de Gironcoli, S., Giannozzi, P., Baroni, S.: Structure and thermodynamics of Si\(_x\) Ge\(_{1-x}\) alloys from ab initio Monte Carlo simulations. Phys. Rev. Lett. 66, 2116 (1991). https://doi.org/10.1103/PhysRevLett.66.2116
Dal Corso, A., Baroni, S., Resta, R.: Density-functional theory of the dielectric constant: gradient-corrected calculation for silicon. Phys. Rev. B 49, 5323 (1994). https://doi.org/10.1103/PhysRevB.49.5323
Quong, A.A., Eguiluz, A.G.: First-principles evaluation of dynamical response and plasmon dispersion in metals. Phys. Rev. Lett. 70, 3955 (1993). https://doi.org/10.1103/PhysRevLett.70.3955
Stengel, M.: Flexoelectricity from density-functional perturbation theory. Phys. Rev. B 88, 174106 (2013). https://doi.org/10.1103/PhysRevB.88.174106
Dreyer, C.E., Stengel, M., Vanderbilt, D.: Current-density implementation for calculating flexoelectric coefficients. Phys. Rev. B 98, 075153 (2018). https://doi.org/10.1103/PhysRevB.98.075153
Royo, M., Stengel, M.: First-principles theory of spatial dispersion: dynamical quadrupoles and flexoelectricity. Phys. Rev. X 9, 021050 (2019). https://doi.org/10.1103/PhysRevX.9.021050
Stott, M., Zaremba, E.: Linear-response theory within the density-functional formalism: application to atomic polarizabilities. Phys. Rev. A 21, 12 (1980). https://doi.org/10.1103/PhysRevA.21.12
Zangwill, A., Soven, P.: Resonant photoemission in barium and cerium. Phys. Rev. Lett. 45, 204 (1980). https://doi.org/10.1103/PhysRevLett.45.204
Mahan, G.: Modified Sternheimer equation for polarizability. Phys. Rev. A 22, 1780 (1980). https://doi.org/10.1103/PhysRevA.22.1780
Ghosh, S.K., Deb, B.M.: Dynamic polarizability of many-electron systems within a time-dependent density-functional theory. Chem. Phys. 71, 295 (1982). https://doi.org/10.1016/0301-0104(82)87030-4
Zein, N.: On density functional calculations of crystal elastic modula and phonon spectra. Fiz. Tverd. Tela 26, 3028 (1984)
Baroni, S., Giannozzi, P., Testa, A.: Green’s-function approach to linear response in solids. Phys. Rev. Lett. 58, 1861 (1987). https://doi.org/10.1103/PhysRevLett.58.1861
Gonze, X., Allan, D.C., Teter, M.P.: Dielectric tensor, effective charges, and phonons in \(\alpha\)-quartz by variational density-functional perturbation theory. Phys. Rev. Lett. 68, 3603 (1992). https://doi.org/10.1103/PhysRevLett.68.3603
Gonze, X., Vigneron, J.-P.: Density-functional approach to nonlinear-response coefficients of solids. Phys. Rev. B 39, 13120 (1989). https://doi.org/10.1103/PhysRevB.39.13120
Hirschfelder, J.O., Brown, W.B., Epstein, S.T.: Recent developments in perturbation theory. In: Advances in Quantum Chemistry. Academic Press Inc., pp. 255–374 (1964)
Baroni, S., De Gironcoli, S., Dal Corso, A., Giannozzi, P.: Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515 (2001). https://doi.org/10.1103/RevModPhys.73.515
Gonze, X.: Adiabatic density-functional perturbation theory. Phys. Rev. A 52, 1096 (1995). https://doi.org/10.1103/PhysRevA.52.1096
Gonze, X.: Perturbation expansion of variational principles at arbitrary order. Phys. Rev. A 52, 1086 (1995). https://doi.org/10.1103/PhysRevA.52.1086
Lam, P.K., Cohen, M.L.: Ab initio calculation of phonon frequencies of Al. Phys. Rev. B 25, 6139 (1982). https://doi.org/10.1103/PhysRevB.25.6139
Togo, A.: First-principles phonon calculations with phonopy and phono3py. J. Phys. Soc. Jpn. 92, 012001 (2023). https://doi.org/10.7566/JPSJ.92.012001
McGaughey, A.J., Kaviany, M.: Phonon transport in molecular dynamics simulations: formulation and thermal conductivity prediction. Adv. Heat Transf. 39, 169 (2006). https://doi.org/10.1016/S0065-2717(06)39002-8
Kong, L.T.: Phonon dispersion measured directly from molecular dynamics simulations. Comput. Phys. Commun. 182, 2201 (2011). https://doi.org/10.1016/j.cpc.2011.04.019
Hellman, O., Abrikosov, I., Simak, S.: Lattice dynamics of anharmonic solids from first principles. Phys. Rev. B 84, 180301 (2011)
Unke, O.T., Chmiela, S., Sauceda, H.E., Gastegger, M., Poltavsky, I., Schütt, K.T., Tkatchenko, A., Müller, K.-R.: Machine learning force fields. Chem. Rev. 121, 10142 (2021)
Haug, H., Jauho, A.-P., Cardona, M.: Quantum Kinetics in Transport and Optics of Semiconductors, vol. 2. Springer (2008)
Stefanucci, G., Van Leeuwen, R.: Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction. Cambridge University Press (2013)
Mahan, G.D.: Condensed matter in a nutshell. In: Condensed Matter in a Nutshell. Princeton University Press (2010)
Kubo, R.: Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570 (1957). https://doi.org/10.1143/JPSJ.12.570
Kubo, R.: The fluctuation-dissipation theorem. Rep. Prog. Phys. 29, 255 (1966). https://doi.org/10.1088/0034-4885/29/1/306
