Quantum Dynamics of Pseudospin Solitons in Double-Layer Quantum Hall Systems

Abstract

Pseudospin solitons in double-layer quantum Hall systems can be introduced by a magnetic field component coplanar with the electrons and can be pinned by applying voltages to external gates. We estimate the temperature below which depinning occurs predominantly via tunneling and calculate low-temperature depinning rates for realistic geometries. We discuss the local changes in charge and current densities and in spectral functions that can be used to detect solitons and observe their temporal evolution. 73.40.Hm,71.10.Pm,73.40.Gk, The study of multicomponent Quantum Hall systems [1] has been enriched by the discovery of a variety of new phases. In double layers, the relevant discrete degrees of freedom are labelled by the electron's layer and spin indices. At Landau level filling factor ν = 2, recent theoretical work predicted several interesting phases [2] in which both layer and spin play a role; the existence of these phases has been confirmed by experiment [3]. The present study is on double-layer systems at fillingfactor ν = 1 [4,5]. At this filling factor, the low-energy electron states are spin-polarized and the system has a broken symmetry ground state with spontaneous interlayer phase coherence [6]. The rich phase diagram for these systems, including the effects of in-plane fields, has been discussed at length in Ref. [5].It is useful to describe this system using a pseudospin language [4,5] in which pseudospin-up (-down) refers to an electron in the top (bottom) layer. The action is that of a two-dimensional ferromagnet with a hard-axis anisotropy and a Zeeman field perpendicular to the hardaxis [5]. The pseudospin configuration is specified by the spherical-coordinate fields θ(x, y), which describes the difference in charge density between the layers, and φ(x, y), which describes the relative phase of electrons in top and bottom layers. Phase solitons φ 0 (x) exist as solutions to the classical equations of motion [5]. In this Letter we address the quantum dynamics of such solitons, predicting that, when pinned by applying gate voltages, depinning occurs at accessible temperatures predominantly via quantum tunneling. This system offers a number of advantages for macroscopic quantum tunneling studies, especially the possibility of using gate voltages and in-plane fields in combination to control metastable-state placement. We also discuss several local properties which can be used to detect solitons and observe their temporal evolution.Neglecting for the moment the effect of in-plane fields, the leading contributions to the imaginary-time effective action for the pseudospin field m(r, τ ) = (sin θ cos φ, sin θ sin φ, cos θ), in the presence of both tunneling and gates, is given by [5](1)The first term is the Berry phase, conveniently expressed asṁ · A =φ (1 − cos θ). The gradients are the exchange terms, with ρ the pseudospin stiffness. The term involving β 0 is a hard-axis anisotropy, and in the following term, t is the tunneling amplitude which acts as an in-plane pseudofield. Finally, V (x) is the ga...

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