Physics - Mesoscopic Systems and Quantum Hall Effect
Résumé :
[en] We study a two-dimensional (2D) electron system with a linear spectrum in the
presence of Rashba spin-orbit (RSO) coupling in the hydrodynamic regime. We
derive a semiclassical Boltzmann equation with a collision integral due to
Coulomb interactions in the basis of the eigenstates of the system with RSO
coupling. Using the local equilibrium distribution functions, we obtain a
generalized hydrodynamic Navier-Stokes equation for electronic systems with RSO
coupling. In particular, we discuss the influence of the spin-orbit coupling on
the viscosity and the enthalpy of the system and present some of its observable
effects in hydrodynamic transport.
Disciplines :
Physique
Auteur, co-auteur :
IDRISOV, Edvin ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Thomas SCHMIDT
HASDEO, Eddwi Hesky ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Radhakrishnan, Byjesh N.
SCHMIDT, Thomas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Hydrodynamic Navier-Stokes equations in two-dimensional systems with Rashba spin-orbit coupling
Date de publication/diffusion :
décembre 2023
Titre du périodique :
Low Temperature Physics
ISSN :
1063-777X
eISSN :
1090-6517
Maison d'édition :
American Institute of Physics, Etats-Unis - New York
R. N. Gurzhi, “ Minimum of resistance in impurity free conductors,” Zh. Eksp. Teor. Fiz. 44, 771 ( 1963); available at http://www.jetp.ras.ru/cgi-bin/e/index/e/17/2/p521?a=list.
M. J. M. de Jong and L. W. Molenkamp, “ Hydrodynamic electron flow in high-mobility wires,” Phys. Rev. B 51, 13389 ( 1995). 10.1103/PhysRevB.51.13389
A. A. Abrikosov, Fundamentals of the Theory of Metals ( North Holland, Amsterdam, 1988).
M. Polini and A. K. Geim, “ Viscous electron fluids,” Phys. Today 73, 28 ( 2020). 10.1063/PT.3.4497
J. Zaanen, “ Electrons go with the flow in exotic material systems,” Science 351, 1026 ( 2016). 10.1126/science.aaf2487
D. Y. H. Ho, I. Yudhistira, N. Chakraborty, and S. Adam, “ Theoretical determination of hydrodynamic window in monolayer and bilayer graphene from scattering rates,” Phys. Rev. B 97, 121404 ( 2018). 10.1103/PhysRevB.97.121404
A. Lucas and K. C. Fong, “ Hydrodynamics of electrons in graphene,” J. Phys. Cond. Matter 30, 053001 ( 2018). 10.1088/1361-648X/aaa274
J. Crossno, J. K. Shi, K. Wang, X. Liu, A. Harzheim, L cs, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe, T. A. Ohki, and K. C. Fong, “ Observation of the dirac fluid and the breakdown of the Wiedemann-Franz law in graphene,” Science 351, 1058 ( 2016). 10.1126/science.aad0343
H. Guo, E. Ilseven, G. Falkovich, and L. S. Levitov, “ Higher-than-ballistic conduction of viscous electron flows,” Proc. Nat. Acad. Sci. 114, 3068 ( 2017). 10.1073/pnas.1612181114
