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arXiv:1111.7238 · Physical Review Letters

Critical Behavior of a Strongly Interacting 2D Electron System

A. Mokashi, Shiqi Li, B. Wen, S. V. Kravchenko, A. A. Shashkin, Valerii T. Dolgopolov, Myriam P. Sarachik

Published Aug 28, 2012• 60 citations
arXivHTMLPDF

Abstract

With decreasing density n(s) the thermopower S of a low-disorder two-dimensional electron system in silicon is found to exhibit a sharp increase by more than an order of magnitude tending to a divergence at a finite disorder-independent density n(t) consistent with the critical form (-T/S) is proportional to (n(s)-n(t))(x) with x=1.0±0.1 (T is the temperature). Our results provide clear evidence for an interaction-induced transition to a new phase at low density in a strongly interacting 2D electron system.

DOI
10.1103/physrevlett.109.096405

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With decreasing density n(s) the thermopower S of a low-disorder two-dimensional electron system in silicon is found to exhibit a sharp increase by more than an order of magnitude tending to a divergence at a finite disorder-independent density n(t) consistent with the critical form (-T/S) is proportional to (n(s)-n(t))(x) with x=1.0±0.1 (T is the temperature). Our results provide clear evidence for an interaction-induced transition to a new phase at low density in a strongly interacting 2D electron system.
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Within the infinite series of ring (or bubble) diagram approximation for the electronic self-energy as appropriate for the long-range Coulomb interaction, we calculate the density-dependent T=0T=0T=0 Fermi-liquid quasiparticle effective-mass renormalization in two-dimensional (2D) electron systems in the random-phase approximation. We find that the quasiparticle effective mass increases very strongly with increasing rs{r}_{s}rs​, exhibiting an unexpected divergence at a critical rs{r}_{s}rs​ value ($\ensuremath{\sim}16$ in the ideal 2D system). We discuss the possibility for and the consequences of such an interaction-induced effective-mass divergence as the electron density decreases and critically comment on the likely theoretical scenarios which could lead to such a low-density effective-mass divergence in electron liquids.
A quantum phase transition that was recently observed in a high-mobility silicon metal-oxide-semiconductor field-effect transistor is analyzed in terms of a scaling theory. The most striking characteristic of the transition is a divergence of the thermopower, according to an inverse linear law, as a critical value of the electron density is approached. A scaling description of this transition yields predictions about the critical behavior of other observables, e.g., the specific heat. We also explore the possibility that this transition realizes a recently predicted transition from a Fermi liquid to a non-Fermi-liquid state.
The fate of the metallic phase in parallel magnetic fields represents one of the major open issues in the studies of dilute, strongly interacting systems in two dimensions (2D). In this experiment, the temperature dependence of conductivity σ(T) of a 2D electron system in silicon has been studied in parallel magnetic fields B. At B = 0, the system displays a new and unexpected kind of metallic behavior with dσ/dT > 0, and a novel type of a metal-insulator transition,1 which occurs at a critical electron density nc(0). At low fields (B ≤ 2 T ), nc increases as nc(B) - nc(0) ∝ Bβ(β ≈ 0.9), and the zero-temperature conductivity scales as σ(ns, B, 0)/σ (ns, 0, 0) = f(Bβ/δn) (where δn = (ns - nc(0))/nc(0), and ns is electron density) as expected for a quantum phase transition. The metallic phase persists in fields up to 18 T, consistent with the saturation of nc at high fields. These results strongly suggest that the 2D metal may exist even for spinless electrons.
The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase's resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.