Abstract
A thin film of superfluid 3He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the superfluidity even in a very thin film, where the system can be considered as quasi two-dimensional topological material. This will allow us to study the effect of disorder on different classes of the 2 + 1 topological materials: the chiral 3He-A with intrinsic quantum Hall effect and the time reversal invariant planar phase with intrinsic spin quantum Hall effect. In the limit of smooth disorder, the system can be considered as a Chern mosaic, i.e., a collection of domains with different values of Chern numbers. In this limit, the quantization of the Hall conductance is determined by the percolated domain, while the density of the fermionic states is determined by the edge modes on the boundaries of the finite domains. This system can be useful for the general consideration of disorder in the topological matter.
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References
M. I. Katsnelson and G. E. Volovik, J. Low Temp. Phys. 175, 655 (2014); arXiv:1310.3581.
G. E. Volovik, Exotic Properties of Superfluid 3He (World Scientific, Singapore, New Jersey, London, Hong Kong, 1992).
Yu. Makhlin, M. Silaev, and G. E. Volovik, Phys. Rev. B 89, 174502 (2014).
G. E. Volovik, Sov. Phys. JETP 67, 1804 (1988).
H. So, Prog. Theor. Phys. 74, 585 (1985).
K. Ishikawa and T. Matsuyama, Z. Phys. C 33, 41 (1986).
K. Ishikawa and T. Matsuyama, Nucl. Phys. B 280, 523 (1987).
G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).
G. E. Volovik, JETP Lett. 55, 368 (1992).
A. A. Burkov, Phys. Rev. Lett. 120, 016603 (2018).
N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667 (1991).
G. E. Volovik, JETP Lett. 93, 66 (2011).
J. Röntynen and T. Ojanen, Phys. Rev. B 93, 094521 (2016).
K. Pöyhönen and T. Ojanen, Phys. Rev. B 96, 174521 (2017).
P. Hořava, Phys. Rev. Lett. 95, 016405 (2005).
E. M. Chudnovsky, Phys. Rev. B 33, 245 (1986).
R. Movassagh, Phys. Rev. Lett. 119, 220504 (2017).
T. Morimoto, A. Furusaki, and Ch. Mudry, Phys. Rev. B 91, 235111 (2015).
J. Song and E. Prodan, Phys. Rev. B 92, 195119 (2015).
R.-J. Slager, L. Rademaker, J. Zaanen, and L. Balents, Phys. Rev. B 92, 085126 (2015).
E. Prodan, arXiv:1602.00306.
B. Lian, J. Wang, X.-Q. Sun, A. Vaezi, and Sh.-Ch. Zhang, arXiv:1709.05558.
B. Wu, J. Song, J. Zhou, and H. Jiang, Chin. Phys. B 25, 117311 (2016); arXiv:1711.10725.
G. E. Volovik, J. Low Temp. Phys. 150, 453 (2008); arXiv:0704.2484.
V. V. Dmitriev, D. A. Krasnikhin, N. Mulders, A. A. Senin, G. E. Volovik, and A. N. Yudin, JETP Lett. 91, 599 (2010).
E. M. Chudnovsky and D. A. Garanin, arXiv:1710.10608.
T. H. R. Skyrme, Nucl. Phys. 31, 556 (1962).
G. E. Volovik and V. P. Mineev, Sov. Phys. JETP 46, 401 (1977).
V. M. H. Ruutu, Ü. Parts, J. H. Koivuniemi, M. Krusius, E. V. Thuneberg, and G. E. Volovik, JETP Lett. 60, 671 (1994).
Yu. G. Makhlin and T. Sh. Misirpashaev, JETP Lett. 61, 49 (1995).
S. W. Hawking, Nucl. Phys. B 144, 349 (1978).
A. J. Hanson and T. Regge, Lect. Notes Phys. 94, 354 (1979).
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Volovik, G.E. Topology of a 3He-A Film on a Corrugated Graphene Substrate. Jetp Lett. 107, 115–118 (2018). https://doi.org/10.1134/S0021364018020054
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DOI: https://doi.org/10.1134/S0021364018020054