Thouless, D.: Relation between the Kubo–Greenwood formula and the Boltzmann equation for electrical conductivity. Phil. Mag. 32, 877 (1975). https://doi.org/10.1080/14786437508221628
Poncé, S., Li, W., Reichardt, S., Giustino, F.: First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials. Rep. Prog. Phys. 83, 036501 (2020). https://doi.org/10.1088/1361-6633/ab6a43
Sangalli, D., Marini, A.: Ultra-fast carriers relaxation in bulk silicon following photo-excitation with a short and polarized laser pulse. Europhys. Lett. 110, 47004 (2015). https://doi.org/10.1209/0295-5075/110/47004
Landau, L.: On the theory of the fermi liquid. Sov. Phys. JETP 8, 70 (1959)
Pines, D.: Theory of Quantum Liquids: Normal Fermi Liquids. CRC Press (2018)
Pottier, N.: Nonequilibrium Statistical Physics: Linear Irreversible Processes. Oxford University Press (2009)
Peierls, R.: Some simple remarks on the basis of transport theory. In: Transport Phenomena. Springer, pp. 1–33 (1974)
Hussey, N.E., Takenaka, K., Takagi, H.: Universality of the Mott–Ioffe–Regel limit in metals. Phil. Mag. 84, 2847 (2004). https://doi.org/10.1080/14786430410001716944
Emery, V.J., Kivelson, S.A.: Superconductivity in bad metals. Phys. Rev. Lett. 74, 3253 (1995). https://doi.org/10.1103/PhysRevLett.74.3253
Hartnoll, S.A.: Theory of universal incoherent metallic transport. Nat. Phys. 11, 54 (2015). https://doi.org/10.1038/nphys3174
Chang, B.K., Zhou, J.-J., Lee, N.-E., Bernardi, M.: Intermediate polaronic charge transport in organic crystals from a many-body first-principles approach. npj Comput. Mater. 8, 63 (2022). https://doi.org/10.1038/s41524-022-00742-6
Kohn, W., Luttinger, J.M.: Quantum theory of electrical transport phenomena. Phys. Rev. 108, 590 (1957). https://doi.org/10.1103/PhysRev.108.590
Luttinger, J.M., Kohn, W.: Quantum theory of electrical transport phenomena. II. Phys. Rev. 109, 1892 (1958). https://doi.org/10.1103/PhysRev.109.1892
Protik, N.H., Li, C., Pruneda, M., Broido, D., Ordejón, P.: The elphbolt ab initio solver for the coupled electron–phonon Boltzmann transport equations. npj Comput. Mater. 8, 28 (2022). https://doi.org/10.1038/s41524-022-00710-0
Xiao, D., Chang, M.-C., Niu, Q.: Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010)
von Neumann, J.: Proof of the ergodic theorem and the H-theorem in quantum mechanics. Eur. Phys. J. H 35, 201 (2010). https://doi.org/10.1140/epjh/e2010-00008-5
Kadanoff, L.P.: Entropy is in flux V3.4. J. Stat. Phys. 167, 1039 (2017). https://doi.org/10.1007/s10955-017-1766-2
Allen, P.: Boltzmann theory and resistivity of metals. Kluwer International Series In Engineering And Computer Science, p. 219 (1996)
Poncé, S., Margine, E.R., Giustino, F.: Towards predictive many-body calculations of phonon-limited carrier mobilities in semiconductors. Phys. Rev. B 97, 121201 (2018). https://doi.org/10.1103/PhysRevB.97.121201
Liu, Y., Yuan, Z., Wesselink, R., Starikov, A.A., Van Schilfgaarde, M., Kelly, P.J.: Direct method for calculating temperature-dependent transport properties. Phys. Rev. B 91, 220405 (2015). https://doi.org/10.1103/PhysRevB.91.220405
Ziman, J.M.: Electrons and Phonons: The Theory of Transport Phenomena in Solids. Oxford University Press (2001)
Grimvall, G.: The electron–phonon interaction in metals. North-Holland, Amsterdam (1981)
Askerov, B.M., Figarova, S.: Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases. Springer Series on Atomic, Optical and Plasma Physics, vol. 57. Springer (2009)
Chaves, A.S., González-Romero, R.L., Meléndez, J.J., Antonelli, A.: Investigating charge carrier scattering processes in anisotropic semiconductors through first-principles calculations: the case of p-type SnSe. Phys. Chem. Chem. Phys. 23, 900 (2021). https://doi.org/10.1039/D0CP05022A
Ahmad, S., Mahanti, S.: Energy and temperature dependence of relaxation time and Wiedemann–Franz law on PbTe. Phys. Rev. B 81, 165203 (2010). https://doi.org/10.1103/PhysRevB.81.165203
Ravich, Y.I., Efimova, B., Tamarchenko, V.: Scattering of current carriers and transport phenomena in lead chalcogenides. Phys. Status Solidi (B) 43, 11 (1971). https://doi.org/10.1002/pssb.2220430102
Li, W.: Electrical transport limited by electron–phonon coupling from Boltzmann transport equation: an ab initio study of Si, Al, and MoS\(_2\). Phys. Rev. B 92, 075405 (2015). https://doi.org/10.1103/PhysRevB.92.075405
Poncé, S., Margine, E.R., Verdi, C., Giustino, F.: Epw: electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions. Comput. Phys. Commun. 209, 116 (2016). https://doi.org/10.1016/j.cpc.2016.07.028
Li, W., Carrete, J., Katcho, N.A., Mingo, N.: ShengBTE: a solver of the Boltzmann transport equation for phonons. Comput. Phys. Commun. 185, 1747–1758 (2014). https://doi.org/10.1016/j.cpc.2014.02.015
