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Thermoelectric response of spin polarization in Rashba spintronic systems |
Cong Xiao,Dingping Li( ),Zhongshui Ma |
School of Physics, Peking University, Beijing 100871, China Collaborative Innovation Center of Quantum Matter, Beijing 100871, China |
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Abstract Motivated by the recent discovery of a strongly spin–orbit-coupled two-dimensional (2D) electron gas near the surface of Rashba semiconductors BiTeX (X= Cl, Br, I), we calculate the thermoelectric responses of spin polarization in a 2D Rashba model. By self-consistently determining the energyand band-dependent transport time, we present an exact solution of the linearized Boltzmann equation for elastic scattering. Using this solution, we find a non-Edelstein electric-field-induced spin polarization that is linear in the Fermi energy EF when EF lies below the band crossing point. The spin polarization efficiency, which is the electric-field-induced spin polarization divided by the driven electric current, increases for smaller EF .We show that, as a function of EF, the temperaturegradient-induced spin polarization increases continuously to a saturation value when EF decreases below the band crossing point. As the temperature tends to zero, the temperature-gradient-induced spin polarization vanishes.
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Keywords
thermoelectric response
spin polarization
Rashba spin–orbit coupling
Boltzmann equation
analytical solution
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Corresponding Author(s):
Dingping Li
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Online First Date: 31 March 2016
Issue Date: 08 June 2016
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1 |
I. Žutić, J. Fabian, and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76(2), 323 (2004)
https://doi.org/10.1103/RevModPhys.76.323
|
2 |
W. Lai, C. Zhang, and Z. Ma, Single molecular shuttle junction: Shot noise and decoherence, Front. Phys. 10(1), 591 (2015)
https://doi.org/10.1007/s11467-014-0443-z
|
3 |
G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Spin caloritronics, Nat. Mater. 11(5), 391 (2012)
https://doi.org/10.1038/nmat3301
|
4 |
X. T. Jia and K. Xia, Electric and thermo spin transfer torques in Fe/Vacuum/Fe tunnel junction, Front. Phys. 9(6), 768 (2014)
https://doi.org/10.1007/s11467-013-0375-z
|
5 |
J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Universal intrinsic spin Hall effect, Phys. Rev. Lett. 92(12), 126603 (2004)
https://doi.org/10.1103/PhysRevLett.92.126603
|
6 |
J. E. Hirsch, Spin Hall effect, Phys. Rev. Lett. 83(9), 1834 (1999)
https://doi.org/10.1103/PhysRevLett.83.1834
|
7 |
V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun. 73(3), 233 (1990)
https://doi.org/10.1016/0038-1098(90)90963-C
|
8 |
E. G. Mishchenko, A. V. Shytov, and B. I. Halperin, Spin current and polarization in impure two-dimensional electron systems with spin-orbit coupling, Phys. Rev. Lett. 93(22), 226602 (2004)
https://doi.org/10.1103/PhysRevLett.93.226602
|
9 |
C. Gorini, P. Schwab, M. Dzierzawa, and R. Raimondi, Spin polarizations and spin Hall currents in a twodimensional electron gas with magnetic impurities, Phys. Rev. B 78(12), 125327 (2008)
https://doi.org/10.1103/PhysRevB.78.125327
|
10 |
Z. Ma, Spin Hall effect generated by a temperature gradient and heat current in a two-dimensional electron gas, Solid State Commun. 150(11-12), 510 (2010)
https://doi.org/10.1016/j.ssc.2009.11.004
|
11 |
H. Akera and H. Suzuura, Extrinsic spin Nernst effect in two-dimensional electron systems, Phys. Rev. B 87(7), 075301 (2013)
https://doi.org/10.1103/PhysRevB.87.075301
|
12 |
J. Borge, C. Gorini, and R. Raimondi, Spin thermoelectrics in a disordered Fermi gas, Phys. Rev. B 87(8), 085309 (2013)
https://doi.org/10.1103/PhysRevB.87.085309
|
13 |
P. E. Iglesias and J. A. Maytorena, Absence of thermospin current response of a spin-orbit-coupled two dimensional electron gas, Phys. Rev. B 89(15), 155432 (2014)
https://doi.org/10.1103/PhysRevB.89.155432
|
14 |
K. Tauber, M. Gradhand, D. V. Fedorov, and I. Mertig, Extrinsic spin Nernst effect from first principles, Phys. Rev. Lett. 109(2), 026601 (2012)
https://doi.org/10.1103/PhysRevLett.109.026601
|
15 |
C. M. Wang and M. Q. Pang, Thermally induced spin polarization and thermal conductivities in a spin-orbit coupled two-dimensional electron gas, Solid State Commun. 150(33-34), 1509 (2010)
https://doi.org/10.1016/j.ssc.2010.06.013
|
16 |
A. Dyrdał, M. Inglot, V. K. Dugaev, and J. Barnas, Thermally induced spin polarization of a two-dimensional electron gas, Phys. Rev. B 87(24), 245309 (2013)
https://doi.org/10.1103/PhysRevB.87.245309
|
17 |
