Friedel oscillations in two-dimensional materials with inverted bands and Mexican-hat dispersion

TL;DR

This paper investigates Friedel oscillations in 2D topological materials with Mexican hat band dispersion, revealing a complex three-mode structure influenced by quantum geometry, electron interactions, and Fermi surface features.

Contribution

It provides a detailed analysis of the three-mode structure of Friedel oscillations in Mexican hat dispersions, highlighting the roles of quantum metric and electron transitions.

Findings

Identification of a three-mode structure in Friedel oscillations

Discovery of a mode with unexpectedly large amplitude

Analysis of factors influencing FO evolution with Fermi energy

Abstract

We study Friedel oscillations (FOs) in two-dimensional topological materials with Mexican hat band dispersion, which attract great interest due to the bunch of its inherent non-trivial features, including the Van Hove singularity, doubly connected Fermi surface, non-trivial quantum-geometric properties, and the presence of states with negative effective mass. These factors are found to lead to a three-mode structure of the FOs. One of the modes, arising from electron transitions between the Fermi contours, has an unexpectedly large amplitude. The evolution of the amplitudes of all modes with Fermi energy is largely determined by the interplay of three main factors: intra-contour and inter-contour electron transitions, the quantum metric of the basis states, and the electron-electron interaction. We traced the role of each factor in the formation of the FO pattern and identified the corresponding features of the FO evolution.