Zhou, J.-J., Park, J., Lu, I.-T., Maliyov, I., Tong, X., Bernardi, M.: Perturbo: a software package for ab initio electron–phonon interactions, charge transport and ultrafast dynamics. Comput. Phys. Commun. 264, 107970 (2021). https://doi.org/10.1016/j.cpc.2021.107970
Cepellotti, A., Coulter, J., Johansson, A., Fedorova, N.S., Kozinsky, B.: Phoebe: a high-performance framework for solving phonon and electron Boltzmann transport equations. J. Phys. Mater. 5, 035003 (2022). https://doi.org/10.1088/2515-7639/ac86f6
Onsager, L.: Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405 (1931). https://doi.org/10.1103/PhysRev.37.405
Onsager, L.: Reciprocal relations in irreversible processes. II. Phys. Rev. 38, 2265 (1931). https://doi.org/10.1103/PhysRev.38.2265
Callen, H.B.: The application of Onsager’s reciprocal relations to thermoelectric, thermomagnetic, and galvanomagnetic effects. Phys. Rev. 73, 1349 (1948). https://doi.org/10.1103/PhysRev.73.1349
Groot, S.R.: Thermodynamics of Irreversible Processes, vol. 3. North-Holland Publishing Company (1963)
Callen, H.B.: Thermodynamics and an Introduction to Thermostatistics. Wiley (1995)
Goupil, C., Seifert, W., Zabrocki, K., Müller, E., Snyder, G.J.: Thermodynamics of thermoelectric phenomena and applications. Entropy 13, 1481 (2011). https://doi.org/10.3390/e13081481
Feldhoff, A.: Thermoelectric material tensor derived from the Onsager–de Groot–Callen model. Energy Harvest. Syst. 2, 5 (2015). https://doi.org/10.1515/ehs-2014-0040
Chaikin, P.: An introduction to thermopower for those who might want to use it to study organic conductors and superconductors. In: Organic Superconductivity. Springer, pp. 101–115 (1990)
Robinson, J.E.: Thermoelectric power in the nearly-free-electron model. Phys. Rev. 161, 533 (1967). https://doi.org/10.1103/PhysRev.161.533
Feldhoff, A., Geppert, B.: A high-temperature thermoelectric generator based on oxides. Energy Harvest. Syst. 1, 69 (2014). https://doi.org/10.1515/ehs-2014-0016
Antončík, E.: On the theory of temperature shift of the absorption curve in non-polar crystals. Cechoslov. Fiz. Z. 5, 449 (1955). https://doi.org/10.1007/BF01687209
Lautenschlager, P., Allen, P., Cardona, M.: Phonon-induced lifetime broadenings of electronic states and critical points in Si and Ge. Phys. Rev. B 33, 5501 (1986). https://doi.org/10.1103/PhysRevB.33.5501
Giustino, F.: Electron–phonon interactions from first principles. Rev. Mod. Phys. 89, 015003 (2017). https://doi.org/10.1103/RevModPhys.89.015003
Keating, P.: Dielectric screening and the phonon spectra of metallic and nonmetallic crystals. Phys. Rev. 175, 1171 (1968). https://doi.org/10.1103/PhysRev.175.1171
Marini, A., Poncé, S., Gonze, X.: Many-body perturbation theory approach to the electron-phonon interaction with density-functional theory as a starting point. Phys. Rev. B 91, 224310 (2015). https://doi.org/10.1103/PhysRevB.91.224310
Baym, G.: Field-theoretic approach to the properties of the solid state. Ann. Phys. 14, 1 (1961). https://doi.org/10.1016/0003-4916(61)90050-1
Hedin, L., Lundqvist, S.: Effects of electron–electron and electron–phonon interactions on the one-electron states of solids. In: Solid State Physics, vol. 23. Elsevier, pp. 1–181 (1970)
Migdal, A.: Interaction between electrons and lattice vibrations in a normal metal. Sov. Phys. JETP 7, 996 (1958)
Allen, P.B., Mitrović, B.: Theory of superconducting \(T_c\). Solid State Phys. 37, 1 (1983). https://doi.org/10.1016/S0081-1947(08)60665-7
Mustafa, J.I., Bernardi, M., Neaton, J.B., Louie, S.G.: Ab initio electronic relaxation times and transport in noble metals. Phys. Rev. B 94, 155105 (2016). https://doi.org/10.1103/PhysRevB.94.155105
Gonze, X., Lee, C.: Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. Phys. Rev. B 55, 10355 (1997). https://doi.org/10.1103/PhysRevB.55.10355
Verdi, C., Giustino, F.: Fröhlich electron–phonon vertex from first principles. Phys. Rev. Lett. 115, 176401 (2015). https://doi.org/10.1103/PhysRevLett.115.176401
Born, M., Huang, K.: Dynamical Theory of Crystal Lattices. Oxford University Press, London (1954)
Frölich, H.: Electrical breakdown in solid crystals. Proc. R. Soc. 160, 230–238 (1937)
Callen, H.B.: Electric breakdown in ionic crystals. Phys. Rev. 76, 1394 (1949). https://doi.org/10.1103/PhysRev.76.1394
Howarth, D., Sondheimer, E.: The theory of electronic conduction in polar semi-conductors. Proc. R. Soc. Lond. A 219, 53 (1953). https://doi.org/10.1098/rspa.1953.0130
Vogl, P.: Microscopic theory of electron–phonon interaction in insulators or semiconductors. Phys. Rev. B 13, 694 (1976). https://doi.org/10.1103/PhysRevB.13.694
Lawaetz, P.: Long-wavelength phonon scattering in nonpolar semiconductors. Phys. Rev. 183, 730 (1969). https://doi.org/10.1103/PhysRev.183.730
Rohlfing, M., Louie, S.G.: Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927 (2000). https://doi.org/10.1103/PhysRevB.62.4927
