Geometric density of states of electronic structures for local responses: Phase information from the amplitudes of STM measurement

TL;DR

This paper introduces the geometric density of states (GDOS), a new concept derived from the curvature of constant-energy contours, which enhances the understanding of local electronic responses and phase information in crystalline materials, especially via STM measurements.

Contribution

The paper proposes GDOS as a novel geometric amplitude that links curvature to local responses, enabling phase extraction from STM without Fourier transforms.

Findings

GDOS provides a transparent physics-based expression for real-space Green's functions.

GDOS allows direct simulation of STM measurements and phase information extraction.

Application to topological insulators demonstrates the method's effectiveness.

Abstract

Electronic band structures underlie the physical properties of crystalline materials, their geometrical exploration renovates the conventional cognition and brings about novel applications. Inspired by geometry phases, we introduce a geometric amplitude named as the geometric density of states (GDOS) dictated by the differential curvature of the constant-energy contour. The GDOS determines the amplitude of the real-space Green's function making it attain the ultimate expression with transparent physics. The local responses of crystalline materials are usually formulated by the real-space Green's function, so the relevant physics should be refreshed by GDOS. As an example of local responses, we suggest using scanning tunneling microscopy (STM) to characterize the surface states of three-dimensional topological insulator under an in-plane magnetic field. The GDOS favors the straightforward simulation of STM measurement without resorting to Fourier transform of the real-space measurement, and also excavates the unexplored potential of STM measurement to extract the phase information of wavefunction through its amplitude, i.e., the spin and curvature textures. Therefore, the proposed GDOS deepens the understanding of electronic band structures and is indispensable in local responses, and it should be universal for any periodic systems.