Valley Hall viscosity in the integer quantum Hall phases of (2+1)D Dirac materials

M. Selch

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arXiv · 2607.08648

Valley Hall viscosity in the integer quantum Hall phases of (2+1)D Dirac materials

M. Selch

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Abstract

We calculate the valley-resolved Hall viscosity for Lorentz-invariant integer quantum Hall phases in Semenoff-semiconducting graphene-like systems at zero temperature. The Kubo formalism based discussion reported in Phys. Rev. B 100, 115421 (2019) revealed the divergence of single valley viscous Hall contributions for this case with only a valley-summed Hall viscosity being finite and therefore well-defined. Our approach to the Hall viscosity calculation is based on an equivalent Green function formulation within Wigner-Weyl calculus. We find that the previously identified divergence seems to be regularized to a finite value in a proper representation of the valley-resolved Hall viscosity in terms of energy eigenfunctions and eigenvalues. Together with the local Hall conductivity and its first nonlocal correction, reported as well in Phys. Rev. B 100, 115421 (2019), we extend the empirical relativistic Hoyos-Son formula to individual valleys. Both the original Hoyos-Son formula for Galilean invariant fluids and its relativistic extension to Dirac materials are found to be structurally identical for integer quantum Hall phases and expressible in terms of local electric and viscous Hall responses. In addition we evaluate the valley(-difference) Hall viscosity for biased Bernal bilayer graphene in the chiral fermion low energy approximation. Prospects of measuring valley Hall viscosity in nonlocal transport for mono- and bilayer graphene- and group-VI TMD-based devices are discussed.

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M. Selch. 2026-07-09. Valley Hall viscosity in the integer quantum Hall phases of (2+1)D Dirac materials. https://arxiv.org/abs/2607.08648

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