Local orbital formulation of the Floquet theory of projectile electronic stopping

TL;DR

This paper develops a local basis Floquet formalism for modeling electronic quantum friction on projectiles in periodic crystals, demonstrated with a simple one-dimensional model, enabling future first-principles calculations.

Contribution

It introduces a local orbital Floquet approach for projectile electronic stopping, including basis transformation and a recurrent solution method, advancing the theoretical framework for quantum friction analysis.

Findings

Demonstrated the formalism with a 1D tight-binding model.

Showed how to handle basis non-orthogonality and Fermi level tilting.

Provided a method to compute the perturbation cloud and stopping power.

Abstract

A recently proposed theoretical framework for the description of electronic quantum friction for constant-velocity nuclear projectiles traversing periodic crystals is here implemented using a local basis representation. The theory requires a change of reference frame to that of the projectile, and a basis set transformation for the target basis functions to a gliding basis is presented, which is time-periodic but does not displace in space with respect to the projectile, allowing a local-basis Floquet impurity-scattering formalism to be used. It is illustrated for a one-dimensional single-band tight-binding model, as the simplest paradigmatic example, displaying the qualitative behaviour of the formalism. The time-dependent non-orthogonality of the gliding basis requires care in the proper (simplest) definition of a local projectile perturbation. The Fermi level is tilted with a slope given by the projectile velocity, which complicates integration over occupied states. It is solved by a recurrent application of the Lippmann-Schwinger equation, in analogy with previous non-equilibrium treatment of electron ballistic transport. Aiming towards a first-principles mean-field-like implementation, the final result is the time-periodic particle density in the region around the projectile, describing the stroboscopically stationary perturbation cloud around the projectile, out of which other quantities can be obtained, such as the electronic stopping power.