# Long-range spin-coherence in a strongly-coupled all electronic dot-cavity system

## TL;DR

This paper provides a comprehensive theoretical analysis of spin-coherent electronic transport in a dot-cavity system, explaining experimental observations and predicting temperature-dependent many-body phase transitions.

## Contribution

It introduces a detailed model combining numerical, effective, and many-body approaches to understand spin coherence and singlet formation in a dot-cavity device.

## Key findings

- Transport features match experimental data
- Evidence of molecular singlet formation across the device
- Predictions of temperature scaling for phase transitions

## Abstract

We present a theoretical analysis of spin-coherent electronic transport across a mesoscopic dot-cavity system. Such spin-coherent transport has been recently demonstrated in an experiment with a dot-cavity hybrid implemented in a high-mobility two-dimensional electron gas [C. R\"ossler et al., Phys. Rev. Lett. 115, 166603 (2015)] and its spectroscopic signatures have been interpreted in terms of a competition between Kondo-type dot-lead and molecular-type dot-cavity singlet-formation. Our analysis brings forward all the transport features observed in the experiments and supports the claim that a spin-coherent molecular singlet forms across the full extent of the dot-cavity device. Our model analysis includes: (i) a single-particle numerical investigation of the two-dimensional geometry, its quantum-coral-type eigenstates and associated spectroscopic transport features, (ii) the derivation of an effective interacting model based on the observations of the numerical and experimental studies, and (iii) the prediction of transport characteristics through the device using a combination of a master-equation approach on top of exact eigenstates of the dot-cavity system, and an equation-of-motion analysis that includes Kondo physics. The latter provides additional temperature scaling predictions for the many-body phase transition between molecular- and Kondo-singlet formation and its associated transport signatures.