Viscoelastic response of quantum Hall fluids in a tilted field

Abstract

In this paper, we examine the viscoelastic properties of integer quantum Hall (IQH) states in a tilted magnetic field. In particular, we explore to what extent the tilted-field system behaves like a two-dimensional electron gas with anisotropic mass in the presence of strain deformations. We first review the Kubo formalism for viscosity in an external magnetic field, paying particular attention to the role of rotational symmetry and contact terms. Next, we compute the conductivity, stress, and viscosity tensors for IQH states in the presence of a tilted field and vertical confining potential. By comparing our results with the recently developed bimetric formalism, we show that, at the level of the contracted Hall viscosity tensor, the mapping between tilted field and effective mass anisotropy holds only if we simultaneously modify the background perpendicular magnetic field; in other words, a simultaneous measurement of the density, contracted Hall viscosity, and Hall conductivity at fixed particle number can distinguish between tilted field and effective mass anisotropy. Additionally, we show that in the presence of a tilted magnetic field, the stress tensor acquires an unusual anisotropic ground state average, leading to anomalous elastic response functions. We develop a formalism for projecting a three-dimensional Hamiltonian with confining potential and magnetic field to a two-dimensional Hamiltonian in order to further address the phenomenology of the tilted-field IQH fluid. We find that the projected fluid couples non-minimally to geometric deformations, indicating the presence of internal geometric degrees of freedom.Let us begin by reviewing the most pertinent results from linear response theory in the context of a timereversal asymmetric fluid. We write down the general Kubo formula, with an eye towards features relevant to topological phases of matter. In particular, we will review the Kubo formula for the (Hall) conductivity, and re-derive the Kubo formulas for the (Hall) viscosity. We will focus especially on the role of rotational symmetry and the interpretation of "contact" (diamagnetic) terms in the response functions. Further background can be found in Refs. 5, 39-41. A. Review of linear response theoryThe typical linear response set-up 42 starts with a system described by an unperturbed (time-independent) Hamiltonian H 0 , an unperturbed density matrix ρ 0 that

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