Mobility Edges in Two-Dimensional Aperiodic Potentials Article Swipe

PDF

Siyuan Chen , Zhifang Chai , Chengwei Yu , Anton M. Graf , Joonas Keski-Rahkonen , Eric J. Heller ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2412.07117

In 1958, Anderson proposed a new insulating mechanism in random lattices, now known as Anderson localization. It has been shown that a metal-insulating transition occurs in three dimensions, and that one-dimensional disordered systems can be solved exactly to show strong localization regardless of the strength of disorders. Meanwhile, the two-dimensional case was known to be localizing from a scaling argument. Here, we report that there exists a mobility edge in certain random potentials which separate the extended-like states from short-ranged localized states. We further observe that the location of the mobility edge depends on the typical wavelength of the potential, and that the localization length are are related to the energy of an eigenstate. Finally, we apply a renormalization group theory to explain the localization effects and the existence of mobility edge and propose an experimental scheme to verify the mobility edge in photonic crystals.

Related Topics

Concepts

Aperiodic graph Statistical physics Computer science Mathematics Physics Combinatorics

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2412.07117
PDF: https://arxiv.org/pdf/2412.07117
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4405255147

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4405255147

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2412.07117

Digital Object Identifier
Title: Mobility Edges in Two-Dimensional Aperiodic Potentials

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2024

Year of publication
Publication date: 2024-12-10

Full publication date if available
Authors: Siyuan Chen, Zhifang Chai, Chengwei Yu, Anton M. Graf, Joonas Keski-Rahkonen, Eric J. Heller

List of authors in order
Landing page: https://arxiv.org/abs/2412.07117

Publisher landing page
PDF URL: https://arxiv.org/pdf/2412.07117

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2412.07117

Direct OA link when available
Concepts: Aperiodic graph, Statistical physics, Computer science, Mathematics, Physics, Combinatorics

