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arXiv:cond-mat/0110091

Coulomb Ordering in Anderson-Localized Electron Systems

A. A. Slutskin, M. Pepper, H. A. Kovtun

Published Oct 4, 2001• 0 citations
arXivHTMLPDF

Abstract

We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We have established that with the electron density going to zero the Coulomb interaction brings the arrangement of the Anderson localized electrons closer and closer to an ideal (Wigner) crystal lattice, provided the temperature is sufficiently low and the dimension of the system is > 1. The ordering occurs despite the fact that a random spread of the energy levels of the localized one-electron states, exceeding the mean Coulomb energy per electron, renders it impossible the electrons to be self-localized due to their mutual Coulomb repulsion This differs principally the Coulomb ordered Anderson localized electron system (COALES) from Wigner crystal, Wigner glass, and any other ordered electron or hole system that results from the Coulomb self-localization of electrons/holes. The residual disorder inherent to COALES is found to bring about a multi-valley ground-state degeneration akin to that in spin glass. With the electron density increasing, COALES is revealed to turn into Wigner glass or a glassy state of a Fermi-glass type depending on the width of the random spread of the electron levels.

DOI
10.48550/arxiv.cond-mat/0110091

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We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We have established that with the electron density going to zero the Coulomb interaction brings the arrangement of the Anderson localized electrons closer and closer to an ideal (Wigner) crystal lattice, provided the temperature is sufficiently low and the dimension of the system is > 1. The ordering occurs despite the fact that a random spread of the energy levels of the localized one-electron states, exceeding the mean Coulomb energy per electron, renders it impossible the electrons to be self-localized due to their mutual Coulomb repulsion This differs principally the Coulomb ordered Anderson localized electron system (COALES) from Wigner crystal, Wigner glass, and any other ordered electron or hole system that results from the Coulomb self-localization of electrons/holes. The residual disorder inherent to COALES is found to bring about a multi-valley ground-state degeneration akin to that in spin glass. With the electron density increasing, COALES is revealed to turn into Wigner glass or a glassy state of a Fermi-glass type depending on the width of the random spread of the electron levels.
For intermediate Coulomb energy to Fermi energy ratios rsr_srs​, spinless fermions in a two-dimensional random potential form a new quantum phase, different from the Fermi glass (weakly interacting Anderson localized states) and the Wigner crystal (regular array of charges pinned by the disorder). The intermediate phase is characterized by an ordered flow of persistent currents with a typical value decreasing with excitation energy. Extending finite size scaling analysis to the many body ground state, we find that electron-electron interactions can drive the Fermi glass towards an intermediate metallic phase (Coulomb metal).
We consider the temperature-induced melting of a Wigner solid in one-dimensional (1D) and two-dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged impurities in the system. The system simulates semiconductor-based 2D electron layers where Wigner crystallization is often claimed to be observed experimentally. Using exact diagonalization and utilizing the inverse participation ratio as well as conductance to distinguish between the localized insulating solid phase and the extended metallic liquid phase, we find that the effective melting temperature may be strongly enhanced by disorder since the disordered crystal typically could be in a localized glassy state incorporating the combined nonperturbative physics of both Anderson localization and Wigner crystallization. This disorder-induced enhancement of the melting temperature may explain why experiments often manage to observe insulating disorder-pinned Wigner solids in spite of the experimental temperature being decisively far above the theoretical melting temperature of the pristine Wigner crystal phase in many cases.
Abstract For intermediate Coulomb energy to Fermi energy ratios r s , spinless fermions in a two‐dimensional random potential form a new quantum phase, different from the Fermi glass (weakly interacting Anderson localized states) and the Wigner crystal (regular array of charges pinned by the disorder). The intermediate phase is characterized by an ordered flow of persistent currents with a typical value decreasing with excitation energy. Extending finite size scaling analysis to the many body ground state, we find that electron‐electron interactions can drive the Fermi glass towards an intermediate metallic phase (Coulomb metal).
We consider a two-dimensional electron or hole system at zero temperature and low carrier densities, where the long-range Coulomb interactions dominate over the kinetic energy. In this limit the clean system will form a Wigner crystal. Nontrivial quantum-mechanical corrections to the classical ground state lead to multiparticle exchange processes that can be expressed as an effective spin Hamiltonian involving competing interactions. Disorder will destroy the Wigner crystal on large length scales, and the resulting state is called a Wigner glass. The notion of multiparticle-exchange processes is still applicable in the Wigner glass, but the exchange frequencies now follow a random distribution. We compute the exchange frequencies for a large number of relevant exchange processes in the Wigner crystal, and the frequency distributions for some important processes in the Wigner glass. The resulting effective low-energy spin Hamiltonian should be the starting point of an analysis of the possible ground-state phases and quantum phase transitions between them. We find that disorder plays a crucial role and speculate on a possible zero-temperature phase diagram.
(received; accepted) PACS. 71.30+h – Metal-insulator transitions and other electronic transitions. PACS. 72.15Rn – Quantum localization. PACS. 71.27+a – Strongly correlated electron systems. Abstract. – Extending finite size scaling theory to the many body ground state, one finds that Coulomb repulsion can drive a system of spinless fermions in a random potential from the Anderson insulator (Fermi glass of localized states) towards a new extended phase in dimension d = 2. The transition occurs at a Coulomb energy to Fermi energy ratio rs ≈ 4, where a change in the nature of the persistent currents has been previously observed. Relevance to the recently observed 2d metallic phase is suggested. Following the scaling theory of localization [1], all 2d systems of electrons (or holes) are localized when electron-electron interaction is negligible. This absence of metals in two dimensions is nowadays questioned after the observation of a transition towards a metallic behavior in silicon based 2d electron gases [2, 3, 4] when the carrier density is varied. This unexpected phenomenon occurs also for hole gases in GaAs heterostructures [5, 6], SiGe [7]
Interplay of electron correlation and randomness is studied by using the Anderson-Hubbard model within the Hartree-Fock approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions, which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator) and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in one dimension (1D) or even faster in two dimensions (2D) and three dimensions (3D) toward the Fermi energy. We call it soft Hubbard gap. Moreover, exact-diagonalization results in 1D support the formation of the soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to a conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, based on a picture of multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the scaling of Efros and Shklovskii. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results of SrRu_{1-x}Ti_xO_3.