Sjakste, J., Vast, N., Calandra, M., Mauri, F.: Wannier interpolation of the electron–phonon matrix elements in polar semiconductors: Polar-optical coupling in GAAS. Phys. Rev. B 92, 054307 (2015). https://doi.org/10.1103/PhysRevB.92.054307
Brunin, G., Miranda, H.P.C., Giantomassi, M., Royo, M., Stengel, M., Verstraete, M.J., Gonze, X., Rignanese, G.-M., Hautier, G.: Electron–phonon beyond Fröhlich: dynamical quadrupoles in polar and covalent solids. Phys. Rev. Lett. 125, 136601 (2020). https://doi.org/10.1103/PhysRevLett.125.136601
Brunin, G., Miranda, H.P.C., Giantomassi, M., Royo, M., Stengel, M., Verstraete, M.J., Gonze, X., Rignanese, G.-M., Hautier, G.: Phonon-limited electron mobility in Si, GAAS, and gap with exact treatment of dynamical quadrupoles. Phys. Rev. B 102, 094308 (2020). https://doi.org/10.1103/PhysRevB.102.094308
Jhalani, V.A., Zhou, J.-J., Park, J., Dreyer, C.E., Bernardi, M.: Piezoelectric electron–phonon interaction from ab initio dynamical quadrupoles: impact on charge transport in wurtzite GaN. Phys. Rev. Lett. 125, 136602 (2020). https://doi.org/10.1103/PhysRevLett.125.136602
Park, J., Zhou, J.-J., Jhalani, V.A., Dreyer, C.E., Bernardi, M.: Long-range quadrupole electron–phonon interaction from first principles. Phys. Rev. B 102, 125203 (2020). https://doi.org/10.1103/PhysRevB.102.125203
Martin, R.M.: Piezoelectricity. Phys. Rev. B 5, 1607 (1972). https://doi.org/10.1103/PhysRevB.5.1607
Poncé, S., Macheda, F., Margine, E.R., Marzari, N., Bonini, N., Giustino, F.: First-principles predictions of hall and drift mobilities in semiconductors. Phys. Rev. Res. 3, 043022 (2021). https://doi.org/10.1103/PhysRevResearch.3.043022
Ren, Q., Fu, C., Qiu, Q., Dai, S., Liu, Z., Masuda, T., Asai, S., Hagihala, M., Lee, S., Torri, S., Kamiyama, T., He, L., Tong, X., Felser, C., Singh, D.J., Zhu, T., Yang, J., Ma, J.: Establishing the carrier scattering phase diagram for ZrNiSn-based half-Heusler thermoelectric materials. Nat. Commun. 11, 1 (2020). https://doi.org/10.1038/s41467-020-16913-2
Macheda, F., Barone, P., Mauri, F.: Electron–phonon interaction and longitudinal-transverse phonon splitting in doped semiconductors. Phys. Rev. Lett. 129, 185902 (2022). https://doi.org/10.1103/PhysRevLett.129.185902
Ehrenreich, H.: Screening effects in polar semiconductors. J. Phys. Chem. Solids 8, 130 (1959). https://doi.org/10.1016/0022-3697(59)90297-5
Chaves, A.S., Larson, D.T., Kaxiras, E., Antonelli, A.: Microscopic origin of the high thermoelectric figure of merit of n-doped SnSe. Phys. Rev. B 104, 115204 (2021). https://doi.org/10.1103/PhysRevB.104.115204
Chaves, A.S., Larson, D.T., Kaxiras, E., Antonelli, A.: Out-of-plane thermoelectric performance for p-doped GeSe. Phys. Rev. B 105, 205201 (2022). https://doi.org/10.1103/PhysRevB.105.205201
Radisavljevic, B., Kis, A.: Mobility engineering and a metal-insulator transition in monolayer MoS\(_2\). Nat. Mater. 12, 815 (2013). https://doi.org/10.1038/nmat3687
Li, S.-L., Tsukagoshi, K., Orgiu, E., Samorì, P.: Charge transport and mobility engineering in two-dimensional transition metal chalcogenide semiconductors. Chem. Soc. Rev. 45, 118 (2016). https://doi.org/10.1039/C5CS00517E
Bergmann, G.: Weak localization in thin films: a time-of-flight experiment with conduction electrons. Phys. Rep. 107, 1 (1984). https://doi.org/10.1016/0370-1573(84)90103-0
Lee, P.A., Stone, A.D.: Universal conductance fluctuations in metals. Phys. Rev. Lett. 55, 1622 (1985). https://doi.org/10.1103/PhysRevLett.55.1622
Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge University Press (1997)
Dewandre, A., Hellman, O., Bhattacharya, S., Romero, A.H., Madsen, G.K., Verstraete, M.J.: Two-step phase transition in SnSe and the origins of its high power factor from first principles. Phys. Rev. Lett. 117, 276601 (2016). https://doi.org/10.1103/PhysRevLett.117.276601
Gunlycke, D., White, C.T.: Graphene valley filter using a line defect. Phys. Rev. Lett. 106, 136806 (2011). https://doi.org/10.1103/PhysRevLett.106.136806
Koenraad, P.M., Flatté, M.E.: Single dopants in semiconductors. Nat. Mater. 10, 91 (2011). https://doi.org/10.1038/nmat2940
Zheng, Y., Slade, T.J., Hu, L., Tan, X.Y., Luo, Y., Luo, Z.-Z., Xu, J., Yan, Q., Kanatzidis, M.G.: Defect engineering in thermoelectric materials: what have we learned? Chem. Soc. Rev. (2021). https://doi.org/10.1039/D1CS00347J
Brooks, H.: Theory of the electrical properties of germanium and silicon. In: Advances in Electronics and Electron Physics, vol. 7. Elsevier, pp. 85–182 (1955)
Chattopadhyay, D., Queisser, H.J.: Electron scattering by ionized impurities in semiconductors. Rev. Mod. Phys. 53, 745 (1981). https://doi.org/10.1103/RevModPhys.53.745
