# Long-range Exchange Interaction in Triple Quantum Dots in the Kondo Regime

## TL;DR

This paper investigates long-range exchange interactions in triple quantum dots within the Kondo regime, revealing a controllable antiferromagnetic interaction that induces phase transitions and affects spectral and transport properties.

## Contribution

It analytically and numerically characterizes long-range antiferromagnetic exchange in TQDs, demonstrating controllability via gate tuning and revealing novel spectral and transport phenomena.

## Key findings

- Demonstration of a long-range antiferromagnetic exchange interaction JAF.
- Identification of a phase transition from Kondo singlet to long-range spin singlet.
- Observation of an unexpected spectral peak and anomalous current enhancement.

## Abstract

Long-range interactions in triple quantum dots (TQDs) in Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of (N1,N2,N3) = (1, 0, 1), a long-range antiferromagnetic exchange interaction (JAF) is demonstrated and induces a continuous phase transition from the separated Kondo singlet (KS) to the long-range spin singlet (LSS) state between edge dots. The expression of JAF is analytically derived and numerically verified, according to which JAF can be conveniently manipulated via gate control of the detuning energy. The long-range entanglement of Kondo clouds are proved to be quite robust at strong inter-dot coupling limit. Under equilibrium condition, it induces an unexpected peak in the spectral function of the middle dot whose singly occupied level keeps much higher than the Fermi level. Under nonequilibrium condition, higher inter-dot tunneling barrier induces an anomalous enhancement of current. These novel features can be observed in routine experiments.