Abstract
In highly viscous electron systems such as, for example, high quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools [1]. Moreover, in a fluid subject to a magnetic field the viscous stress tensor has a dissipationless antisymmetric component controlled by the so-called Hall viscosity. We propose an all-electrical scheme that allows a determination of the Hall viscosity of a two-dimensional electron liquid in a solid-state device.
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References
P.J.W. Moll, P. Kushwaha, N. Nandi, B. Schmidt, A.P. Mackenzie, Science 351(6277), 1061 (2016). https://doi.org/10.1126/science.aac8385
M. Mendoza, H.J. Herrmann, S. Succi, Phys. Rev. Lett. 106, 156601 (2011). https://doi.org/10.1103/PhysRevLett.106.156601
M.J.M. de Jong, L.W. Molenkamp, Phys. Rev. B 51, 13389 (1995). https://doi.org/10.1103/PhysRevB.51.13389
L.D. Landau, E.M. Lifshitz, Fluid mechanics, Course of theoretical physics, vol. 6 (Pergamon, New York, 1987). ISBN 9780080339337
U. Briskot, M. Schütt, I.V. Gornyi, M. Titov, B.N. Narozhny, A.D. Mirlin, Phys. Rev. B 92, 115426 (2015). https://doi.org/10.1103/PhysRevB.92.115426
M.I. Dyakonov, M.S. Shur, Phys. Rev. B 51, 14341 (1995). https://doi.org/10.1103/PhysRevB.51.14341
L. Levitov, G. Falkovich, Nat. Phys. 12(7), 672 (2016). https://doi.org/10.1038/nphys3667
A. Lucas, J. Crossno, K.C. Fong, P. Kim, S. Sachdev, Phys. Rev. B 93, 075426 (2016). https://doi.org/10.1103/PhysRevB.93.075426
M. Mendoza, H.J. Herrmann, S. Succi, 3, 1052 EP (2013). https://doi.org/10.1038/srep01052
M. Müller, S. Sachdev, Phys. Rev. B 78, 115419 (2008). https://doi.org/10.1103/PhysRevB.78.115419
B.N. Narozhny, I.V. Gornyi, M. Titov, M. Schütt, A.D. Mirlin, Phys. Rev. B 91, 035414 (2015). https://doi.org/10.1103/PhysRevB.91.035414
D. Svintsov, V. Vyurkov, S. Yurchenko, T. Otsuji, V. Ryzhii, J. Appl. Phys. 111(8), 083715 (2012). https://doi.org/10.1063/1.4705382
L.W. Molenkamp, M.J.M. de Jong, Solid-State Electron. 37(4), 551 (1994). https://doi.org/10.1016/0038-1101(94)90244-5
V.N. Kotov, B. Uchoa, V.M. Pereira, F. Guinea, A.H. Castro Neto, Rev. Mod. Phys. 84, 1067 (2012). https://doi.org/10.1103/RevModPhys.84.1067
J. Crossno, J.K. Shi, K. Wang, X. Liu, A. Harzheim, A. Lucas, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe, T.A. Ohki, K.C. Fong, Science 351(6277), 1058 (2016). https://doi.org/10.1126/science.aad0343
T. Schäfer, D. Teaney, Rep. Prog. Phys. 72(12), 126001 (2009). https://doi.org/10.1088/0034-4885/72/12/126001
M. Polini, G. Vignale, in No-Nonsense Physicist: An Overview of Gabriele Giuliani’s Work and Life, ed. by M. Polini, G. Vignale, V. Pellegrini, J.K. Jain (Scuola Normale Superiore, Pisa, 2016), pp. 107–124, arXiv:1404.5728 [cond-mat.mes-hall], https://doi.org/10.1007/978-88-7642-536-3_9
A. Principi, G. Vignale, M. Carrega, M. Polini, Phys. Rev. B 93, 125410 (2016). https://doi.org/10.1103/PhysRevB.93.125410
D.A. Bandurin, I. Torre, R.K. Kumar, M. Ben Shalom, A. Tomadin, A. Principi, G.H. Auton, E. Khestanova, K.S. Novoselov, I.V. Grigorieva, L.A. Ponomarenko, A.K. Geim, M. Polini, Science 351(6277), 1055 (2016). https://doi.org/10.1126/science.aad0201
N. Read, E.H. Rezayi, Phys. Rev. B 84, 085316 (2011). https://doi.org/10.1103/PhysRevB.84.085316
I.V. Tokatly, G. Vignale, Phys. Rev. B 76, 161305 (2007). https://doi.org/10.1103/PhysRevB.76.161305
I.V. Tokatly, G. Vignale, J. Phys. Condens. Matter 21(27), 275603 (2009). https://doi.org/10.1088/0953-8984/21/27/275603
D.A. Abanin, S.V. Morozov, L.A. Ponomarenko, R.V. Gorbachev, A.S. Mayorov, M.I. Katsnelson, K. Watanabe, T. Taniguchi, K.S. Novoselov, L.S. Levitov, A.K. Geim, Science 332(6027), 328 (2011). https://doi.org/10.1126/science.1199595
