An Exact Solution for Spin and Charge Correlations in Quantum Dots: The Effect of Level Fluctuations and Zeeman Splitting

Abstract

The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty. We calculate the tunneling density of states and the spin susceptibility. We demonstrate that near the Stoner instability the spin susceptibility follows a Curie law with an effective spin. The latter depends logarithmically on temperature due to the statistical fluctuations of the single-particle levels. Near the Stoner instability the tunneling density of states exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. This is due to ehnanced spin correlations. Our results could be tested in quantum dots made of nearly ferromagnetic materials.

LaTeX, 23 pages, 7 figures

References in corpus (6)

• Spin-orbit interaction in quantum dots in the presence of exchange correlations
• 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
• Anisotropy in Ferromagnetic Nanoparticles: Level-to-Level Fluctuations of a Collective Effect
• A Universal Interacting Crossover Regime in Two-Dimensional Quantum Dots

Cited by in corpus (14)

• Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems
• Geometric Quantum Noise of Spin
• Thermodynamics of ultrasmall metallic grains in the presence of pairing and exchange correlations: Mesoscopic fluctuations
• Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade
• Mesoscopic Stoner instability in open quantum dots: suppression of Coleman-Weinberg mechanism by electron tunneling
• A quantum dot close to Stoner instability: the role of Berry's Phase
• Spin fluctuations in quantum dots
• The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains
• Wei-Norman-Kolokolov approach for Landau-Zener problems
• 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
• Magnetic response of energy levels of superconducting nanoparticles with spin-orbit scattering
• U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Schön approaches
• Tunneling density of states in quantum dots with anisotropic exchange