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Delocalized Coulomb phase in two dimensions

Xavier Waintal, Giuliano Benenti, Jean‐Louis Pichard

Published Jan 1, 1999• 7 citations
OpenAlex

Abstract

(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]

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Delocalized Coulomb phase in two dimensions

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Extending the 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 r s ≈ 4, where a change in the nature of the persistent currents has been previously observed. Relevance to the recently observed 2 d metallic phase is suggested.

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Metallic phase between the Fermi glass and the Wigner crystal in two dimensions

Xavier Waintal, Giuliano Benenti, J.‐L. Pichard

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).

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Metal–insulator transition in two-dimensional electron systems

S V Kravchenko, M P Sarachik

The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization in two-dimensional systems of non-interacting or weakly interacting electrons, the ever-present randomness causes the resistance to rise as the temperature is decreased, leading to an insulating ground state. However, new evidence has emerged within the past decade indicating a transition from the insulating to metallic phase in two-dimensional systems of strongly interacting electrons. We review earlier experiments that demonstrate the unexpected presence of a metallic phase in two dimensions, and present an overview of recent experiments with emphasis on the anomalous magnetic properties that have been observed in the vicinity of the transition.

arXiv:cond-mat/0309140•Reports on Progress in Physics•Dec 2, 2003•448 citations
(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]
Extending the 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 r s ≈ 4, where a change in the nature of the persistent currents has been previously observed. Relevance to the recently observed 2 d metallic phase is suggested.
Using a combination of ground state quantum Monte Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localization length of a disordered two-dimensional electron gas. We find that correlations delocalize the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalization is much more dramatic in the presence of valley degeneracy [as in Si metal-oxide-semiconductor field-effect transistors], where the localization length increases drastically. We find that a simple mechanism accounts for the main features of the metallic behavior observed in two-dimensional gases. Our findings support the claim that this behavior is a genuine effect of the presence of interactions, yet that the system is not a "true" metal in the thermodynamic sense.
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).
Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.
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).
The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization in two-dimensional systems of non-interacting or weakly interacting electrons, the ever-present randomness causes the resistance to rise as the temperature is decreased, leading to an insulating ground state. However, new evidence has emerged within the past decade indicating a transition from the insulating to metallic phase in two-dimensional systems of strongly interacting electrons. We review earlier experiments that demonstrate the unexpected presence of a metallic phase in two dimensions, and present an overview of recent experiments with emphasis on the anomalous magnetic properties that have been observed in the vicinity of the transition.