Danyu Shu | Searcharxiv

arXiv2026

Quantum Geometric Origin of Hall Viscosity and Nonlocal Hall Conductivity in Lattice Bands

We show that Hall viscosity in lattice bands is governed by a band-projected electric quadrupole encoded within the quantum geometry: Berry curvature sets the projected-coordinate algebra, while the quantum metric determines the quadrupolar spread of a wave packet. The same structure enters the quadratic wave-vector coefficient of the nonlocal Hall conductivity, yielding a lattice viscosity-conductivity relation. In ideal bands, the deviation from the Landau-level form is quantified by Berry curvature fluctuations. Our results establish the nonlocal Hall response as an electrical signature of the quantum geometry underlying Hall viscosity and as a transport diagnostic of geometric idealness.

cond-mat.mes-hall↗

arXiv2025

Valley Hall Viscosity in Gapped Graphene with and without a Magnetic Field

Hall viscosity is conventionally defined through the stress response to time-dependent strain, a perturbation that is difficult to implement in solid-state experiments. We formulate a related viscoelastic response to static, spatially inhomogeneous electric fields and compare it with the strain-based response. For gapped graphene in a perpendicular magnetic field, the two formulations give the same Landau-level response, whose Hall viscosity is asymmetric between the two valleys. At zero magnetic field, a valley-even quantum-metric coefficient combines with the valley-odd Hall conductivity to produce equal and opposite valley-resolved responses; global time-reversal symmetry therefore forces the net Hall viscosity to vanish. In an insulating state, exact particle--hole symmetry eliminates this zero-field response, whereas particle--hole-symmetry breaking generates a cutoff-dependent geometric contribution from the occupied Fermi sea. These results connect valley-dependent viscoelasticity with electromagnetic response in gapped Dirac materials and clarify the conditions under which a valley Hall viscosity can arise.

cond-mat.mes-hall↗