Abstract
We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal O(\partial^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large filling factor $N$.
Highlights
The family of multilayer graphite is one of the most intriguing paradigms in the realm of modern condensed matter
Its linear dispersion at low energy makes it a low-dimensional example of a particle-hole symmetric ultrarelativistic Dirac fermion, the unconventional electronic property of which distinguishes it from other semiconductors made up of ordinary nonrelativistic quasiparticles
We show that for the low-energy model of bilayer graphene in a background magnetic field, the Hall conductivity in an inhomogeneous and time-dependent electric field Ei(ω, q) at filling factor N is σH (ω, q)
Summary
The family of multilayer graphite is one of the most intriguing paradigms in the realm of modern condensed matter. In the AB-stacked configuration as shown, the low-energy projection of the model forms another family without any relativistic analog: a particle-hole symmetric two-band semiconductor with parabolic dispersion [4]. It serves as a model possessing a. We show that for the low-energy model of bilayer graphene in a background magnetic field, the Hall conductivity in an inhomogeneous and time-dependent electric field Ei(ω, q) at filling factor N is σH (ω, q). III, we construct the stress tensor and compute the Hall viscosity and orbital magnetic susceptibility for our model Details of the computations and an alternative derivation of the stress tensor are given in the Appendixes for completeness
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