Unquantized anomalies in topological semimetals

Gioia, L.; Wang, Chong; Burkov, A. A.

doi:10.1103/physrevresearch.3.043067

Cited by 24 publications

(9 citation statements)

References 63 publications

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“…Our work opens up several intriguing directions for future research. First, our microscopic edge theory approach to HOTIs can allow for an examination of how crystalline gauge fields emerge in effective descriptions of topological crystalline phases [66,68,70,71,[102][103][104][105][106][107], by completing the analogy between rotational symmetrybreaking mass terms and the Higgs mechanism described in the previous paragraph. More generally, our work shows that focusing on the boundary theory offers a new window into bulk geometric response.…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

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Effective action approach to the filling anomaly in crystalline topological matter

Rao¹,

Bradlyn²

2023

Preprint

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In two dimensions, magnetic higher-order topological insulators (HOTIs) are characterized by excess boundary charge and a compensating bulk "filling anomaly." At the same time, without additional noncrystalline symmetries, the boundaries of two-dimensional HOTIs are gapped and featureless at low energies, while the bulk of the system is predicted to have a topological response to the insertion of lattice (particularly disclination) defects. Until recently, a precise connection between these effects has remained elusive. In this work, we provide a unifying field-theoretic description for the bulk and boundary response of magnetic HOTIs. By focusing on the low-energy description of the gapped boundary of a HOTI, we show that the boundary charge and filling anomaly arise from the gravitational "Gromov-Jensen-Abanov" (GJA) response action first introduced in [Phys. Rev. Lett. 116, 126802 (2016)] in the context of the quantum Hall effect. As in quantum Hall systems the GJA action cancels apparent anomalies associated with bulk response to disclinations, allowing us to derive a concrete connection between the bulk and boundary theories of HOTIs. We show how our results elucidate the connection between higher order topology and geometric response both in band insulators, and point towards a new route to understanding interacting higher order topological phases.

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Section: Discussion and Future Directionsmentioning

confidence: 99%

“…Such an extension would be particularly relevant to experimental searches for non-magnetic obstructed atomic limit phases [115][116][117]. Additionally, our work can be extended to three-dimensional systems with "R ∧F " responses [118], and topological semimetals with unquantized anomalies [103].…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

Effective action approach to the filling anomaly in crystalline topological matter

Rao¹,

Bradlyn²

2023

Preprint

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“…Refs. [38,39,42,69]. The lattice fields E a , with units of lattice momenta, are also closely related to foliations and subsystem symmetries [71,72]; here we focused on generalized symmetries defined with flat gauge fields on cycles of the lattice torus T d , following [11].…”

Section: Discussionmentioning

confidence: 99%

“…The same fields have been utilized in gapless superconductors and semimetals e.g. in [40][41][42][43][44].…”

Section: Crystalline Topology Of Elasticity Tetrads: Almost Conserved...mentioning

confidence: 99%

Field theory of higher-order topological crystalline response, generalized global symmetries and elasticity tetrads

Nissinen

2022

Annals of Physics

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“…This includes the BF -theories of gravity [8][9][10][11][12][13] and the model of superplastic vacuum, 14 described in terms of the so-called elasticity tetrads. [15][16][17][18][19][20] Some of these features emerge also for acoustic metric, 21,22 see Refs. 6,7 .…”

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confidence: 99%

Acoustic metric and Planck constants

Volovik¹

2023

Preprint

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Based on Akama-Diakonov (AD) theory of emergent tetrads, it was suggested that one can introduce two Planck constants, and / h, which are the parameters of the corresponding components of Minkowski metric, g µν Mink = diag(− 2 , / h 2 , / h 2 , / h 2 ). In the AD theory, the interval ds is dimensionless, as a result the metric elements and thus the Planck constants have nonzero dimensions. The Planck constant has dimension of time, and the Planck constant / h has dimension of length. It is natural to compare / h with the Planck length l P . However, this connection remains an open question, because the microscopic (trans-Planckian) physics of the quantum vacuum is not known. Here we study this question using the effective gravity emerging for sound wave quanta (phonons) in superfluid Bose liquid, where the microscopic physics is known, and the elements of the effective acoustic metric are determined by the parameters of the Bose liquid. Since the acoustic interval is dimensionless, one may introduce the effective "acoustic Planck constants". The acoustic Planck constant / h ac has dimension of length and is on the order of the interatomic distance. This supports the scenario in which / h ∼ l P . We also use the acoustic metric for consideration of dependence of on the Hubble parameter in expanding Universe.

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Unquantized anomalies in topological semimetals

Cited by 24 publications

References 63 publications

Effective action approach to the filling anomaly in crystalline topological matter

Effective action approach to the filling anomaly in crystalline topological matter

Field theory of higher-order topological crystalline response, generalized global symmetries and elasticity tetrads

Acoustic metric and Planck constants

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