Non-linear edge dynamics of an integer quantum Hall fluid

Abstract

We report a theoretical study of the linear and nonlinear dynamics of edge excitations of an integer quantum Hall state of non-interacting fermions. New features beyond the chiral Luttinger liquid picture are anticipated to arise from the interplay of the curvature of the Landau level dispersion and of the Pauli exclusion principle. For long-wavelength perturbations, the microscopic numerical results are captured by a chiral nonlinear hydrodynamic equation including a density-dependent velocity term. In the wave-breaking regime, shock waves are found to be regularized into a complex ripple pattern by higher-order dispersive effects. Our results are of specific relevance for experiments with synthetic quantum matter, in particular ultracold atomic gases.

Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets beyond the chiral Luttinger liquid paradigm

“…However, in contrast to the IQH case, the DSF weights at fixed l are non-flat: the weight is suppressed close to the high-energy threshold and peaked at the low-energy one. This behavior is in close analogy to what was found for a fermionic LL beyond the linear dispersion approximation [57][58][59][60] and will be the subject of further investigation [61]. Group velocity dispersion -This asymmetrical distribution of the DSF makes its center-of-mass frequency shift from the low-energy result ω l Ω l. EE experience a wavevector-dependent frequency-shift and, thus, a finite group velocity dispersion.…”

“…cl , a quantity related to the second l-derivative of the LLL projection of V conf (r), which physically corresponds to the radial gradient of the angular velocity. Like in the IQH case [40], the broadening is responsible for the decay of the oscillations at late time that is visible in Fig. 4(b).…”

“…In this work, we investigate the physics beyond the the regime of validity of the χLL description and perform numerical studies of the linear and nonlinear edge dynamics of a fractional QH liquid trapped by a generic, non-harmonic external potential. As compared to our previous study of integer QH liquids [40], the strongly correlated nature of FQH liquids poses enormous technical challenges to the theoretical description and requires the development of a novel numerical approach to follow the dynamics of macroscopic FQH clouds. In particular, we focus on the neutral edge excitations (EE) generated by applying an external time-dependent potential to an incompressible FQH cloud.…”

“…The physical mechanism underlying the nonlinearity can be understood in analogy with the IQH case [40]. Because of the incompressibility condition, a local variation δρ(θ) of the radially-integrated angular density must correspond to a variation of the cloud radius δR(θ) δρ(θ)/(ρ 0 R cl ).…”