Rashba spin-orbit interaction effects on thermal and magnetic properties of parabolic GaAs quantum dot in the presence of donor impurity under external electric and magnetic fields

Rashba, 1960, Properties of semiconductors with an extremum loop. I. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop, Sov. Phys. Solid State, 2, 1109 Bychkov, 1984, Oscillatory effects and the magnetic susceptibility of carriers in inversion layers, J. Phys. C Solid State Phys., 17, 6039, 10.1088/0022-3719/17/33/015 Moroz, 2000, Spin-orbit interaction as a source of spectral and transport properties in quasi-one-dimensional systems, Phys. Rev. B, 61, R2464, 10.1103/PhysRevB.61.R2464 Destefani, 2004, Spin-orbit coupling and intrinsic spin mixing in quantum dots, Phys. Rev. B, 69, 10.1103/PhysRevB.69.125302 Kloeffel, 2018, Direct Rashba spin-orbit interaction in Si and Ge nanowires with different growth directions, Phys Rev. B, 97, 235422, 10.1103/PhysRevB.97.235422 Bagga, 2006, Spin hot spots in vertically coupled few-electron isolated quantum dots, Phys. Rev. B, 74, 10.1103/PhysRevB.74.033313 Meir, 1990, Magnetic-field and spin-orbit interaction in restricted geometries: Solvable models, Phys. Rev. B, 42, 8351, 10.1103/PhysRevB.42.8351 Žutić, 2004, Spintronics: fundamentals and applications, Rev. Mod. Phys., 76, 323, 10.1103/RevModPhys.76.323 Hoi, 2017, Spin-and valley-dependent electronic band structure and electronic heat capacity of ferromagnetic silicene in the presence of strain, exchange field and Rashba spin-orbit coupling, J. Magn. Magn. Mater., 439, 203, 10.1016/j.jmmm.2017.04.092 Koga, 2002, Spin-filter device based on the Rashba effect using a nonmagnetic resonant tunneling diode, Phys. Rev. Lett., 88, 10.1103/PhysRevLett.88.126601 Datta, 1990, Electronic analog of the electro‐optic modulator, Appl. Phys. Lett., 56, 665, 10.1063/1.102730 Wang, 2002, Spin-current modulation and square-wave transmission through periodically stubbed electron waveguides, Phys. Rev. B, 65, 10.1103/PhysRevB.65.165217 Elsaid, 2019, The magnetization and magnetic susceptibility of GaAs Gaussian quantum dot with donor impurity in a magnetic field, Mod. Phys. Lett. B, 33, 10.1142/S0217984919504220 Bose, 1998, Effect of a parabolic potential on the impurity binding energy in spherical quantum dots, Physica B, 253, 238, 10.1016/S0921-4526(98)00407-4 Kırak, 2011, The electric field effects on the binding energies and the nonlinear optical properties of a donor impurity in a spherical quantum dot, J. Appl. Phys., 109, 10.1063/1.3582137 Hoi, 2018, Insulator-semimetallic transition in quasi-1D charged impurity-infected armchair boron-nitride nanoribbons, Phys. Lett. A, 382, 995, 10.1016/j.physleta.2018.02.016 Murillo, 2000, Effects of an electric field on the binding energy of a donor impurity in a spherical GaAs– (Ga, Al) As quantum dot with parabolic confinement, Phys. Status Solidi (B), 220, 187, 10.1002/1521-3951(200007)220:1<187::AID-PSSB187>3.0.CO;2-D Bose, 1998, Binding energy of impurity states in spherical quantum dots with parabolic confinement, J. Appl. Phys., 83, 3089, 10.1063/1.367065 Zhu, 1990, Confined electron and hydrogenic donor states in a spherical quantum dot of GaAs-Ga 1− x Al x As, Phys. Rev. B, 41, 6001, 10.1103/PhysRevB.41.6001 Hoi, 2018, Combined effect of the perpendicular magnetic field and dilute charged impurity on the electronic phase of bilayer AA-stacked hydrogenated graphene, Phys. Lett. A, 382, 3298, 10.1016/j.physleta.2018.09.028 