Moore, E.J.: Quantum-transport theories and multiple scattering in doped semiconductors. I. Formal theory. Phys. Rev. 160, 607 (1967). https://doi.org/10.1103/PhysRev.160.607
Papanikolaou, N., Zeller, R., Dederichs, P., Stefanou, N.: Lattice distortion in Cu-based dilute alloys: a first-principles study by the KKR Green-function method. Phys. Rev. B 55, 4157 (1997). https://doi.org/10.1103/PhysRevB.55.4157
Settels, A., Korhonen, T., Papanikolaou, N., Zeller, R., Dederichs, P.: Ab initio study of acceptor-donor complexes in silicon and germanium. Phys. Rev. Lett. 83, 4369 (1999). https://doi.org/10.1103/PhysRevLett.83.4369
Höhler, H., Atodiresei, N., Schroeder, K., Zeller, R., Dederichs, P.: Cd-vacancy and Cd-interstitial complexes in Si and Ge. Phys. Rev. B 70, 155313 (2004). https://doi.org/10.1103/PhysRevB.70.155313
Ebert, H., Koedderitzsch, D., Minar, J.: Calculating condensed matter properties using the KKR-Green’s function method-recent developments and applications. Rep. Prog. Phys. 74, 096501 (2011). https://doi.org/10.1088/0034-4885/74/9/096501
Restrepo, O., Varga, K., Pantelides, S.: First-principles calculations of electron mobilities in silicon: phonon and coulomb scattering. Appl. Phys. Lett. 94, 212103 (2009). https://doi.org/10.1063/1.3147189
Lordi, V., Erhart, P., Åberg, D.: Charge carrier scattering by defects in semiconductors. Phys. Rev. B 81, 235204 (2010). https://doi.org/10.1103/PhysRevB.81.235204
Lu, I.-T., Zhou, J.-J., Bernardi, M.: Efficient ab initio calculations of electron-defect scattering and defect-limited carrier mobility. Phys. Rev. Mater. 3, 033804 (2019). https://doi.org/10.1103/PhysRevMaterials.3.033804
Lu, I.-T., Park, J., Zhou, J.-J., Bernardi, M.: Ab initio electron-defect interactions using Wannier functions. npj Comput. Mater. 6, 1 (2020). https://doi.org/10.1038/s41524-020-0284-y
Fugallo, G., Lazzeri, M., Paulatto, L., Mauri, F.: Ab initio variational approach for evaluating lattice thermal conductivity. Phys. Rev. B 88, 045430 (2013). https://doi.org/10.1103/PhysRevB.88.045430
Feng, T., Ruan, X.: Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids. Phys. Rev. B 93, 045202 (2016). https://doi.org/10.1103/PhysRevB.93.045202
Han, Z., Yang, X., Li, W., Feng, T., Ruan, X.: Fourphonon: an extension module to Shengbte for computing four-phonon scattering rates and thermal conductivity. Comput. Phys. Commun. 270, 108179 (2022). https://doi.org/10.1016/j.cpc.2021.108179
Garg, J., Bonini, N., Kozinsky, B., Marzari, N.: Role of disorder and anharmonicity in the thermal conductivity of silicon–germanium alloys: a first-principles study. Phys. Rev. Lett. 106, 045901 (2011). https://doi.org/10.1103/PhysRevLett.106.045901
Liao, B., Qiu, B., Zhou, J., Huberman, S., Esfarjani, K., Chen, G.: Significant reduction of lattice thermal conductivity by the electron–phonon interaction in silicon with high carrier concentrations: a first-principles study. Phys. Rev. Lett. 114, 115901 (2015). https://doi.org/10.1103/PhysRevLett.114.115901
Madsen, G.K., Singh, D.J.: Boltztrap. a code for calculating band-structure dependent quantities. Comput. Phys. Commun. 175, 67 (2006). https://doi.org/10.1016/j.cpc.2006.03.007
Bardeen, J., Shockley, W.: Deformation potentials and mobilities in non-polar crystals. Phys. Rev. 80, 72 (1950). https://doi.org/10.1103/PhysRev.80.72
Xi, J., Long, M., Tang, L., Wang, D., Shuai, Z.: First-principles prediction of charge mobility in carbon and organic nanomaterials. Nanoscale 4, 4348 (2012). https://doi.org/10.1039/C2NR30585B
Xi, L., Pan, S., Li, X., Xu, Y., Ni, J., Sun, X., Yang, J., Luo, J., Xi, J., Zhu, W., et al.: Discovery of high-performance thermoelectric chalcogenides through reliable high-throughput material screening. J. Am. Chem. Soc. 140, 10785 (2018). https://doi.org/10.1021/jacs.8b04704
Ganose, A.M., Park, J., Faghaninia, A., Woods-Robinson, R., Persson, K.A., Jain, A.: Efficient calculation of carrier scattering rates from first principles. Nat. Commun. 12, 1 (2021). https://doi.org/10.1038/s41467-021-22440-5
Ma, J., Nissimagoudar, A.S., Li, W.: First-principles study of electron and hole mobilities of Si and GaAs. Phys. Rev. B 97, 045201 (2018). https://doi.org/10.1103/PhysRevB.97.045201
Giustino, F., Cohen, M.L., Louie, S.G.: Electron–phonon interaction using Wannier functions. Phys. Rev. B 76, 165108 (2007). https://doi.org/10.1103/PhysRevB.76.165108
Agapito, L.A., Bernardi, M.: Ab initio electron–phonon interactions using atomic orbital wave functions. Phys. Rev. B (2018). https://doi.org/10.1103/PhysRevB.97.235146
Samsonidze, G., Kozinsky, B.: Accelerated screening of thermoelectric materials by first-principles computations of electron–phonon scattering. Adv. Energy Mater. 8, 1800246 (2018). https://doi.org/10.1002/aenm.201800246
