{"title":"Quantum metric induced hole dispersion and emergent particle-hole symmetry in topological flat bands","authors":"Guangyue Ji, Bo Yang","doi":"arxiv-2409.08324","DOIUrl":null,"url":null,"abstract":"The emergent hole dispersion in flat bands is an invaluable platform to study\nthe interplay of quantum geometry and electron-electron interaction with a\nrelatively simple setting. In this work, we find that the hole dispersion in\nideal bands has a linear relationship with the trace of the quantum geometry\ntensor at every $\\boldsymbol{k}$-point for a wide range of interactions to a\ngood approximation. Next, we give a microscopic analysis on the hole dispersion\nand show that the linear relationships for short-range and long-range\ninteractions in $\\boldsymbol{k}$-space have different origins. Moreover, we\nshow how to exploit this observation to engineer particle-hole symmetry in a\nChern band with fluctuating quantum geometry. Our results will be useful for\nfurther studying the physics in particle-hole symmetric flat bands both in\ntheory and in experiment.","PeriodicalId":501171,"journal":{"name":"arXiv - PHYS - Strongly Correlated Electrons","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Strongly Correlated Electrons","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08324","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The emergent hole dispersion in flat bands is an invaluable platform to study
the interplay of quantum geometry and electron-electron interaction with a
relatively simple setting. In this work, we find that the hole dispersion in
ideal bands has a linear relationship with the trace of the quantum geometry
tensor at every $\boldsymbol{k}$-point for a wide range of interactions to a
good approximation. Next, we give a microscopic analysis on the hole dispersion
and show that the linear relationships for short-range and long-range
interactions in $\boldsymbol{k}$-space have different origins. Moreover, we
show how to exploit this observation to engineer particle-hole symmetry in a
Chern band with fluctuating quantum geometry. Our results will be useful for
further studying the physics in particle-hole symmetric flat bands both in
theory and in experiment.