Anisotropy of the hydrostatic stress for Hall droplets with in-plane magnetic field

Abstract

We examine the hydrostatic stress of electrons strongly confined in a quasi-2D quantum well in the presence of a strong perpendicular and weak in-plane magnetic field. This introduces anisotropy into the stress tensor which is inconsistent with the notion of the quantum Hall droplet as a simple two-dimensional electron fluid. We show that the breaking of rotational symmetry is a necessary but not a sufficient condition for an anisotropic ground state stress tensor, and that the anisotropic stress originates primarily from quantum effects. We demonstrate this by decomposing the semiclassical trajectories of electrons in the system onto planes in phase space which must be rotated relative to the plane of the fluid to decouple the Hamiltonian.

v2: Accepted version. 16 pages, 4 figures

References in corpus (13)

• Hydrodynamics of electrons in graphene
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Low-energy effective theory in the bulk for transport in a topological phase
• Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes
• Transport signatures of Hall viscosity
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions
• Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field
• Hydrodynamic effective field theories with discrete rotational symmetry
• General formulation of transverse hydrodynamics
• Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions
• Hydrodynamics with triangular point group
• Hele-Shaw flow for parity odd three-dimensional fluids