Mapping of the unoccupied states and relevant bosonic modes via the time dependent momentum distribution

TL;DR

This paper introduces a novel time-resolved Compton scattering technique to measure unoccupied electronic states in complex materials by analyzing the time-dependent momentum distribution, supported by theoretical modeling and feasibility demonstration.

Contribution

It proposes a new experimental method to access unoccupied states using TDMD measurements and establishes its relation to unoccupied state dispersion through a non-equilibrium formalism.

Findings

Temporal oscillations in TDMD relate directly to unoccupied state dispersion.

The method is experimentally feasible with realistic parameters.

Application demonstrated on a MgB₂ model.

Abstract

The unoccupied states of complex materials are difficult to measure, yet play a key role in determining their properties. We propose a technique that can measure the unoccupied states, called time-resolved Compton scattering, which measures the time-dependent momentum distribution (TDMD). Using a non-equilibrium Keldysh formalism, we study the TDMD for electrons coupled to a lattice in a pump-probe setup. We find a direct relation between temporal oscillations in the TDMD and the dispersion of the underlying unoccupied states, suggesting that both can be measured by time-resolved Compton scattering. We demonstrate the experimental feasibility by applying the method to a model of MgB$_2$ with realistic material parameters.