Drude weight in systems with open boundary conditions

TL;DR

This paper demonstrates that the Drude weight, a measure of electron inertia in conducting systems, can be evaluated in bounded samples with open boundary conditions through low-frequency response analysis, challenging the traditional reliance on periodic boundaries.

Contribution

It introduces a method to determine the Drude weight in systems with open boundary conditions by analyzing low-frequency forced oscillations.

Findings

Low-frequency response reveals the Drude weight in open systems.

Simulations confirm the dominance of adiabatic inertia in bounded samples.

The approach provides an alternative to periodic boundary condition calculations.

Abstract

A many-electron conducting system undergoes free acceleration in response to a macroscopic field. The Drude weight $D$---also called charge stiffness---measures the adiabatic (inverse) inertia of the electrons; the $D$ formal expression requires periodic boundary conditions. When instead a bounded sample is addressed within open boundary conditions, no current flows and a constant (external) field only polarizes the sample: the Faraday cage effect. Nonetheless a low-frequency field induces forced oscillations: we show here that the low-frequency linear response of the bounded system is dominated by the adiabatic inertia and allows an alternative evaluation of $D$. Simulations on model one-dimensional systems demonstrate our main message.