Jonas F. Karcher, Sarang Gopalakrishnan, Mikael C. Rechtsman
{"title":"The effect of hyperuniform disorder on band gaps","authors":"Jonas F. Karcher, Sarang Gopalakrishnan, Mikael C. Rechtsman","doi":"arxiv-2406.11710","DOIUrl":null,"url":null,"abstract":"The properties of semiconductors, insulators, and photonic crystals are\ndefined by their electronic or photonic bands, and the gaps between them. When\nthe material is disordered, Lifshitz tails appear: these are localized states\nthat bifurcate from the band edge and act to effectively close the band gap.\nWhile Lifshitz tails are well understood when the disorder is spatially\nuncorrelated, there has been recent interest in the case of hyperuniform\ndisorder, i.e., when the disorder fluctuations are highly correlated and\napproach zero at long length scales. In this paper, we analytically solve the\nLifshitz tail problem for hyperuniform systems using a path integral and\ninstanton approach. We find the functional form of the density-of-states as a\nfunction of the energy difference from the band edge. We also examine the\neffect of hyperuniform disorder on the density of states of Weyl semimetals,\nwhich do not have a band gap.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.11710","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 properties of semiconductors, insulators, and photonic crystals are
defined by their electronic or photonic bands, and the gaps between them. When
the material is disordered, Lifshitz tails appear: these are localized states
that bifurcate from the band edge and act to effectively close the band gap.
While Lifshitz tails are well understood when the disorder is spatially
uncorrelated, there has been recent interest in the case of hyperuniform
disorder, i.e., when the disorder fluctuations are highly correlated and
approach zero at long length scales. In this paper, we analytically solve the
Lifshitz tail problem for hyperuniform systems using a path integral and
instanton approach. We find the functional form of the density-of-states as a
function of the energy difference from the band edge. We also examine the
effect of hyperuniform disorder on the density of states of Weyl semimetals,
which do not have a band gap.