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, A.K. Geim, Nat. Phys. advance online publication (2017). https://doi.org/10.1038/nphys4240
R.N. Gurzhi, Sov. Phys. Uspekhi 11(2), 255 (1968). https://doi.org/10.1070/PU1968v011n02ABEH003815
S. Das Sarma, S. Adam, E.H. Hwang, E. Rossi, Rev. Mod. Phys. 83(2), 407 (2011). https://doi.org/10.1103/RevModPhys.83.407
M. Müller, J. Schmalian, L. Fritz, Phys. Rev. Lett. 103, 025301 (2009). https://doi.org/10.1103/PhysRevLett.103.025301
I. Torre, A. Tomadin, A.K. Geim, M. Polini, Phys. Rev. B 92, 165433 (2015). https://doi.org/10.1103/PhysRevB.92.165433
L. Fritz, J. Schmalian, M. Müller, S. Sachdev, Phys. Rev. B 78, 085416 (2008). https://doi.org/10.1103/PhysRevB.78.085416
C. Hoyos, D.T. Son, Phys. Rev. Lett. 108, 066805 (2012). https://doi.org/10.1103/PhysRevLett.108.066805
A.O. Govorov, J.J. Heremans, Phys. Rev. Lett. 92, 026803 (2004). https://doi.org/10.1103/PhysRevLett.92.026803
A.K. Geim, K.S. Novoselov, Nat. Mater. 6(3), 183 (2007). https://doi.org/10.1038/nmat1849
P.S. Alekseev, Phys. Rev. Lett. 117, 166601 (2016). https://doi.org/10.1103/PhysRevLett.117.166601
J.E. Avron, R. Seiler, P.G. Zograf, Phys. Rev. Lett. 75, 697 (1995). https://doi.org/10.1103/PhysRevLett.75.697
R. Bistritzer, A.H. MacDonald, Phys. Rev. B 80, 085109 (2009). https://doi.org/10.1103/PhysRevB.80.085109
Q. Li, S. Das Sarma, Phys. Rev. B 87, 085406 (2013). https://doi.org/10.1103/PhysRevB.87.085406
F.M.D. Pellegrino, I. Torre, M. Polini, (2017), to appear, arXiv:1706.08363 [cond-mat.mes-hall]
G. Falkovich, Fluid Mechanics: A Short Course for Physicists (Cambridge University Press, Cambridge, 2011)
A.V. Andreev, S.A. Kivelson, B. Spivak, Phys. Rev. Lett. 106, 256804 (2011). https://doi.org/10.1103/PhysRevLett.106.256804
M.I. Dyakonov, M.S. Shur, IEEE Trans. Electron Devices 43, 380 (1996). https://doi.org/10.1109/16.485650
M. Dyakonov, M. Shur, Phys. Rev. Lett. 71, 2465 (1993). https://doi.org/10.1103/PhysRevLett.71.2465
A. Tomadin, M. Polini, Phys. Rev. B 88, 205426 (2013). https://doi.org/10.1103/PhysRevB.88.205426
A. Tomadin, G. Vignale, M. Polini, Phys. Rev. Lett. 113, 235901 (2014). https://doi.org/10.1103/PhysRevLett.113.235901
B. Bradlyn, M. Goldstein, N. Read, Phys. Rev. B 86, 245309 (2012). https://doi.org/10.1103/PhysRevB.86.245309
A. Cortijo, Y. Ferreirós, K. Landsteiner, M.A.H. Vozmediano, 2D Mater. 3(1), 011002 (2016). https://doi.org/10.1088/2053-1583/3/1/011002
F.D.M. Haldane, Phys. Rev. Lett. 107, 116801 (2011). https://doi.org/10.1103/PhysRevLett.107.116801
N. Read, Phys. Rev. B 79, 045308 (2009). https://doi.org/10.1103/PhysRevB.79.045308
T. Scaffidi, N. Nandi, B. Schmidt, A.P. Mackenzie, J.E. Moore, Phys. Rev. Lett. 118, 226601 (2017). https://doi.org/10.1103/PhysRevLett.118.226601
M. Sherafati, A. Principi, G. Vignale, Phys. Rev. B 94, 125427 (2016). https://doi.org/10.1103/PhysRevB.94.125427
F.M.D. Pellegrino, I. Torre, A.K. Geim, M. Polini, Phys. Rev. B 94, 155414 (2016). https://doi.org/10.1103/PhysRevB.94.155414
I. Torre, A. Tomadin, R. Krahne, V. Pellegrini, M. Polini, Phys. Rev. B 91, 081402 (2015). https://doi.org/10.1103/PhysRevB.91.081402
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Pellegrino, F.M.D., Torre, I., Polini, M. (2018). All-Electrical Scheme for Hall Viscosity Measurement. In: Angilella, G., Amovilli, C. (eds) Many-body Approaches at Different Scales. Springer, Cham. https://doi.org/10.1007/978-3-319-72374-7_2
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