Dynamical and point symmetry of the Kondo effect in triangular quantum dot

TL;DR

This paper investigates how point and spin rotation symmetries in a symmetric triangular quantum dot influence Kondo tunneling, revealing the role of combined symmetries in the resulting exchange interactions and Kondo temperature.

Contribution

It analyzes the interplay of point and spin symmetries in a symmetric triangular quantum dot, deriving the exchange Hamiltonian and calculating the Kondo temperature.

Findings

Symmetries determine the form of the exchange Hamiltonian.

The product of discrete and continuous symmetries influences Kondo physics.

Kondo temperature is explicitly calculated from the symmetry considerations.

Abstract

In this work we concentrate on the {\it point symmetry} of triangular triple quantum dot and its interplay with the {\it spin rotation symmetry} in the context of Kondo tunneling through this kind of artificial molecule. A fully symmetric triangular triple quantum dot is considered, consisting of three identical puddles with the same individual properties (energy levels and Coulomb blockade parameters) and inter-dot coupling (tunnel amplitudes and electrostatic interaction). The underlying Kondo physics is determined by the product of a discrete rotation symmetry group in real space and a continuous rotation symmetry in spin space. These symmetries are reflected in the resulting exchange hamiltonian which naturally involves spin and orbital degrees of freedom. The ensuing poor-man scaling equations are solved and the Kondo temperature is calculated.