R. Krishna Kumar, D. A. Bandurin, F. M. D. Pellegrino, Y. Cao, A. Principi, H. Guo, G. H. Auton, M. Ben Shalom, L. A. Ponomarenko, G. Falkovich, K. Watanabe, T. Taniguchi, I. V. Grigorieva, L. S. Levitov, M. Polini, and A. K. Geim, “ Superballistic flow of viscous electron fluid through graphene constrictions,” Nature Phys. 13, 1182 ( 2017). 10.1038/nphys4240
L. Levitov and G. Falkovich, “ Electron viscosity, current vortices and negative nonlocal resistance in graphene,” Nature Phys. 12, 672 ( 2016). 10.1038/nphys3667
F. Ghahari, H.-Y. Xie, T. Taniguchi, K. Watanabe, M. S. Foster, and P. Kim, “ Enhanced thermoelectric power in graphene: Violation of the mott relation by inelastic scattering,” Phys. Rev. Lett. 116, 136802 ( 2016). 10.1103/PhysRevLett.116.136802
M. J. H. Ku, T. X. Zhou, Q. Li, Y. J. Shin, J. K. Shi, C. Burch, L. E. Anderson, A. T. Pierce, Y. Xie, Hm, U. Vool, H. Zhang, F. Casola, T. Taniguchi, K. Watanabe, M. M. Fogler, P. Kim, A. Yacoby, and R. L. Walsworth, “ Imaging viscous flow of the dirac fluid in graphene,” Nature 583, 537 ( 2020). 10.1038/s41586-020-2507-2
E. H. Hasdeo, J. Ekström, E. G. Idrisov, and T. L. Schmidt, “ Electron hydrodynamics of two-dimensional anomalous Hall materials,” Phys. Rev. B 103, 125106 ( 2021). 10.1103/PhysRevB.103.125106
G. Varnavides, A. S. Jermyn, P. Anikeeva, C. Felser, and P. Narang, “ Electron hydrodynamics in anisotropic materials,” Nature Commun. 11, 4710 ( 2020). 10.1038/s41467-020-18553-y
S. S. Apostolov, A. Levchenko, and A. V. Andreev, “ Hydrodynamic Coulomb drag of strongly correlated electron liquids,” Phys. Rev. B 89, 121104 ( 2014). 10.1103/PhysRevB.89.121104
W. Chen, A. V. Andreev, and A. Levchenko, “ Boltzmann-langevin theory of Coulomb drag,” Phys. Rev. B 91, 245405 ( 2015). 10.1103/PhysRevB.91.245405
E. H. Hasdeo, E. G. Idrisov, and T. L. Schmidt, “ Coulomb drag of viscous electron fluids: Drag viscosity and negative drag conductivity,” Phys. Rev. B 107, L121107 ( 2023). 10.1103/PhysRevB.107.L121107
B. Coquinot, L. Bocquet, and N. Kavokine, “ Quantum feedback at the solid-liquid interface: Flow-induced electronic current and its negative contribution to friction,” Phys. Rev. X 13, 011019 ( 2023). 10.1103/PhysRevX.13.011019
S. Zhu, G. Bednik, and S. Syzranov, “ Weyl hydrodynamics in a strong magnetic field,” Phys. Rev. B 105, 125132 ( 2022). 10.1103/PhysRevB.105.125132
A. C. Keser, D. Q. Wang, O. Klochan, D. Y. H. Ho, O. A. Tkachenko, V. A. Tkachenko, D. Culcer, S. Adam, I. Farrer, D. A. Ritchie, O. P. Sushkov, and A. R. Hamilton, “ Geometric control of universal hydrodynamic flow in a two-dimensional electron fluid,” Phys. Rev. X 11, 031030 ( 2021). 10.1103/PhysRevX.11.031030
R. J. Doornenbal, M. Polini, and R. A. Duine, “ Spin-vorticity coupling in viscous electron fluids,” J. Phys. Mater. 2, 015006 ( 2019). 10.1088/2515-7639/aaf8fb
M. Matsuo, D. A. Bandurin, Y. Ohnuma, Y. Tsutsumi, and S. Maekawa, Spin hydrodynamic generation in graphene ( 2020), arXiv:2005.01493 [cond-mat.mes-hall].
