Energy Bands of Incommensurate Systems

TL;DR

This paper extends the concept of energy bands to incommensurate systems lacking translational symmetry, supported by numerical validation and a new ARPES theory, broadening the fundamental understanding of condensed matter physics.

Contribution

It introduces a generalized energy band theory applicable to incommensurate systems and develops an ARPES framework for such systems, surpassing traditional paradigms.

Findings

Validated the incommensurate energy band concept with numerical models.

Developed a theory of ARPES for incommensurate systems.

Established a comprehensive energy band framework for incommensurate materials.

Abstract

Energy band theory is a fundamental cornerstone of condensed matter physics. According to conventional wisdom, discrete translational symmetry is mandatory for defining energy bands. Here, we illustrate that, in fact, the concept of energy band can be generalized to incommensurate systems lacking such symmetry, thus transcending the traditional paradigm of energy band. The validity of our theory is verified by extensive numerical calculations in the celebrated Aubry-Andr\'e-Harper model and a two-dimensional incommensurate model of graphene. Building upon the proposed concept of incommensurate energy bands, we further develop a theory of angle-resolved photoemission spectroscopy (ARPES) for incommensurate systems, providing a clear physical picture for the incommensurate ARPES spectra. Our work establishes a comprehensive energy band theory for incommensurate systems.