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4405255147
doi	https://doi.org/10.48550/arxiv.2412.07117
ids.doi	https://doi.org/10.48550/arxiv.2412.07117
ids.openalex	https://openalex.org/W4405255147
fwci	0.0
type	preprint
title	Mobility Edges in Two-Dimensional Aperiodic Potentials
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T11476
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9810000061988831
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2608
topics[0].subfield.display_name	Geometry and Topology
topics[0].display_name	Graph theory and applications
topics[1].id	https://openalex.org/T11261
topics[1].field.id	https://openalex.org/fields/31
topics[1].field.display_name	Physics and Astronomy
topics[1].score	0.9785000085830688
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/3109
topics[1].subfield.display_name	Statistical and Nonlinear Physics
topics[1].display_name	Quantum chaos and dynamical systems
topics[2].id	https://openalex.org/T10304
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9573000073432922
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2608
topics[2].subfield.display_name	Geometry and Topology
topics[2].display_name	Geometric and Algebraic Topology
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C104247578
concepts[0].level	2
concepts[0].score	0.9556073546409607
concepts[0].wikidata	https://www.wikidata.org/wiki/Q4779368
concepts[0].display_name	Aperiodic graph
concepts[1].id	https://openalex.org/C121864883
concepts[1].level	1
concepts[1].score	0.33821266889572144
concepts[1].wikidata	https://www.wikidata.org/wiki/Q677916
concepts[1].display_name	Statistical physics
concepts[2].id	https://openalex.org/C41008148
concepts[2].level	0
concepts[2].score	0.33417510986328125
concepts[2].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[2].display_name	Computer science
concepts[3].id	https://openalex.org/C33923547
concepts[3].level	0
concepts[3].score	0.32254350185394287
concepts[3].wikidata	https://www.wikidata.org/wiki/Q395
concepts[3].display_name	Mathematics
concepts[4].id	https://openalex.org/C121332964
concepts[4].level	0
concepts[4].score	0.2952531576156616
concepts[4].wikidata	https://www.wikidata.org/wiki/Q413
concepts[4].display_name	Physics
concepts[5].id	https://openalex.org/C114614502
concepts[5].level	1
concepts[5].score	0.2516302764415741
concepts[5].wikidata	https://www.wikidata.org/wiki/Q76592
concepts[5].display_name	Combinatorics
keywords[0].id	https://openalex.org/keywords/aperiodic-graph
keywords[0].score	0.9556073546409607
keywords[0].display_name	Aperiodic graph
keywords[1].id	https://openalex.org/keywords/statistical-physics
keywords[1].score	0.33821266889572144
keywords[1].display_name	Statistical physics
keywords[2].id	https://openalex.org/keywords/computer-science
keywords[2].score	0.33417510986328125
keywords[2].display_name	Computer science
keywords[3].id	https://openalex.org/keywords/mathematics
keywords[3].score	0.32254350185394287
keywords[3].display_name	Mathematics
keywords[4].id	https://openalex.org/keywords/physics
keywords[4].score	0.2952531576156616
keywords[4].display_name	Physics
keywords[5].id	https://openalex.org/keywords/combinatorics
keywords[5].score	0.2516302764415741
keywords[5].display_name	Combinatorics
language	en
locations[0].id	pmh:oai:arXiv.org:2412.07117
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2412.07117
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2412.07117
locations[1].id	doi:10.48550/arxiv.2412.07117
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license	cc-by
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2412.07117
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5100429223
authorships[0].author.orcid	https://orcid.org/0000-0001-7376-9644
authorships[0].author.display_name	Siyuan Chen
authorships[0].author_position	first
authorships[0].raw_author_name	Chen, Si-Yuan
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5016909151
authorships[1].author.orcid	https://orcid.org/0000-0003-0680-6067
authorships[1].author.display_name	Zhifang Chai
authorships[1].author_position	middle
authorships[1].raw_author_name	Chai, Zixuan
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5064832242
authorships[2].author.orcid	https://orcid.org/0000-0001-9915-5739
authorships[2].author.display_name	Chengwei Yu
authorships[2].author_position	middle
authorships[2].raw_author_name	Yu, Chenzheng
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5005918087
authorships[3].author.orcid	https://orcid.org/0000-0002-0573-8907
authorships[3].author.display_name	Anton M. Graf
authorships[3].author_position	middle
authorships[3].raw_author_name	Graf, Anton M.
authorships[3].is_corresponding	False
authorships[4].author.id	https://openalex.org/A5028891846
authorships[4].author.orcid	https://orcid.org/0000-0002-7906-4407
authorships[4].author.display_name	Joonas Keski-Rahkonen
authorships[4].author_position	middle
authorships[4].raw_author_name	Keski-Rahkonen, Joonas
authorships[4].is_corresponding	False
authorships[5].author.id	https://openalex.org/A5050626727