Li, 2007, Binding energy of a hydrogenic donor impurity in a rectangular parallelepiped-shaped quantum dot: quantum confinement and Stark effects, J. Appl. Phys., 101, 10.1063/1.2734097 Charrour, 2000, Magnetic field effect on the binding energy of a hydrogenic impurity in cylindrical quantum dot, Physica B, 293, 137, 10.1016/S0921-4526(00)00495-6 Sali, 2017, The effects of polaronic mass and conduction band non-parabolicity on a donor binding energy under the simultaneous effect of pressure and temperature basing on the numerical FEM in a spherical quantum dot, Superlattices Microstruct., 104, 93, 10.1016/j.spmi.2017.02.014 Hoi, 2018, Zeeman-magnetic-field–induced magnetic phase transition in doped armchair boron-nitride nanoribbons, EPL (Europhys. Lett.), 122, 17005, 10.1209/0295-5075/122/17005 Qu, 2011, Tunable magnetic property of lateral quantum dot molecules, J. Phy.: Conf. Ser., 334 Ciftja, 2007, Generalized description of few-electron quantum dots at zero and nonzero magnetic fields, J. Phys. Condens. Matter, 19, 10.1088/0953-8984/19/4/046220 Soylu, 2012, The influence of external fields on the energy of two interacting electrons in a quantum dot, Ann. Phys., 327, 3048, 10.1016/j.aop.2012.06.008 Karimi, 2011, Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots, Physica B, 406, 4423, 10.1016/j.physb.2011.08.105 Wang, 2009, Effect of a tilted electric field on the magnetoexciton ground state in a semiconductor quantum dot, J. Appl. Phys., 105, 10.1063/1.3088886 Liang, 2011, The hydrostatic pressure and temperature effects on a hydrogenic impurity in a spherical quantum dot, Eur. Phys. J. B, 81, 79, 10.1140/epjb/e2011-10831-9 Akbas, 2011, Hydrostatic pressure effects on impurity states in GaAs/AlGaAs quantum wells, Superlattices Microstruct., 50, 80, 10.1016/j.spmi.2011.05.006 Bzour, 2017, The effects of pressure and temperature on the magnetic susceptibility of semiconductor quantum dot in a magnetic field, App. Phys. Res., 9, 77, 10.5539/apr.v9n1p77 Peter, 2005, The effect of hydrostatic pressure on binding energy of impurity states in spherical quantum dots, Physica E, 28, 225, 10.1016/j.physe.2005.03.018 Bzour, 2017, The effects of pressure and temperature on the exchange energy of a parabolic quantum dot under a magnetic field, J. Taibah. Univ. Med. Sci., 11, 1122, 10.1016/j.jtusci.2017.02.004 Boda, 2016, Transition energies and magnetic properties of a neutral donor complex in a Gaussian GaAs quantum dot, Superlattices Microstruct., 97, 268, 10.1016/j.spmi.2016.06.009 Tojo, 2017, Effect of isotropy and anisotropy of the confinement potential on the Rashba spin–orbit interaction for an electron in a two-dimensional quantum dot system, Japan. J. Appl. Phys., 56, 10.7567/JJAP.56.075201 Boda, 2016, Effect of Rashba spin–orbit coupling on the electronic, thermodynamic, magnetic and transport properties of GaAs, InAs and InSb quantum dots with Gaussian confinement, Physica B, 498, 43, 10.1016/j.physb.2016.06.012 Pournaghavi, 2017, Extrinsic Rashba spin–orbit coupling effect on silicene spin polarized field effect transistors, J. Phys. Condens. Matter, 29, 10.1088/1361-648X/aa5b06 Sinova, 2004, Universal intrinsic spin Hall effect, Phys. Rev. Lett., 92, 10.1103/PhysRevLett.92.126603 Hwang, 2004, Numerical simulation of three-dimensional pyramid quantum dot, J. Comput. Phys., 196, 208, 10.1016/j.jcp.2003.10.026 Johnson, 1998, Finite element analysis of strain effects on electronic and transport properties in