Fractional Disclination Charge and Discrete Shift in the Hofstadter Butterfly

Zhang, Yuxuan; Manjunath, Naren; Gautam, Nambiar,; Barkeshli, Maissam

doi:10.1103/physrevlett.129.275301

Cited by 24 publications

(12 citation statements)

References 37 publications

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“…Our point of view also offers a new perspective on crystalline gauge fields [66,70,71] and the geometric response of topological phases that has promise for broader studies. By probing the boundary physics, we are able to make statements about the bulk geometric response without needing to directly gauge a discrete spatial symmetry.…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

“…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%

“…At the same time, recent work has indicated thatin addition to quantized multipole moments-twodimensional HOTIs can host nontrivial excitations on lattice defects in the bulk [65][66][67][68][69][70][71]. Particularly relevant for this work, it has been shown that for magnetic (timereversal breaking) C 2n -symmetric HOTIs, disclination defects in the bulk with deficit angle π/n bind fractional electric charge (fractional fermion number).…”

Section: Introductionmentioning

confidence: 92%

“…Some progress has been made viewing the excess corner and disclination charges that stem from higher-order topology as a (discrete) geometric response. For instance, it was recently shown that the charge bound to disclinations in 2D magnetic HOTIs could be captured by a Wen-Zee like response involving the coupling of the electromagnetic field to discrete rota-tional gauge fields [66,68,70,71,78].…”

Section: Introductionmentioning

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%

Section: Discussion and Future Directionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effective action approach to the filling anomaly in crystalline topological matter

Rao¹,

Bradlyn²

2023

Preprint

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“…see the recent papers [61,62] for a lattice calculations of these terms. The new mixed term represent the jump of the topological polarization dipole-moment with value P a = p⋆ sgn(δm ⋆ ) p⋆a 2π , summed over the nodes across the δm ⋆ = 0 [63,64,61].…”

Section: Topological Polarization In a 2+1d Trb Semimetalmentioning

confidence: 99%

Emergent geometry, torsion and anomalies in non-relativistic topological matter

Nissinen

2023

J. Phys.: Conf. Ser.

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I review and discuss aspects of the interplay of emergent geometry and anomalies in topological semimetals and insulators, focusing on effects of torsion. This correspondence identifies torsional topological responses in terms of anomalies and anomaly related hydrodynamic phenomena involving gauge fields and geometry. I discuss how torsional emergent geometry arises from elastic deformations in crystalline materials and how this background couples to thee low-energy continuum models inherited from lattice models, utilizing the semiclassical expansion. Via the coupling of momentum space topology and emergent vielbein geometry, non-relativistic topological matter can realise new geometrical responses of mixed gauge-gravitational character. The topological low-energy torsional responses depend momentum space geometry, lattice momenta and the regularization and UV completion, provided by the non-relativistic physics and symmetries of topological materials.

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Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

Herzog-Arbeitman,

Bernevig

2025

Encyclopedia of Mathematical Physics

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Fractional Disclination Charge and Discrete Shift in the Hofstadter Butterfly

Cited by 24 publications

References 37 publications

Effective action approach to the filling anomaly in crystalline topological matter

Effective action approach to the filling anomaly in crystalline topological matter

Emergent geometry, torsion and anomalies in non-relativistic topological matter

Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

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