Weak Localization, Hole-Hole Interactions, and the “Metal”-Insulator Transition in Two Dimensions

Abstract

A detailed investigation of the metallic behaviour in high quality GaAs-AlGaAs two dimensional hole systems reveals the presence of quantum corrections to the resistivity at low temperatures. Despite the low density (rs > 10) and high quality of these systems, both weak localisation (observed via negative magnetoresistance) and weak hole-hole interactions (giving a correction to the Hall constant) are present in the so-called metallic phase where the resistivity decreases with decreasing temperature. The results suggest that even at high rs there is no metallic phase at T=0 in two dimensions.PACS numbers: 73.40. Qv, 71.30.+h, 73.20.Fz Since the claimed observation of metallic behaviour in strongly interacting two-dimensional (2D) systems over 5 years ago 1 experimentalists have tried to provide data from which an understanding of the conduction processes in high quality 2D systems can be obtained. Initial studies of these new strongly interacting systems revealed that the resistivity data can be "scaled" over a wide range of temperatures indicating the presence of a true phase transition between insulating and metallic states 1-3 . Following this an empirical formula for ρ(T) has been put forward which fits all the available experimental data of the metallic state 4,5 . This formula describes a saturation of the resistivity as the temperature is reduced, giving a finite resistance at T=0, further testifying the existence of a 2D metallic state. Despite these results the nature of the metallic state and whether it really persists to the zero of temperature remains unclear. Early theoretical 6,7 and experimental 8 studies of weakly interacting systems (low r s ) revealed that the presence of any disorder would give rise to logarithmic corrections to the conductivity. Since these corrections become increasingly important as T is reduced the question of what happens to the metallic behaviour as T→ 0 in 2D systems remains. This paper reports the observation of both weak localisation and weak hole-hole interactions in the "metallic" phase of a high quality 2D GaAs hole system. First we demonstrate that the system studied here exhibits all of the characteristics previously associated with the 2D "metal"-insulator transition. Magnetoresistance measurements are then used to extract the logarithmic corrections to the Drude conductivity at low temperatures. The data show that: (1) the anomalous exponential decrease of resistivity with decreasing temperature in the metallic phase is not due to quantum interference or strong interaction effects, (2) phase coherence is preserved in the metallic regime with evidence for normal Fermi liquid behaviour, and (3) hole-hole interactions provide a localising correction to the conductivity.The sample used here is a gated, modulation doped GaAs quantum well grown on a (311)A substrate 3 . Four terminal magnetoresistance measurements were performed at temperatures down to 100mK using low frequency (4 Hz) ac lockin techniques and currents of 0.1-5 nA to avoid electron heating. The hol...

Quantum phase transitions in two-dimensional systems

“…The concentration n c corresponding to a change in the sign of the derivative dR/dT , varied widely from sam- ple to sample, depending on the disorder in the electron system under investigation. A similar change in the sign of the derivative dR/dT , corresponding to the critical carrier concentration n c (p c ), was subsequently found in AlGaAs/GaAs heterostructures with two-dimensional electron 71,72 and hole 73,74,75,76,77,78,79,80 gas, quantum wells AlAs with two-dimensional electron gas 81 , as well as quantum SiGe wells with electron 82 and hole 83,84 gas. However, the temperature dependence of the resistance of these low-dimensional systems in the temperature range T < 1K turned out to be much less than that in silicon MOS structures (Fig.…”

Low-Temperature Collapse of Electron Localization in Two Dimensions

“…Neither the unusually high values of 0 nor the behavior of T is understood at present. Furthermore, the question remains if the metallic T dependence is the signature of a metallic ground state in 2D or if it will disappear at lower temperatures due to the onset of quantum corrections [30].…”

Fermi-Liquid Behavior of the Low-Density 2D Hole Gas in aGaAs/AlGaAsHeterostructure at Large Values ofrs

“…As conventional theories of weak localisation and electron interactions [7,8] are derived for r s ≪ 1, their applicability to r s ∼ 10 − 14 in [5,6] is already a surprising fact. One can argue though that in the structures studied the carrier density was not low enough and mobility not high enough for the deviations from the Fermi liquid description to be seen (p ≃ 4.6 × 10 10 cm −2 and peak mobility µ p = 2.5 × 10 5 cm 2 V −1 s −1 in [5]).…”

“…At small r s , the two corrections are related as δR H (T )/R H = −2δσ(T )/σ [7]. In [5] it was argued that in p-GaAs heterostructures the weak hole-hole interaction effect persists up to r s ∼ 10 − 14. Now we have measured the temperature dependence of the Hall coefficient at much larger r s .…”