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Wave-function geometry of band crossing points in two dimensions

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Title
Wave-function geometry of band crossing points in two dimensions
Author(s)
Yoonseok Hwang; Junseo Jung; Jun-Won Rhim; Bohm-Jung Yang
Publication Date
2021-06
Journal
PHYSICAL REVIEW B, v.103, no.24
Publisher
American Physical Society
Abstract
© 2021 American Physical Society.Geometry of the wave function is a central pillar of modern solid state physics. In this work, we unveil the wave-function geometry of two-dimensional semimetals with band crossing points (BCPs). We show that the Berry phase of BCPs are governed by the quantum metric describing the infinitesimal distance between quantum states. For generic linear BCPs, we show that the corresponding Berry phase is determined either by an angular integral of the quantum metric, or equivalently, by the maximum quantum distance of Bloch states. This naturally explains the origin of the π-Berry phase of a linear BCP. In the case of quadratic BCPs, the Berry phase can take an arbitrary value between 0 and 2π. We find simple relations between the Berry phase, maximum quantum distance, and the quantum metric in two cases: (i) when one of the two crossing bands is flat; (ii) when the system has rotation and/or time-reversal symmetries. To demonstrate the implication of the continuum model analysis in lattice systems, we study tight-binding Hamiltonians describing quadratic BCPs. We show that, when the Berry curvature is absent, a quadratic BCP with an arbitrary Berry phase always accompanies another quadratic BCP so that the total Berry phase of the periodic system becomes zero. This work demonstrates that the quantum metric plays a critical role in understanding the geometric properties of topological semimetals.
URI
https://pr.ibs.re.kr/handle/8788114/10000
DOI
10.1103/PhysRevB.103.L241102
ISSN
2469-9950
Appears in Collections:
Center for Correlated Electron Systems(강상관계 물질 연구단) > 1. Journal Papers (저널논문)
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