quantum dots and wires, J. Appl. Phys., 84, 3714, 10.1063/1.368549 El-Said, 1994, Effects of applied magnetic field on the energy levels of shallow donors in a parabolic quantum dot, Physica B, 202, 202, 10.1016/0921-4526(94)00163-4 Abuzaid, 2019, Combined effects of pressure, temperature, and magnetic field on the ground state of donor impurities in a GaAs/AlGaAs quantum heterostructure, Int. J. Nano Dimens., 10, 375 Bulaev, 2005, Spin relaxation and anticrossing in quantum dots: Rashba versus Dresselhaus spin-orbit coupling, Phys. Rev. B, 71, 10.1103/PhysRevB.71.205324 Florescu, 2006, Spin relaxation in lateral quantum dots: effects of spin-orbit interaction, Phys. Rev. B, 73, 10.1103/PhysRevB.73.045304 Halperin, 2001, Spin-orbit effects in a GaAs quantum dot in a parallel magnetic field, Phys. Rev. Lett., 86, 2106, 10.1103/PhysRevLett.86.2106 Jacak, 1997, Spin-orbit interaction in the quantum dot, Physica B, 229, 279, 10.1016/S0921-4526(96)00853-8 Voskoboynikov, 2001, Spin-orbit splitting in semiconductor quantum dots with a parabolic confinement potential, Phys. Rev. B, 63, 10.1103/PhysRevB.63.165306 Voskoboynikov, 2003, Magnetic properties of parabolic quantum dots in the presence of the spin–orbit interaction, J. Appl. Phys., 94, 5891, 10.1063/1.1614426 Governale, 2002, Quantum dots with Rashba spin-orbit coupling, Phys. Rev. Lett., 89, 10.1103/PhysRevLett.89.206802 Manaselyan, 2011, Tunability of Raman spectral signatures by Rashba spin-orbit interaction in few-electron quantum dots, EPL (Europhys. Lett.), 94, 57005, 10.1209/0295-5075/94/57005 Lee, 2006, Rashba spin splitting in parabolic quantum dots, J. Appl. Phys., 99, 10.1063/1.2201847 Pietiläinen, 2006, Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling, Phys. Rev. B, 73, 10.1103/PhysRevB.73.155315 Kuan, 2004, Energy levels of a parabolically confined quantum dot in the presence of spin-orbit interaction, J. Appl. Phys., 95, 6368, 10.1063/1.1710726 Kumar, 2013, Effect of Rashba interaction and Coulomb correlation on the ground state energy of a GaAs quantum dot with parabolic confinement, Physica E, 47, 270, 10.1016/j.physe.2012.10.030 Gumber, 2016, Thermodynamic behaviour of Rashba quantum dot in the presence of magnetic field, Chin. Phys. B, 25, 10.1088/1674-1056/25/5/056502 Kumar, 2016, Magnetization and susceptibility of a parabolic InAs quantum dot with electron–electron and spin–orbit interactions in the presence of a magnetic field at finite temperature, J. Magn. Magn. Mater., 418, 169, 10.1016/j.jmmm.2016.02.071 Schwarz, 2002, Magnetization of semiconductor quantum dots, J. Appl. Phys., 91, 6875, 10.1063/1.1450762 Turyanska, 2014, Tuneable paramagnetic susceptibility and exciton g-factor in Mn-doped PbS colloidal nanocrystals, Nanoscale, 6, 8919, 10.1039/C4NR02336F Shorman, 2018, Heat capacity and entropy of two electrons quantum dot in a magnetic field with parabolic interaction, Chin. J. Phys., 56, 1057, 10.1016/j.cjph.2018.04.012 Nguyen, 2011, Impurity effects on semiconductor quantum bits in coupled quantum dots, Phys. Rev. B, 83, 10.1103/PhysRevB.83.235322 Shaer, 2016, The magnetic properties of a quantum dot in a magnetic field, Turkish J. Phys., 40, 209, 10.3906/fiz-1510-4 Shaer, 2016, Magnetization of GaAs parabolic quantum dot by variation method, J. Phys. Sci. Appl., 6, 39 Yahyah, 2019, Heat capacity and entropy of Gaussian spherical quantum dot in the presence of donor impurity, J. Theor. Appl. Phys., 13, 277, 10.1007/s40094-019-0336-1