Deng, T., Wu, G., Sullivan, M.B., Wong, Z.M., Hippalgaonkar, K., Wang, J.-S., Yang, S.-W.: EPIC STAR: a reliable and efficient approach for phonon- and impurity-limited charge transport calculations. npj Comput. Mater. 6, 1 (2020). https://doi.org/10.1038/s41524-020-0316-7
Yao, M., Wang, Y., Li, X., Sheng, Y., Huo, H., Xi, L., Yang, J., Zhang, W.: Materials informatics platform with three dimensional structures, workflow and thermoelectric applications. Sci. Data 8, 1 (2021). https://doi.org/10.1038/s41597-021-01022-6
Engel, M., Marsman, M., Franchini, C., Kresse, G.: Electron-phonon interactions using the projector augmented-wave method and Wannier functions. Phys. Rev. B 101, 184302 (2020). https://doi.org/10.1103/PhysRevB.101.184302
Brouder, C., Panati, G., Calandra, M., Mourougane, C., Marzari, N.: Exponential localization of Wannier functions in insulators. Phys. Rev. Lett. 98, 046402 (2007). https://doi.org/10.1103/PhysRevLett.98.046402
Souza, I., Marzari, N., Vanderbilt, D.: Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001). https://doi.org/10.1103/PhysRevB.65.035109
Fetter, A.L., Walecka, J.D.: Quantum Theory of Many-Particle Systems. Courier Corporation, Berlin (2012)
Chaves, A.S., Antonelli, A., Larson, D.T., Kaxiras, E.: Boosting the efficiency of ab initio electron–phonon coupling calculations through dual interpolation. Phys. Rev. B 102, 125116 (2020). https://doi.org/10.1103/PhysRevB.102.125116
Chadi, D.J., Cohen, M.L.: Special points in the Brillouin zone. Phys. Rev. B 8, 5747 (1973). https://doi.org/10.1103/PhysRevB.8.5747
Shankland, D.G.: Interpolation in k-space with functions of arbitrary smoothness. In: Computational Methods in Band Theory. Springer, pp. 362–367 (1971). https://doi.org/10.1007/978-1-4684-1890-328
Koelling, D., Wood, J.: On the interpolation of eigenvalues and a resultant integration scheme. J. Comput. Phys. 67, 253 (1986). https://doi.org/10.1016/0021-9991(86)90261-5
Pickett, W.E., Krakauer, H., Allen, P.B.: Smooth Fourier interpolation of periodic functions. Phys. Rev. B 38, 2721 (1988). https://doi.org/10.1103/PhysRevB.38.2721
Togo, A., Chaput, L., Tanaka, I.: Distributions of phonon lifetimes in Brillouin zones. Phys. Rev. B 91, 094306 (2015). https://doi.org/10.1103/PhysRevB.91.094306
Carrete, J., Mingo, N., Curtarolo, S.: Low thermal conductivity and triaxial phononic anisotropy of SnSe. Appl. Phys. Lett. 105, 101907 (2014). https://doi.org/10.1063/1.4895770
Pei, Y., Shi, X., LaLonde, A., Wang, H., Chen, L., Snyder, G.J.: Convergence of electronic bands for high performance bulk thermoelectrics. Nature 473, 66 (2011). https://doi.org/10.1038/nature09996
Pei, Y., Wang, H., Snyder, G.J.: Band engineering of thermoelectric materials. Adv. Mater. 24, 6125 (2012). https://doi.org/10.1002/adma.201202919
Liu, W., Tan, X., Yin, K., Liu, H., Tang, X., Shi, J., Zhang, Q., Uher, C.: Convergence of conduction bands as a means of enhancing thermoelectric performance of n-type Mg\(_2\)Si\(_{1-x}\)Sn\(_x\) solid solutions. Phys. Rev. Lett. 108, 166601 (2012). https://doi.org/10.1103/PhysRevLett.108.166601
Dehkordi, A.M., Zebarjadi, M., He, J., Tritt, T.M.: Thermoelectric power factor: enhancement mechanisms and strategies for higher performance thermoelectric materials. Mater. Sci. Eng. R. Rep. 97, 1 (2015). https://doi.org/10.1016/j.mser.2015.08.001
Parker, D.S., May, A.F., Singh, D.J.: Benefits of carrier-pocket anisotropy to thermoelectric performance: the case of p-type AgBiSe\(_2\). Phys. Rev. Appl. 3, 064003 (2015). https://doi.org/10.1103/PhysRevApplied.3.064003
Morelli, D., Jovovic, V., Heremans, J.: Intrinsically minimal thermal conductivity in cubic I–V–VI\(_2\) semiconductors. Phys. Rev. Lett. 101, 035901 (2008). https://doi.org/10.1103/PhysRevLett.101.035901
He, J., Amsler, M., Xia, Y., Naghavi, S.S., Hegde, V.I., Hao, S., Goedecker, S., Ozoliņš, V., Wolverton, C.: Ultralow thermal conductivity in full Heusler semiconductors. Phys. Rev. Lett. 117, 046602 (2016). https://doi.org/10.1103/PhysRevLett.117.046602
González-Romero, R.L., Antonelli, A., Chaves, A.S., Meléndez, J.J.: Ultralow and anisotropic thermal conductivity in semiconductor As\(_2\)Se\(_3\). Phys. Chem. Chem. Phys. 20, 1809 (2018). https://doi.org/10.1039/C7CP07242B
Hochbaum, A.I., Chen, R., Delgado, R.D., Liang, W., Garnett, E.C., Najarian, M., Majumdar, A., Yang, P.: Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163 (2008). https://doi.org/10.1038/nature06381
Boukai, A.I., Bunimovich, Y., Tahir-Kheli, J., Yu, J.-K., Goddard, W.A., III., Heath, J.R.: Silicon nanowires as efficient thermoelectric materials. Nature 451, 168 (2008). https://doi.org/10.1038/nature06458
Kanatzidis, M.G.: Nanostructured thermoelectrics: the new paradigm? Chem. Mater. 22, 648 (2009). https://doi.org/10.1021/cm902195j
