The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles

Lutchyn, R. M., Sau, J. D. & Sarma, S. D. Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).

Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).

Alicea, J., Oreg, Y., Refael, G., von Oppen, F. & Fisher, M. P. A. Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nature Phys. 7, 412–417 (2011).

Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Usp. 44, 131–136 (2001).

Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

Majorana, E. Symmetrical theory of electrons and positrons. Nuovo Cimento. 14, 171–184 (1937).

Dirac, P. A. M. The quantum theory of the electron. Proc. R. Soc. Lond. A 117, 610–624 (1928).

Wilczek, F. Majorana returns. Nature Phys. 5, 614–618 (2009).

Cho, A. The sterile neutrino: Fertile concept or dead end? Science 334, 304–306 (2011).

Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

Sengupta, K., Žutić, I., Kwon, H-J., Yakovenko, V. M. & Das Sarma, S. Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors. Phys. Rev. B 63, 144531 (2001).

Das Sarma, S., Nayak, C. & Tewari, S. Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-abelian braiding statistics of vortices in a p x+i p y superconductor. Phys. Rev. B 73, 220502 (2006).

Read, N. & Green, D. Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Phys. Rev. B 61, 10267–10297 (2000).

Fu, L. & Kane, C. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

Sau, J., Lutchyn, R., Tewari, S. & Das Sarma, S. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 040502 (2010).

Quay, C. et al. Observation of a one-dimensional spin–orbit gap in a quantum wire. Nature Phys. 6, 336–339 (2010).

Alicea, J. Majorana fermions in a tunable semiconductor device. Phys. Rev. B 81, 125318 (2010).

Lutchyn, R. M., Stanescu, T. & Sarma, S. D. Search for Majorana fermions in multiband semiconducting nanowires. Phys. Rev. Lett. 106, 127001 (2011).

Potter, A. C. & Lee, P. A. Multichannel generalization of Kitaev’s Majorana end states and a practical route to realize them in thin films. Phys. Rev. Lett. 105, 227003 (2010).

Stanescu, T., Lutchyn, R. M. & Sarma, S. D. Majorana fermions in semiconductor nanowires. Phys. Rev. B 84, 144522 (2011).

Law, K. T., Lee, P. A. & Ng, T. K. Majorana fermion induced resonant Andreev reflection. Phys. Rev. Lett. 103, 237001 (2009).

Sau, J. D., Tewari, S., Lutchyn, R., Stanescu, T. & Sarma, S. D. Non-abelian quantum order in spin–orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems. Phys. Rev. B 82, 214509 (2010).

Koren, G., Kirzhner, T., Lahoud, E., Chashka, K. B. & Kanigel, A. Proximity-induced superconductivity in topological Bi2Te2Se and Bi2Se3 films: Robust zero-energy bound state possibly due to Majorana fermions. Phys. Rev. B 84, 224521 (2011).

Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).

Deng, M. T. et al. Observation of Majorana fermions in a Nb-InSb nanowire-Nb hybrid quantum device. Preprint at http://arxiv.org/abs/1204.4130  (2012).

Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).

Rokhinson, L. P., Guo, L. J., Chou, S. Y. & Tsui, D. C. Kondo-like zero-bias anomaly in electronic transport through an ultrasmall Si quantum dot. Phys. Rev. B 60, R16319–R16321 (1999).

Cronenwett, S. M. et al. Low-temperature fate of the 0.7 structure in a point contact: A Kondo-like correlated state in an open system. Phys. Rev. Lett. 88, 226805 (2002).

Rokhinson, L., Pfeiffer, L. & West, K. Spontaneous spin polarization in quantum point contacts. Phys. Rev. Lett. 96, 156602 (2006).

Kwon, H-J., Sengupta, K. & Yakovenko, V. Fractional a.c. Josephson effect in p- and d-wave superconductors. Eur. Phys. J. B 37, 349–361 (2003).

Fu, L. & Kane, C. L. Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction. Phys. Rev. B 79, 161408 (2009).

Akhmerov, A. R., Dahlhaus, J. P., Hassler, F., Wimmer, M. & Beenakker, C. W. J. Quantized conductance at the Majorana phase transition in a disordered superconducting wire. Phys. Rev. Lett. 106, 057001 (2011).

Sau, J. D., Tewari, S. & Das Sarma, S. Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures. Phys. Rev. B 85, 064512 (2012).

Tinkham, M. Introduction to Superconductivity (McGraw-Hill, 1996).

Andreev, A. Thermal conductivity of the intermediate state of superconductors. Zh. Eksp. Teor. Fiz. 46, 1823–1828 (1964).

Doh, Y-J. et al. Tunable supercurrent through semiconductor nanowires. Science 309, 272–275 (2005).

Shapiro, S. Josephson currents in superconducting tunnelling: The effect of microwaves and other observations. Phys. Rev. Lett. 11, 80–82 (1963).

Likharev, K. K. Dynamics of Josephson Junctions and Circuits (Gordon and Breach Science Publishing, 1984).

Jiang, L. et al. Unconventional Josephson signatures of Majorana bound states. Phys. Rev. Lett. 107, 236401 (2011).

Pikulin, D. I. & Nazarov, Y. V. Phenomenology and dynamics of Majorana Josephson junction. Preprint at http://arxiv.org/abs/1112.6368  (2011).

San-Jose, P., Prada, E. & Aguado, R. AC Josephson effect in finite-length nanowire junctions with Majorana modes. Phys. Rev. Lett. 108, 257001 (2011).

Domínguez, F., Hassler, F. & Platero, G. On the dynamical detection of Majorana fermions in current-biased nanowires. Preprint at http://arxiv.org/abs/1202.0642  (2012).