X. Chen, K. Shehzad, L. Gao, M. Long, H. Guo, S. Qin, X. Wang, F. Wang, Y. Shi, W. Hu, Y. Xu, and X. Wang, “ Graphene hybrid structures for integrated and flexible optoelectronics,” Adv. Mater. 32, 1902039 ( 2020). 10.1002/adma.201902039
A. Castro Neto, V. Kotov, J. Nilsson, V. Pereira, N. Peres, and B. Uchoa, “ Adatoms in graphene,” Solid State Commun. 149, 1094 ( 2009), recent Progress in Graphene Studies. 10.1016/j.ssc.2009.02.040
M. Gmitra and J. Fabian, “ Graphene on transition-metal dichalcogenides: A platform for proximity spin-orbit physics and optospintronics,” Phys. Rev. B 92, 155403 ( 2015). 10.1103/PhysRevB.92.155403
Y. S. Dedkov, M. Fonin, U. Rüdiger, and C. Laubschat, “ Rashba effect in the graphene/Ni(111) system,” Phys. Rev. Lett. 100, 107602 ( 2008). 10.1103/PhysRevLett.100.107602
D. Marchenko, A. Varykhalov, M. R. Scholz, G. Bihlmayer, E. I. Rashba, A. Rybkin, A. M. Shikin, and O. Rader, “ Giant Rashba splitting in graphene due to hybridization with gold,” Nature Commun. 3, 1232 ( 2012). 10.1038/ncomms2227
D. Marchenko, J. Sánchez-Barriga, M. R. Scholz, O. Rader, and A. Varykhalov, “ Spin splitting of Dirac fermions in aligned and rotated graphene on Ir(111),” Phys. Rev. B 87, 115426 ( 2013). 10.1103/PhysRevB.87.115426
W. Han, R. K. Kawakami, M. Gmitra, and J. Fabian, “ Graphene spintronics,” Nature Nanotechn. 9, 794 ( 2014). 10.1038/nnano.2014.214
C. L. Kane and E. J. Mele, “ Quantum spin Hall effect in graphene,” Phys. Rev. Lett. 95, 226801 ( 2005). 10.1103/PhysRevLett.95.226801
C. L. Kane and E. J. Mele, “ Z2 topological order and the quantum spin Hall effect,” Phys. Rev. Lett. 95, 146802 ( 2005). 10.1103/PhysRevLett.95.146802
M. Kurpas, P. E. Faria Junior, M. Gmitra, and J. Fabian, “ Spin-orbit coupling in elemental two-dimensional materials,” Phys. Rev. B 100, 125422 ( 2019). 10.1103/PhysRevB.100.125422
B. N. Narozhny, “ Electronic hydrodynamics in graphene,” Annals Phys. 411, 167979 ( 2019). 10.1016/j.aop.2019.167979
A. V. Shytov, E. G. Mishchenko, H.-A. Engel, and B. I. Halperin, “ Small-angle impurity scattering and the spin Hall conductivity in two-dimensional semiconductor systems,” Phys. Rev. B 73, 075316 ( 2006). 10.1103/PhysRevB.73.075316
J. Rammer and H. Smith, “ Quantum field-theoretical methods in transport theory of metals,” Rev. Mod. Phys. 58, 323 ( 1986). 10.1103/RevModPhys.58.323
T. Kita, “ Introduction to nonequilibrium statistical mechanics with quantum field theory,” Progr. Theor. Phys. 123, 581 ( 2010). 10.1143/PTP.123.581
P. I. Arseev, “ On the nonequilibrium diagram technique: Derivation, some features, and applications,” Phys.-Usp. 58, 1159 ( 2015). 10.3367/UFNe.0185.201512b.1271
E. G. Idrisov and T. L. Schmidt, “ Entropy production in one-dimensional quantum fluids,” Phys. Rev. B 100, 165404 ( 2019). 10.1103/PhysRevB.100.165404
L. D. Landau and E. M. Lifshitz, Fluid Mechanics ( Pergamon Press, London, 1959).
P. J. Ledwith, H. Guo, and L. Levitov, “ The hierarchy of excitation lifetimes in two-dimensional Fermi gases,” Annals Phys. 411, 167913 ( 2019). 10.1016/j.aop.2019.167913
K. W. K. Shung, “ Dielectric function and plasmon structure of stage-1 intercalated graphite,” Phys. Rev. B 34, 979 ( 1986). 10.1103/PhysRevB.34.979
F. M. D. Pellegrino, I. Torre, and M. Polini, “ Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids,” Phys. Rev. B 96, 195401 ( 2017). 10.1103/PhysRevB.96.195401