Ground-state properties of a triangular triple quantum dot connected to superconducting leads

TL;DR

This paper investigates the complex ground-state phases of a triangular triple quantum dot system connected to superconducting leads, revealing various quantum effects and phase transitions influenced by electron filling and superconducting coupling.

Contribution

It provides a comprehensive phase diagram and classification of quantum states using exact diagonalization and NRG, highlighting the impact of superconductivity on quantum dot states.

Findings

Identification of quantum phases like Kondo and Nagaoka ferromagnetism

Phase diagram mapping across multiple parameters

Role of Bogoliubov zero-energy excitation in π Josephson junctions

Abstract

We study ground-state properties of a triangular triple quantum dot connected to two superconducting (SC) leads. In this system orbital motion along the triangular configuration causes various types of quantum phases, such as a Kondo effect with a four-fold degenerate state and the Nagaoka ferromagnetic mechanism, depending on the electron filling. The ground state also evolves as the Cooper pairs penetrate from the SC leads. We describe the phase diagram in a wide range of the parameter space, varying the gate voltage, the couplings between the dots and leads, and also the Josephson phase between the SC gaps. The results are obtained in the limit of large SC gap, carrying out exact diagonalization of an effective Hamiltonian. We also discuss a classification of the quantum states according to the fixed point of the Wilson numerical renormalization group (NRG). Furthermore, we show that the Bogoliubov zero-energy excitation determines the ground state of a $\pi$ Josephson junction at small electron fillings.