Zhao, L.-D., Hao, S., Lo, S.-H., Wu, C.-I., Zhou, X., Lee, Y., Li, H., Biswas, K., Hogan, T.P., Uher, C., Wolverton, C., Dravid, V.P., G, K.M.: High thermoelectric performance via hierarchical compositionally alloyed nanostructures. J. Am. Chem. Soc. 135, 7364 (2013). https://doi.org/10.1021/ja403134b
McKinney, R.W., Gorai, P., Stevanović, V., Toberer, E.S.: Search for new thermoelectric materials with low Lorenz number. J. Mater. Chem. A 5, 17302 (2017). https://doi.org/10.1039/C7TA04332E
Mahan, G., Sofo, J.: The best thermoelectric. Proc. Natl. Acad. Sci. 93, 7436 (1996). https://doi.org/10.1073/pnas.93.15.7436
Baranowski, L.L., Jeffrey Snyder, G., Toberer, E.S.: Effective thermal conductivity in thermoelectric materials. J. Appl. Phys. 113, 204904 (2013). https://doi.org/10.1063/1.4807314
Ortiz, B.R., Gorai, P., Krishna, L., Mow, R., Lopez, A., McKinney, R., Stevanović, V., Toberer, E.S.: Potential for high thermoelectric performance in n-type Zintl compounds: a case study of Ba doped KAlSb\(_4\). J. Mater. Chem. A 5, 4036 (2017). https://doi.org/10.1039/C6TA09532A
Putatunda, A., Singh, D.J.: Lorenz number in relation to estimates based on the Seebeck coefficient. Mater. Today Phys. 8, 49 (2019). https://doi.org/10.1016/j.mtphys.2019.01.001
He, J., Tritt, T.M.: Advances in thermoelectric materials research: looking back and moving forward. Science 357, eaak9997 (2017). https://doi.org/10.1126/science.aak9997
Biswas, K., He, J., Blum, I.D., Wu, C.-I., Hogan, T.P., Seidman, D.N., Dravid, V.P., Kanatzidis, M.G.: High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature 489, 414 (2012). https://doi.org/10.1038/nature11439
Liu, H., Shi, X., Xu, F., Zhang, L., Zhang, W., Chen, L., Li, Q., Uher, C., Day, T., Snyder, G.J.: Copper ion liquid-like thermoelectrics. Nat. Mater. 11, 422 (2012). https://doi.org/10.1038/nmat3273
Fu, T., Yue, X., Wu, H., Fu, C., Zhu, T., Liu, X., Hu, L., Ying, P., He, J., Zhao, X.: Enhanced thermoelectric performance of PbTe bulk materials with figure of merit zT \(>\) 2 by multi-functional alloying. J. Mater. 2, 141 (2016). https://doi.org/10.1016/j.jmat.2016.05.005
Olvera, A., Moroz, N., Sahoo, P., Ren, P., Bailey, T., Page, A., Uher, C., Poudeu, P.: Partial indium solubility induces chemical stability and colossal thermoelectric figure of merit in Cu\(_2\)Se. Energy Environ. Sci. 10, 1668 (2017). https://doi.org/10.1039/C7EE01193H
Cheng, Y., Yang, J., Jiang, Q., He, D., He, J., Luo, Y., Zhang, D., Zhou, Z., Ren, Y., Xin, J.: New insight into InSb-based thermoelectric materials: from a divorced eutectic design to a remarkably high thermoelectric performance. J. Mater. Chem. A 5, 5163 (2017). https://doi.org/10.1039/C6TA10827J
Ma, N., Li, Y.-Y., Chen, L., Wu, L.-M.: \(\alpha\)-CsCu\(_5\)Se\(_3\): discovery of a low-cost bulk selenide with high thermoelectric performance. J. Am. Chem. Soc. 142, 5293 (2020). https://doi.org/10.1021/jacs.0c00062
Roychowdhury, S., Ghosh, T., Arora, R., Samanta, M., Xie, L., Singh, N.K., Soni, A., He, J., Waghmare, U.V., Biswas, K.: Enhanced atomic ordering leads to high thermoelectric performance in AgSbTe\(_2\). Science 371, 722 (2021). https://doi.org/10.1126/science.abb3517
Terasaki, I., Sasago, Y., Uchinokura, K.: Large thermoelectric power in NaCo\(_2\)O\(_4\) single crystals. Phys. Rev. B 56, R12685 (1997). https://doi.org/10.1103/PhysRevB.56.R12685
Rhyee, J.-S., Lee, K.H., Lee, S.M., Cho, E., Kim, S.I., Lee, E., Kwon, Y.S., Shim, J.H., Kotliar, G.: Peierls distortion as a route to high thermoelectric performance in In\(_4\)Se\(_{3-\delta }\) crystals. Nature 459, 965 (2009). https://doi.org/10.1038/nature08088
Ohta, H., Kim, S.W., Kaneki, S., Yamamoto, A., Hashizume, T.: High thermoelectric power factor of high-mobility 2D electron gas. Adv. Sci. 5, 1700696 (2018). https://doi.org/10.1002/advs.201700696
Cheng, L., Zhang, C., Liu, Y.: The optimal electronic structure for high-mobility 2D semiconductors: exceptionally high hole mobility in 2D antimony. J. Am. Chem. Soc. 141, 16296 (2019). https://doi.org/10.1021/jacs.9b05923
Li, Z., Xiao, C., Xie, Y.: Layered thermoelectric materials: structure, bonding, and performance mechanisms. Appl. Phys. Rev. 9, 011303 (2022). https://doi.org/10.1063/5.0074489
Zhao, L.-D., Lo, S.-H., Zhang, Y., Sun, H., Tan, G., Uher, C., Wolverton, C., Dravid, V.P., Kanatzidis, M.G.: Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 508, 373 (2014). https://doi.org/10.1038/nature13184
Zhao, L.-D., Tan, G., Hao, S., He, J., Pei, Y., Chi, H., Wang, H., Gong, S., Xu, H., Dravid, V.P., et al.: Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe. Science 351, 141 (2016). https://doi.org/10.1126/science.aad3749
Chang, C., Wu, M., He, D., Pei, Y., Wu, C.-F., Wu, X., Yu, H., Zhu, F., Wang, K., Chen, Y., et al.: 3D charge and 2D phonon transports leading to high out-of-plane ZT in n-type SnSe crystals. Science 360, 778 (2018). https://doi.org/10.1126/science.aaq1479
