Inequivalence of the zero-momentum Limits of Transverse and Longitudinal Dielectric Response in the Cuprates

TL;DR

This paper investigates the non-commutativity of zero-momentum limits of transverse and longitudinal dielectric functions in cuprates, revealing that vertex interactions can cause these limits to differ even in isotropic systems.

Contribution

It demonstrates that a scaleless vertex interaction depending on electron momentum angles can lead to non-commuting dielectric limits, challenging previous assumptions in isotropic materials.

Findings

Non-commutativity occurs due to vertex interactions in isotropic systems.

The order of zero-momentum limits affects dielectric response measurements.

Implications for optical and EELS experiments near zero momentum transfer.

Abstract

We address the question of the mismatch between the zero momentum limits of the transverse and longitudinal dielectric functions for a fixed direction of the driving field observed in the cuprates. This question translates to whether or not the order in which the longitudinal and transverse momentum transfers are taken to zero commute. While the two limits commute for both isotropic and anisotropic Drude metals, we argue that a scaleless vertex interaction that depends solely on the angle between scattered electron momenta is sufficient to achieve non-commutativity of the two limits even for a system that is inherently isotropic. We demonstrate this claim for a simple case of the Drude conductivity modified by electron-boson interactions through appropriate vertex corrections, and outline possible consequences of our result to optical and electron energy loss spectroscopy (EELS) measurements close to zero momentum transfer