

Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
April 26, 2017 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)






Wigner transformation, Momentum space topology, and anomalous
transport: anomalous quantum Hall effect, (the
absence of) chiral magnetic effect, chiral separation effect
M. A. Zubkov^{} ^{} State Scientific Center of the Russian Federation  Institute for Theoretical and Experimental Physics, Moscow

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Abstract:
We use derivative expansion applied to the Wigner transform of the
twopoint Green function in the lattice models of solid state
physics and in the lattice regularized relativistic quantum field
theory. This approach allows to analyze the anomalous
quantum Hall effect (AQHE), the chiral magnetic effect (CME), and the
chiral separation effect (CSE) taking into account
properly the ultraviolet effects. We find for the first time that the
corresponding currents are proportional to the momentum space
topological invariants. We reproduce the conventional expression for
the Hall conductivity in the ideal tight – binding models of $(2+1) D$
topological insulators and in the $3+1 D$ Weyl semimetals. At the same
time we predict the appearance of the AQHE in $3+1 D$ topological
insulators of certain types. Using the same method we prove that in the
equilibrium $(3+1) D$ theory the CME is absent both is solids and in the
properly regularized relativistic quantum field theory. We demonstrate
that the chiral separation effect appears in the continuum limit of the
lattice theory with the current given by its conventional expression.
References

M. A. Zubkov, “Absence of equilibrium chiral magnetic effect”, Phys. Rev. D, 93:10 (2016), 105036, arXiv: 1605.08724

M. A. Zubkov, “Wigner transformation, momentum space topology, and anomalous transport”, Annals Phys., 373 (2016), 298–324, arXiv: 1603.03665

Z. V. Khaidukov, M. A. Zubkov, “Chiral Separation effect in lattice regularization”, Phys. Rev. D, 95 (2017), 074502

