Kosterlitz–Thouless transition, spectral property and magnetic moment for a two-dot structure with level difference

Abstract

By means of the numerical renormalization group method, we study the phase transition, the spectral property, and the temperature-dependent magnetic moment for a parallel double dot system with level difference, where the dot energies are kept symmetric to the half-filled level. A Kosterlitz-Thouless (KT) transition between local spin triplet and singlet is found. In the triplet regime, the local spin is partially screened by the conduction leads and spin−1 Kondo effect is realized. While for the singlet, the Kondo peak is strongly suppressed and the magnetic moment decreases to 0 at a definite low temperature. We attribute this KT transition to the breaking of the reflection symmetry, resulting from the difference of the charge occupations of the two dots. To understand this KT transition and related critical phenomena, detailed scenarios are given in the transmission coefficient and the magnetic moment, and an effective Kondo model refers to the Rayleigh-Schrödinger perturbation theory is used.

Quantum phase transition in a realistic double-quantum-dot system

“…In this paper we demonstrate that a realistic device, consisting of two QDs with different energies and with different inter-dot and intra-dot Coulomb interactions, coupled in parallel to two leads, displays a QPT by simply gate tuning the on-site energy difference between the two QDs at the chemical potential corresponding to the particle-hole (PH) symmetric point, where the two-dot system is doubly occupied. (Similar setups have already been studied, but with no energy difference between the dots 16 or in the absence of inter-impurity repulsion 17 , both of which play an important role in our formulation.) After demonstrating the transition numerically, employing the numerical-renormalization-group (NRG) method, and semi-analytically, using slave-boson mean field theory (SBMFT), we show, by transforming the system Hamiltonian to an even-odd basis, that the difference between the dot energies, relative to the difference between the inter-and intra-dot repulsions, plays the role of a magnetic interaction, which changes its sign, from FM to AFM, at the point where the QPT takes place.…”