# Non-equilibrium spectral functions from multi-terminal steady-state density functional theory

## TL;DR

This paper extends steady-state density functional theory to multi-terminal nanoscale systems, enabling the extraction of non-equilibrium spectral functions and capturing phenomena like Kondo resonance splitting under bias.

## Contribution

It develops a multi-terminal i-DFT formalism that can describe complex transport setups and non-equilibrium spectral features in nanoscale junctions.

## Key findings

- Successfully extracts non-equilibrium spectral functions in a three-terminal setup.
- Capable of describing Kondo resonance splitting under bias.
- Validates the formalism against numerically exact many-body approaches.

## Abstract

Multi-terminal transport setups allow to realize more complex measurements and functionalities (e.g., transistors) of nanoscale systems than the simple two-terminal arrangement. Here the steady-state density functional formalism (i-DFT) for the description of transport through nanoscale junctions with an arbitrary number of leads is developed. In a three-terminal setup and in the ideal STM limit where one of the electrodes (the `STM tip') is effectively decoupled from the junction, the formalism allows to extract its non-equilibrium spectral function (at arbitrary temperature) while a bias is applied between the other two electrodes. Multi-terminal i-DFT is shown to be capable of describing the splitting of the Kondo resonance in an Anderson impurity in the presence of an applied bias voltage, as predicted by numerically exact many-body approaches.