Ding, G., Gao, G., Yao, K.: High-efficient thermoelectric materials: the case of orthorhombic IV–VI compounds. Sci. Rep. 5, 1 (2015). https://doi.org/10.1038/srep09567
Guo, R., Wang, X., Kuang, Y., Huang, B.: First-principles study of anisotropic thermoelectric transport properties of IV–VI semiconductor compounds SnSe and SnS. Phys. Rev. B 92, 115202 (2015). https://doi.org/10.1103/PhysRevB.92.115202
Skelton, J.M., Burton, L.A., Parker, S.C., Walsh, A., Kim, C.-E., Soon, A., Buckeridge, J., Sokol, A.A., Catlow, C.R.A., Togo, A., et al.: Anharmonicity in the high-temperature Cmcm phase of SnSe: soft modes and three-phonon interactions. Phys. Rev. Lett. 117, 075502 (2016). https://doi.org/10.1103/PhysRevLett.117.075502
Li, S., Tong, Z., Bao, H.: Resolving different scattering effects on the thermal and electrical transport in doped SnSe. J. Appl. Phys. 126, 025111 (2019). https://doi.org/10.1063/1.5098340
Aseginolaza, U., Bianco, R., Monacelli, L., Paulatto, L., Calandra, M., Mauri, F., Bergara, A., Errea, I.: Phonon collapse and second-order phase transition in thermoelectric SnSe. Phys. Rev. Lett. 122, 075901 (2019). https://doi.org/10.1103/PhysRevLett.122.075901
Zhang, X., Shen, J., Lin, S., Li, J., Chen, Z., Li, W., Pei, Y.: Thermoelectric properties of GeSe. J. Mater. 2, 331 (2016). https://doi.org/10.1016/j.jmat.2016.09.001
Shaabani, L., Aminorroaya-Yamini, S., Byrnes, J., Akbar Nezhad, A., Blake, G.R.: Thermoelectric performance of Na-doped GeSe. ACS Omega 2, 9192 (2017). https://doi.org/10.1021/acsomega.7b01364
Hao, S., Shi, F., Dravid, V.P., Kanatzidis, M.G., Wolverton, C.: Computational prediction of high thermoelectric performance in hole doped layered GeSe. Chem. Mater. 28, 3218 (2016)
Roychowdhury, S., Samanta, M., Perumal, S., Biswas, K.: Germanium chalcogenide thermoelectrics: electronic structure modulation and low lattice thermal conductivity. Chem. Mater. 30, 5799 (2018). https://doi.org/10.1021/acs.chemmater.8b02676
Yuan, K., Sun, Z., Zhang, X., Tang, D.: Tailoring phononic, electronic, and thermoelectric properties of orthorhombic GeSe through hydrostatic pressure. Sci. Rep. 9, 1 (2019). https://doi.org/10.1038/s41598-019-45949-8
Asen-Palmer, M., Bartkowski, K., Gmelin, E., Cardona, M., Zhernov, A., Inyushkin, A., Taldenkov, A., Ozhogin, V., Itoh, K.M., Haller, E.: Thermal conductivity of germanium crystals with different isotopic compositions. Phys. Rev. B 56, 9431 (1997). https://doi.org/10.1103/PhysRevB.56.9431
Omini, M., Sparavigna, A.: An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity. Phys. B 212, 101 (1995). https://doi.org/10.1016/0921-4526(95)00016-3
Simoncelli, M., Marzari, N., Mauri, F.: Unified theory of thermal transport in crystals and glasses. Nat. Phys. 15, 809 (2019). https://doi.org/10.1038/s41567-019-0520-x
Zhou, C., Lee, Y.K., Yu, Y., Byun, S., Luo, Z.-Z., Lee, H., Ge, B., Lee, Y.-L., Chen, X., Lee, J.Y., et al.: Polycrystalline SnSe with a thermoelectric figure of merit greater than the single crystal. Nat. Mater. 20, 1378 (2021). https://doi.org/10.1038/s41563-021-01064-6
Ibrahim, D., Vaney, J.-B., Sassi, S., Candolfi, C., Ohorodniichuk, V., Levinsky, P., Semprimoschnig, C., Dauscher, A., Lenoir, B.: Reinvestigation of the thermal properties of single-crystalline SnSe. Appl. Phys. Lett. 110, 032103 (2017). https://doi.org/10.1063/1.4974348
Sarkar, D., Ghosh, T., Roychowdhury, S., Arora, R., Sajan, S., Sheet, G., Waghmare, U.V., Biswas, K.: Ferroelectric instability induced ultralow thermal conductivity and high thermoelectric performance in rhombohedral p-type GeSe crystal. J. Am. Chem. Soc. 142, 12237 (2020). https://doi.org/10.1021/jacs.0c03696
Xia, Y.: Revisiting lattice thermal transport in PbTe: the crucial role of quartic anharmonicity. Appl. Phys. Lett. 113, 073901 (2018). https://doi.org/10.1063/1.5040887
Wei, P.-C., Bhattacharya, S., He, J., Neeleshwar, S., Podila, R., Chen, Y., Rao, A.: The intrinsic thermal conductivity of SnSe. Nature 539, E1 (2016). https://doi.org/10.1038/nature19832
Zhao, L.-D., Lo, S.-H., Zhang, Y., Sun, H., Tan, G., Uher, C., Wolverton, C., Dravid, V.P., Kanatzidis, M.G.: The intrinsic thermal conductivity of SnSe: Reply. Nature 539, E2 (2016). https://doi.org/10.1038/nature19833
Wu, D., Wu, L., He, D., Zhao, L.-D., Li, W., Wu, M., Jin, M., Xu, J., Jiang, J., Huang, L., et al.: Direct observation of vast off-stoichiometric defects in single crystalline SnSe. Nano Energy 35, 321 (2017). https://doi.org/10.1016/j.nanoen.2017.04.004
Lee, Y.K., Luo, Z., Cho, S.P., Kanatzidis, M.G., Chung, I.: Surface oxide removal for polycrystalline SnSe reveals near-single-crystal thermoelectric performance. Joule 3, 719 (2019). https://doi.org/10.1016/j.joule.2019.01.001