authorships[5].author.orcid	https://orcid.org/0000-0002-5398-0861
authorships[5].author.display_name	Eric J. Heller
authorships[5].author_position	last
authorships[5].raw_author_name	Heller, Eric J.
authorships[5].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2412.07117
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Mobility Edges in Two-Dimensional Aperiodic Potentials
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T11476
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9810000061988831
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2608
primary_topic.subfield.display_name	Geometry and Topology
primary_topic.display_name	Graph theory and applications
related_works	https://openalex.org/W2899084033, https://openalex.org/W2748952813, https://openalex.org/W4391375266, https://openalex.org/W2037661079, https://openalex.org/W2339191433, https://openalex.org/W4287817191, https://openalex.org/W4298800952, https://openalex.org/W2039582600, https://openalex.org/W1992569127, https://openalex.org/W2072159299
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2412.07117
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2412.07117
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2412.07117
primary_location.id	pmh:oai:arXiv.org:2412.07117
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2412.07117
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2412.07117
publication_date	2024-12-10
publication_year	2024
referenced_works_count	0
abstract_inverted_index.a	4, 21, 57, 66, 117
abstract_inverted_index.In	0
abstract_inverted_index.It	16
abstract_inverted_index.We	82
abstract_inverted_index.an	112, 134
abstract_inverted_index.as	13
abstract_inverted_index.be	34, 54
abstract_inverted_index.in	8, 25, 69, 142
abstract_inverted_index.of	42, 45, 88, 97, 111, 129
abstract_inverted_index.on	93
abstract_inverted_index.to	37, 53, 108, 121, 137
abstract_inverted_index.we	61, 115
abstract_inverted_index.and	28, 100, 126, 132
abstract_inverted_index.are	105, 106
abstract_inverted_index.can	33
abstract_inverted_index.has	17
abstract_inverted_index.new	5
abstract_inverted_index.now	11
abstract_inverted_index.the	43, 48, 75, 86, 89, 94, 98, 102, 109, 123, 127, 139
abstract_inverted_index.was	51
abstract_inverted_index.been	18
abstract_inverted_index.case	50
abstract_inverted_index.edge	68, 91, 131, 141
abstract_inverted_index.from	56, 78
abstract_inverted_index.show	38
abstract_inverted_index.that	20, 29, 63, 85, 101
abstract_inverted_index.1958,	1
abstract_inverted_index.Here,	60
abstract_inverted_index.apply	116
abstract_inverted_index.group	119
abstract_inverted_index.known	12, 52
abstract_inverted_index.shown	19
abstract_inverted_index.there	64
abstract_inverted_index.three	26
abstract_inverted_index.which	73
abstract_inverted_index.energy	110
abstract_inverted_index.exists	65
abstract_inverted_index.length	104
abstract_inverted_index.occurs	24
abstract_inverted_index.random	9, 71
abstract_inverted_index.report	62
abstract_inverted_index.scheme	136
abstract_inverted_index.solved	35
abstract_inverted_index.states	77
abstract_inverted_index.strong	39
abstract_inverted_index.theory	120
abstract_inverted_index.verify	138
abstract_inverted_index.certain	70
abstract_inverted_index.depends	92
abstract_inverted_index.effects	125
abstract_inverted_index.exactly	36
abstract_inverted_index.explain	122
abstract_inverted_index.further	83
abstract_inverted_index.observe	84
abstract_inverted_index.propose	133
abstract_inverted_index.related	107
abstract_inverted_index.scaling	58
abstract_inverted_index.states.	81
abstract_inverted_index.systems	32
abstract_inverted_index.typical	95
abstract_inverted_index.Anderson	2, 14
abstract_inverted_index.Finally,	114
abstract_inverted_index.location	87
abstract_inverted_index.mobility	67, 90, 130, 140
abstract_inverted_index.photonic	143
abstract_inverted_index.proposed	3
abstract_inverted_index.separate	74
abstract_inverted_index.strength	44
abstract_inverted_index.argument.	59
abstract_inverted_index.crystals.	144
abstract_inverted_index.existence	128
abstract_inverted_index.lattices,	10
abstract_inverted_index.localized	80
abstract_inverted_index.mechanism	7
abstract_inverted_index.Meanwhile,	47
abstract_inverted_index.disordered	31
abstract_inverted_index.disorders.	46
abstract_inverted_index.insulating	6
abstract_inverted_index.localizing	55
abstract_inverted_index.potential,	99
abstract_inverted_index.potentials	72
abstract_inverted_index.regardless	41
abstract_inverted_index.transition	23
abstract_inverted_index.wavelength	96
abstract_inverted_index.dimensions,	27
abstract_inverted_index.eigenstate.	113
abstract_inverted_index.experimental	135
abstract_inverted_index.localization	40, 103, 124
abstract_inverted_index.short-ranged	79
abstract_inverted_index.extended-like	76
abstract_inverted_index.localization.	15
abstract_inverted_index.one-dimensional	30
abstract_inverted_index.renormalization	118
abstract_inverted_index.two-dimensional	49
abstract_inverted_index.metal-insulating	22
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	6
citation_normalized_percentile