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Physical review. B, Condensed matter

Freezing of strongly correlated electrons in bilayer systems with weak disorder

J. S. Thakur, D. Neilson

Published Oct 15, 1997• 1 citation
Publisher

Abstract

We investigate a freezing transition of correlated electrons in coupled two-dimensional layers in the presence of small levels of disorder using mode-coupling theory. The transition is primarily driven by correlations within the layers, but coupling between the layers is essential for the transition to occur. When the layers are far apart the ground state is a coupled electron liquid, but as the layers are brought closer, the Coulomb interactions between the layers drives the system to a coupled solid phase. The presence of one solid layer acts like additional disorder for the other layer. If the density of one layer is increased, at some critical value there is a transition in that layer to a solid phase that is weakly localized.

DOI
10.1103/physrevb.56.10297

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We investigate a freezing transition of correlated electrons in coupled two-dimensional layers in the presence of small levels of disorder using mode-coupling theory. The transition is primarily driven by correlations within the layers, but coupling between the layers is essential for the transition to occur. When the layers are far apart the ground state is a coupled electron liquid, but as the layers are brought closer, the Coulomb interactions between the layers drives the system to a coupled solid phase. The presence of one solid layer acts like additional disorder for the other layer. If the density of one layer is increased, at some critical value there is a transition in that layer to a solid phase that is weakly localized.
Electrons in two-dimensional (2D) layers at semiconductor interfaces may be driven to a solid phase by reducing their density. Understandmg of this electron liquid-solid transition at mK-temperatures and the origin of the 2D electron solid phase remain challenging. The experimental system under study is subject to strong interactions and disorder. Charge transport in the electron solid phase demonstrates many features anticipated for the pinned crystal, though no direct imaging of a spatial charge- or magnetic-ordering is available by now. Rich information has been recently obtained for dilute electron liquid phase on strong renormalization of the Pauli spin susceptibility, magnetization, and the effective mass. These data provide a set of the Fermi-liquid coupling parameters for densities down to and at the transition. The steep density dependence of the susceptibility is intriguing because it might indicate a developing magnetic transition, though it is more likely reflects a tendency to crystallization.
We reconcile the possible presence of a quantum critical point in metal insulator transition phenomena in two-dimensional electron systems with observed electronic properties in the low resistivity region which are those of a weakly disordered Fermi liquid. The central issue of whether the ground state of an interacting 2D electron system in the presence of weak potential scattering from disorder is a metal or an insulator remains unresolved. Additional new effects which may become important at extremely low electron densities are briefly mentioned.
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At small layer separations, the ground state of a nu = 1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence. The evolution of this state with increasing layer separation d has been a matter of controversy. We report on small system exact diagonalization calculations which suggest that a single-phase transition, likely of first order, separates incompressible states with strong interlayer correlations from compressible states with weak interlayer correlations. We find a dependence of the phase boundary on d and interlayer tunneling amplitude that is in very good agreement with recent experiments.
The metal–insulator transition (MIT) observed in a two-dimensional dilute electron liquid raises the question about the applicability of the scaling theory of disordered electrons, the approach pioneered by Phil Anderson and his collaborators,8 for the description of this transition. In this context, we review here the scaling theory of disordered electrons with electron–electron interactions. We start with the disordered Fermi liquid, and show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions. This model has a direct relation with the disordered Fermi liquid, but can be more generally applicable, since it is a minimal model for disordered interacting electrons. The discussion is mostly about the general structure of the theory emphasizing the connection of the scaling parameters entering the NLSM with conservation laws. Next, we show that the MIT, as described by the NLSM with interactions, is a quantum phase transition and identify the parameters needed for the description of the kinetics and thermodynamics of the interacting liquid in the critical region of the transition. Finally, we discuss the MIT observed in Si -MOSFETs. We consider it as an example of the Anderson transition in the presence of the electron interactions. We demonstrate that the two-parameter RG equations, which treat disorder in the one-loop approximation but incorporate the full dependence on the interaction amplitudes, describe accurately the experimental data in Si -MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The fact that this drop can be reproduced theoretically, together with the argument that Anderson localization should occur at strong disorder, justified the existence of the MIT within the scaling theory.
What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should exceed the enhancement in the kinetic (Fermi) energy, leading to a (Bloch) ferromagnetic transition. At even lower densities, another transition to a (Wigner) solid, an ordered array of electrons, should occur. Experimental access to these regimes, however, has been limited because of the absence of a material platform that supports an electron system with very high quality (low disorder) and low density simultaneously. Here we explore the ground states of interacting electrons in an exceptionally clean, two-dimensional electron system confined to a modulation-doped AlAs quantum well. The large electron effective mass in this system allows us to reach very large values of the interaction parameter [Formula: see text], defined as the ratio of the Coulomb to Fermi energies. As we lower the electron density via gate bias, we find a sequence of phases, qualitatively consistent with the above scenario: a paramagnetic phase at large densities, a spontaneous transition to a ferromagnetic state when [Formula: see text] surpasses 35, and then a phase with strongly nonlinear current-voltage characteristics, suggestive of a pinned Wigner solid, when [Formula: see text] exceeds [Formula: see text] However, our sample makes a transition to an insulating state at [Formula: see text], preceding the onset of the spontaneous ferromagnetism, implying that besides interaction, the role of disorder must also be taken into account in understanding the different phases of a realistic dilute electron system.