Hole-Hole Interaction Effect in the Conductance of the Two-Dimensional Hole Gas in the Ballistic Regime

Abstract

On a high mobility two-dimensional hole gas (2DHG) in a GaAs/GaAlAs heterostructure we study the interaction correction to the Drude conductivity in the ballistic regime, kBT τ /h > 1. It is shown that the 'metallic' behaviour of the resistivity (dρ/dT > 0) of the low-density 2DHG is caused by hole-hole interaction effect in this regime. We find that the temperature dependence of the conductivity and the parallelfield magnetoresistance are in agreement with this description, and determine the Fermi-liquid interaction constant F σ 0 which controls the sign of dρ/dT .It is well known that electron-electron interaction gives rise to a quantum correction to the classical (Drude) conductivity caused by impurity scattering [1]. Its manifestation can be quite different in the two regimes which relate the quasi-particle interaction time,h/k B T , to momentum relaxation time, τ : diffusive (k B T τ /h < 1), and ballistic (k B T τ /h > 1). So far the interaction correction to the conductivity of two-dimensional (2D) systems has been studied, both theoretically and experimentally, only in the diffusive regime, which is applicable to lowmobility (small τ ) systems [1]. Experimentally, the interaction correction was seen to be negative and produce a logarithmic decrease of the resistivity with increasing temperature, similar to the interference correction due to weak localisation (WL). Theory, however, suggests that the sign of the interaction effect in the diffusive regime can be different, dependent on the value of the interaction constant F σ 0 . Thus the correction can become positive and give rise to a 'metallic' temperature dependenceThe role of interactions in the conductance of 2D systems has now been intensely discussed, after the observation of the'metallic' behaviour in some low-density, highmobility 2D systems [3]. If one attempts to apply the conventional interaction theory, it can be seen that in high mobility structures the diffusion approximation becomes invalid even at low T . Recently, a theory of the interaction correction in the ballistic and intermediate regimes has been developed [4]. Stimulated by this theory, in this work we examine the role of the hole-hole interaction effects in a 2D hole gas (2DHG) which shows a 'metallic' ρ(T ). We analyse the temperature dependence of the conductivity and positive magnetoresistance in parallel field, and show that these two main features of the 'metallic' state can be explained by the interaction effect. It has the same origin as the logarithmic correction studied earlier [1], but now manifests itself in the ballistic regime.The interaction theory [4] considers elastic (coherent) electron scattering on the modulated density of other electrons (Friedel oscillation) caused by an impurity with a short-range potential. The phase of the Friedel oscillation, ∆p ∝ exp(i2k F r), is such that the wave scattered from the impurity interferes constructively with the wave scattered from the oscillation, Fig. 1 (a), leading to the quantum correction to the Drude conductivity σ...

Interaction-induced magnetoresistance in a two-dimensional electron gas

“…The latter assumption is believed to be justified for Si-based and some (those with a very large spacer) GaAs structures, and the results of Refs. 18,19,20 have been by and large confirmed by most recent experiments 26,27,28,29,30,31,32 on such systems. On the other hand, the random potential in typical GaAs heterostructures is due to remote donors and has a longrange character.…”

“…Here the contributions of individual diagrams a, b, and c have the form 28) where the matrixT αβ has the same form as T αβ with a replacement τ → τ s ,…”

Role of finite layer thickness in spin polarization of GaAs two-dimensional electrons in strong parallel magnetic fields

“…The results of some of these measurements [8,9,10], however, appear to be at odds with what is theoretically expected [1, 2] for a dilute, interacting 2D system that is otherwise ideal, i.e., has zero layer thickness and is disorder-free. In particular, when g * m * is deduced from parallel magnetic field at which the 2D system becomes fully spin-polarized, then the experimental results for GaAs 2D electrons [8] and holes [9,10] suggest a decreasing value of g * m * with decreasing n, opposite to the theoretical predictions.Here we report a combination of measurements and calculations for the parallel magnetic field-induced spinpolarization of 2D electrons at the GaAs/AlGaAs heterojunction. The results highlight the importance of the finite thickness of the electron layer and the resulting deformation of the energy surface E(k ), where k is the in-plane wave vector, that occurs in the presence of a strong parallel field.…”

“…Recently, there has been much renewed interest in this problem, thanks to the availability of highquality dilute 2D systems, and the belief that it may shed light on the controversial issue of a metal-insulator transition in 2D [3]. A technique commonly used to study the spin-polarization is to measure the response of the 2D system to a tilted or parallel magnetic field [4,5,6,7,8,9,10,11]. The results of some of these measurements [8,9,10], however, appear to be at odds with what is theoretically expected [1,2] for a dilute, interacting 2D system that is otherwise ideal, i.e., has zero layer thickness and is disorder-free.…”

Friedel Oscillations, Impurity Scattering, and Temperature Dependence of Resistivity in Graphene

“…In a nonrelativistic degenerate two-dimensional (2D) Fermi gas [2], δρ ∝ cos(2k F r + δ)/r 2 . In 2D electron systems Bragg scattering off the potential created by these long-range FO strongly renormalises the momentum relaxation rate, τ −1 for quasi-particles near the Fermi level, ǫ ≈ ǫ F , which leads to a linear temperature dependence of the resistivity [3, 4, 5, 6] in a 'ballistic' temperature range ǫ F > T > h/τ confirmed in recent experiments on semiconductor heterostructures and Si field-effect transistors [7].Graphene-based transistor [8,9] is a recent invention which attracts a lot of attention. Improvement of the performance of this device requires identification of the dominant source of electron scattering limiting its mobility.…”