Interactions and Disorder in Quantum Dots: Instabilities and Phase Transitions

Abstract

Using a fermionic renormalization group approach we analyse a model where the electrons diffusing on a quantum dot interact via Fermi-liquid interactions. Describing the single-particle states by Random Matrix Theory, we find that interactions can induce phase transitions (or crossovers for finite systems) to regimes where fluctuations and collective effects dominate at low energies. Implications for experiments and numerical work on quantum dots are discussed.

4 pages, 1 figure; version to appear in Phys Rev Letters

References in corpus (4)

• The Statistical Theory of Quantum Dots
• Quantum Effects in Coulomb Blockade
• Interactions in Chaotic Nanoparticles: Fluctuations in Coulomb Blockade Peak Spacings
• Coulomb Blockade Peak Spacing Distribution: The Interplay of Temperature and Spin

Cited by in corpus (21)

• Many-Body Physics and Quantum Chaos
• Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit
• Random Matrices with Correlated Elements: A Model for Disorder with Interactions
• A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
• Spin magnetization of small metallic grains
• Interplay between the mesoscopic Stoner and Kondo effects in quantum dots
• Chaotic quantum dots with strongly correlated electrons
• Random Matrix Crossovers and Quantum Critical Crossovers for Interacting Electrons in Quantum Dots
• On the scaling approach to electron-electron interactions in a chaotic quantum dot
• Quantum criticality near the Stoner transition in a two-dot with spin-orbit coupling
• A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots
• Large spin-orbit effects in small quantum dots
• Ballistic Quantum Dots with Disorder and Interactions: A numerical study on the Robnik-Berry billiard
• Interactions, superconducting $T_c$, and fluctuation magnetization for two coupled dots in the crossover between the Gaussian Orthogonal and Unitary ensembles
• Diamagnetic Persistent Currents and Spontaneous Time-Reversal Symmetry Breaking in Mesoscopic Structures
• Diamagnetic persistent currents for electrons in ballistic billiards subject to a point flux
• Magnetic-field-induced binding of few-electron systems in shallow quantum dots
• Superconducting fluctuations in small grains - the Universal Hamiltonian and the reduced BCS model
• Ballistic dynamics of a convex smooth-wall billiard with finite escape rate along the boundary
• The renormalization group for interacting fermions: from Fermi liquids to quantum dots
• A nearly closed ballistic billiard with random boundary transmission