Bilayer counterflow transport at filling factor 1 in the strong interacting regime

Abstract

We review magneto-transport properties of interacting GaAs bilayer hole systems, with very small inter-layer tunneling, in a geometry where equal currents are passed in opposite directions in the two, independently contacted layers (counterflow). In the quantum Hall state at total bilayer filling $\nu =1$ both the longitudinal and Hall counterflow resistances tend to vanish in the limit of zero temperature, suggesting the existence of a superfluid transport mode in the counterflow geometry. As the density of the two layers is reduced, making the bilayer more interacting, the counterflow Hall resistivity $({\rho }_{\mathit{xy}})$ decreases at a given temperature while the counterflow longitudinal resistivity $({\rho }_{\mathit{xx}})$, which is much larger than ${\rho }_{\mathit{xy}}$, hardly depends on density. Our data suggest that the counterflow dissipation present at any finite temperature is a result of mobile vortices in the superfluid created by the ubiquitous disorder in this system.

Introduction

Two-dimensional (2D) systems have been host to a number of major discoveries in condensed matter physics, of which the most notable are the integer and fractional quantum Hall (QH) effects [1], [2]. With the advent of new technologies in semiconductor crystal growth and the availability of better quality samples, experimental studies have revealed the existence of a number of new quantum phases in addition to the QH phases. Among these are the Wigner crystal phase at low Landau level filling factors $(\nu )$ [3], the stripe [4] and bubble phases at even denominator fillings (e.g. at $\nu =\frac{7}{2}$ and $\nu =\frac{9}{2}$). Making use of state-of-the-art techniques, such as molecular beam epitaxy, energy band engineering, and modulation doping of semiconductors, 2D carrier systems can be fabricated today with exceptionally high mobilities [5].

For more than a decade, a new class of quasi-2D carriers, namely the bilayer carrier system has also been the subject of significant experimental and theoretical investigation. These systems are realized by bringing two layers of carriers in close proximity. Experimentally this is done by either growing two layers (quantum wells) of the lower band gap semiconductor (e.g. GaAs) separated by a barrier (e.g. AlAs), or by growing a wide well with sufficiently high density so that the carriers occupy two (symmetric and antisymmetric) subbands.

Several landmark contributions have stimulated the interest in studying bilayers. One of the most important was the observation of a quantum Hall state (QHS) at total filling factor $\nu =\frac{1}{2}$, by Suen et al. [6] and Eisenstein et al. [7], a quantum phase that is not observable in single layers. Murphy et al. [8] have shown that a QHS at total filling factor $\nu =1$ ($\nu =\frac{1}{2}$ in each layer) can be stabilized in bilayers with negligible tunneling between the two layers. These special QHSs form when the inter-layer Coulomb interaction is comparable in strength to the intra-layer interaction, leading to many-particle ground states that involve the carriers of both layers.

Here we examine the physics of the bilayer $\nu =1$ QHS, which forms at a layer filling factor $\nu =\frac{1}{2}$ where normally no QHS is observed in a single layer 2D system. At filling factor $\nu =\frac{1}{2}$ in a single layer 2D system, each carrier pairs with two flux quanta resulting in quasi-particles which are fermions (composite fermions). The composite fermions form a degenerate gas at the lowest temperatures much like a weekly interacting Fermi gas. On the other hand, if two layers, each at filling factor $\frac{1}{2}$, are brought into close proximity, their physics dramatically changes and the systems can form a QHS. The simplest way to understand this is to regard the lowest Landau levels of the two layers at filling $\frac{1}{2}$ as half filled with particles and half filled with vacancies. Pairing a particle in one layer with a vacancy in another results in composite, electrically neutral particles, namely excitons. The excitons are bosons and can condense at the lowest temperatures, thus forming a peculiar QHS at this filling factor.