Spin and Charge Correlations in Quantum Dots: An Exact Solution

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 {\it exact} analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We calculate several observables, including the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotropic spin interaction. Our results could be tested in nearly ferromagnetic materials.

JETPL class, 6 pages, 2 figures

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• Effects of spin and exchange interaction on the Coulomb-blockade peak statistics in quantum dots
• Exchange and the Coulomb blockade: Peak height statistics in quantum dots
• Spin-orbit interaction in quantum dots in the presence of exchange correlations
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Cited by in corpus (16)

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• Mesoscopic Stoner instability in metallic nanoparticles revealed by shot noise
• A quantum dot close to Stoner instability: the role of Berry's Phase
• The Interplay of Charge and Spin in Quantum Dots: The Ising Case
• Mesoscopic Stoner instability in open quantum dots: suppression of Coleman-Weinberg mechanism by electron tunneling
• Spin fluctuations in quantum dots
• The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains
• 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
• Co-tunneling current through the two-level quantum dot coupled to magnetic leads: A role of exchange interaction
• Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles
• Tunneling density of states in quantum dots with anisotropic exchange