S. Tölle, C. Gorini, and U. Eckern, Room temperature spin thermoelectrics in metallic films, Phys. Rev. B 90(23), 235117 (2014)
https://doi.org/10.1103/PhysRevB.90.235117
|
18 |
E. Cappelluti, C. Grimaldi, and F. Marsiglio, Topological change of the Fermi surface in low-density Rashba gases: Application to superconductivity, Phys. Rev. Lett. 98(16), 167002 (2007)
https://doi.org/10.1103/PhysRevLett.98.167002
|
19 |
C. Grimaldi, Electron spin dynamics in impure quantum wells for arbitrary spin-orbit coupling, Phys. Rev. B 72(7), 075307 (2005)
https://doi.org/10.1103/PhysRevB.72.075307
|
20 |
L. Wu, J. Yang, S. Wang, P. Wei, J. Yang, W. Zhang, and L. Chen, Thermopower enhancement in quantum wells with the Rashba effect, Appl. Phys. Lett. 105(20), 202115 (2014)
https://doi.org/10.1063/1.4902134
|
21 |
C. Grimaldi, E. Cappelluti, and F. Marsiglio, Off-Fermi surface cancellation effects in spin-Hall conductivity of a two-dimensional Rashba electron gas, Phys. Rev. B 73, 081303(R) (2006)
|
22 |
K. Tsutsui and S. Murakami, Spin-torque efficiency enhanced by Rashba spin splitting in three dimensions, Phys. Rev. B 86(11), 115201 (2012)
https://doi.org/10.1103/PhysRevB.86.115201
|
23 |
J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, Gate control of spin-orbit interaction in an inverted In0.53G a0.47As/In0.52Al 0.48As heterostructure, Phys. Rev. Lett. 78(7), 1335 (1997)
https://doi.org/10.1103/PhysRevLett.78.1335
|
24 |
S. V. Eremeev, I. A. Nechaev, Yu. M. Koroteev, P. M. Echenique, and E. V. Chulkov, Ideal two-dimensional electron systems with a giant Rashba-type spin splitting in real materials: Surfaces of Bismuth tellurohalides, Phys. Rev. Lett. 108(24), 246802 (2012)
https://doi.org/10.1103/PhysRevLett.108.246802
|
25 |
S. V. Eremeev, I. P. Rusinov, I. A. Nechaev, and E. V. Chulkov, Rashba split surface states in BiTeBr, New J. Phys. 15(7), 075015 (2013)
https://doi.org/10.1088/1367-2630/15/7/075015
|
26 |
G. Landolt, S. V. Eremeev, Y. M. Koroteev, B. Slomski, S. Muff, T. Neupert, M. Kobayashi, V. N. Strocov, T. Schmitt, Z. S. Aliev, M. B. Babanly, I. R. Amiraslanov, E. V. Chulkov, J. Osterwalder, and J. H. Dil, Disentanglement of surface and bulk Rashba spin splittings in noncentrosymmetric BiTeI, Phys. Rev. Lett. 109(11), 116403 (2012)
https://doi.org/10.1103/PhysRevLett.109.116403
|
27 |
G. Landolt, S. V. Eremeev, O. E. Tereshchenko, S. Muff, B. Slomski, K. A. Kokh, M. Kobayashi, T. Schmitt, V. N. Strocov, J. Osterwalder, E. V. Chulkov, and J. Hugo Dil, Bulk and surface Rashba splitting in single termination BiTeCl, New J. Phys. 15(8), 085022 (2013)
https://doi.org/10.1088/1367-2630/15/8/085022
|
28 |
A. Crepaldi, L. Moreschini, G. Autes, C. Tournier-Colletta, S. Moser, N. Virk, H. Berger, P. Bugnon, Y. J. Chang, K. Kern, A. Bostwick, E. Rotenberg, O. V. Yazyev, and M. Grioni, Giant ambipolar Rashba effect in the semiconductor BiTeI, Phys. Rev. Lett. 109(9), 096803 (2012)
https://doi.org/10.1103/PhysRevLett.109.096803
|
29 |
M. Sakano, M. S. Bahramy, A. Katayama, T. Shimojima, H. Murakawa, Y. Kaneko, W. Malaeb, S. Shin, K. Ono, H. Kumigashira, R. Arita, N. Nagaosa, H. Y. Hwang, Y. Tokura, and K. Ishizaka, Strongly spin-orbit coupled two-dimensional electron gas emerging near the surface of polar semiconductors, Phys. Rev. Lett. 110(10), 107204 (2013)
https://doi.org/10.1103/PhysRevLett.110.107204
|
30 |
I. P. Rusinov, I. A. Nechaev, S. V. Eremeev, C. Friedrich, S. Blugel, and E. V. Chulkov, Many-body effects on the Rashba-type spin splitting in bulk bismuth tellurohalides, Phys. Rev. B 87(20), 205103 (2013)
https://doi.org/10.1103/PhysRevB.87.205103
|
31 |
J. M. Ziman, Principles of the Theory of Solids, Cambridge: Cambridge University Press, 1972
https://doi.org/10.1017/CBO9781139644075
|
32 |
N. A. Sinitsyn, Semiclassical theories of the anomalous Hall effect, J. Phys.: Condens. Matter 20(2), 023201 (2008)
https://doi.org/10.1088/0953-8984/20/02/023201
|
33 |
C. Xiao, D. P. Li, and Z. S. Ma, Unconventional thermoelectric behaviors and enhancement of figure of merit in Rashba spintronic systems, arXiv: 1507.04237
|
34 |
M. Trushin and J. Schliemann, Anisotropic current induced spin accumulation in the two-dimensional electron gas with spin-orbit coupling, Phys. Rev. B 75(15), 155323 (2007)
https://doi.org/10.1103/PhysRevB.75.155323
|
35 |
K. Výborný, A. A. Kovalev, J. Sinova, and T. Jungwirth, Semiclassical framework for the calculation of transport anisotropies, Phys. Rev. B 79(4), 045427 (2009)
https://doi.org/10.1103/PhysRevB.79.045427
|
36 |
M. Trushin, K. Vyborny, P. Moraczewski, A. A. Kovalev, J. Schliemann, and T. Jungwirth, Anisotropic magnetoresistance of spin-orbit coupled carriers scattered from polarized magnetic impurities, Phys. Rev. B 80(13), 134405 (2009)
https://doi.org/10.1103/PhysRevB.80.134405
|
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