A quantum dot close to Stoner instability: the role of Berry's Phase

Abstract

The physics of a quantum dot with electron-electron interactions is well captured by the so called "Universal Hamiltonian" if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close the the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].

This is the published version

References in corpus (5)

• Tunnelling density of states at Coulomb blockade peaks
• The Interplay of Spin and Charge Channels in Zero Dimensional Systems
• Mesoscopic competition of superconductivity and ferromagnetism: conductance peak statistics in metallic grains
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• A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots

Cited by in corpus (9)

• Nonadiabatic Dynamics of a Dissipative Two-level System
• Geometric Quantum Noise of Spin
• Mesoscopic Stoner instability in open quantum dots: suppression of Coleman-Weinberg mechanism by electron tunneling
• Spin fluctuations in quantum dots
• Statistics of Spin Fluctuations in Quantum Dots with Ising Exchange
• Inelastic electron scattering off a quantum dot in the cotunneling regime: the signature of mesoscopic Stoner instability
• U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Schön approaches
• Breaking of Coulomb blockade by macrospin-assisted tunneling
• Tunneling density of states in quantum dots with anisotropic exchange