Elasticity tetrads, mixed axial-gravitational anomalies, and (3+1)-d quantum Hall effect

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorNissinen, J.en_US
dc.contributor.authorVolovik, G. E.en_US
dc.contributor.departmentDepartment of Applied Physicsen
dc.contributor.groupauthorTopological Quantum Fluidsen
dc.date.accessioned2021-01-25T10:10:35Z
dc.date.available2021-01-25T10:10:35Z
dc.date.issued2019-09-06en_US
dc.description| openaire: EC/H2020/694248/EU//TOPVAC
dc.description.abstractFor two-dimensional topological insulators, the integer and intrinsic (without external magnetic field) quantum Hall effect is described by the gauge anomalous (2+1)-dimensional [(2+1)-d] Chern-Simons (CS) response for the background gauge potential of the electromagnetic U(1) field. The Hall conductance is given by the quantized prefactor of the CS term, which is a momentum-space topological invariant. Here, we show that three-dimensional crystalline topological insulators with no other symmetries are described by a topological (3+1)-dimensional [(3+1)-d] mixed CS term. In addition to the electromagnetic U(1) gauge field, this term contains elasticity tetrad fields E-mu(a) (r, t) = partial derivative X-mu(a) (r, t) which are gradients of crystalline U(1) phase fields X-a (r, t) and describe the deformations of the crystal. For a crystal in three spatial dimensions a = 1, 2, 3 and the mixed axial-gravitational response contains three parameters protected by crystalline symmetries: the weak momentum-space topological invariants. The response of the Hall conductance to the deformations of the crystal is quantized in terms of these invariants. In the presence of dislocations, the anomalous (3+1)-d CS term describes the Callan-Harvey anomaly inflow mechanism. The response can be extended to all odd spatial dimensions. The elasticity tetrads, being the gradients of the lattice U(1) fields, have canonical dimension of inverse length. Similarly, if such tetrad fields enter general relativity, the metric becomes dimensionful, but the physical parameters, such as Newton's constant, the cosmological constant, and masses of particles, become dimensionless.en
dc.description.versionPeer revieweden
dc.format.extent9
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationNissinen, J & Volovik, G E 2019, ' Elasticity tetrads, mixed axial-gravitational anomalies, and (3+1)-d quantum Hall effect ', PHYSICAL REVIEW RESEARCH, vol. 1, no. 2, 023007 . https://doi.org/10.1103/PhysRevResearch.1.023007en
dc.identifier.doi10.1103/PhysRevResearch.1.023007en_US
dc.identifier.issn2643-1564
dc.identifier.otherPURE UUID: 3fa507a2-e26a-45d2-81bf-22612b17e85fen_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/3fa507a2-e26a-45d2-81bf-22612b17e85fen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/55239130/Nissinen_Elasticity.PhysRevResearch.1.023007.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/102127
dc.identifier.urnURN:NBN:fi:aalto-202101251437
dc.language.isoenen
dc.publisherAmerican Physical Society
dc.relationinfo:eu-repo/grantAgreement/EC/H2020/694248/EU//TOPVACen_US
dc.relation.ispartofseriesPHYSICAL REVIEW RESEARCHen
dc.relation.ispartofseriesVolume 1, issue 2en
dc.rightsopenAccessen
dc.subject.keywordPOISSON BRACKETSen_US
dc.subject.keywordMOMENTUM-SPACEen_US
dc.subject.keywordFIELD-THEORYen_US
dc.subject.keywordZERO MODESen_US
dc.subject.keywordFERMIONSen_US
dc.subject.keywordGRAVITYen_US
dc.subject.keywordLATTICEen_US
dc.subject.keywordSTRINGSen_US
dc.subject.keywordPARITYen_US
dc.subject.keywordSTATESen_US
dc.titleElasticity tetrads, mixed axial-gravitational anomalies, and (3+1)-d quantum Hall effecten
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion

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