Crystalline responses for rotation-invariant higher-order topological insulators

  title={Crystalline responses for rotation-invariant higher-order topological insulators},
  author={Julian May-Mann and Taylor L. Hughes},
  journal={Physical Review B},
Two-dimensional higher-order topological insulators can display a number of exotic phenomena such as half-integer charges localized at corners or disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with C 4 rotation symmetry, and present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical… 

Figures from this paper

Effective action approach to the filling anomaly in crystalline topological matter

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



Higher-order topological insulators

The notion of three-dimensional topological insulators is extended to systems that host no gapless surface states but exhibit topologically protected gapless hinge states and it is shown that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topology insulators.

Acoustic higher-order topological insulator on a kagome lattice

A second-order topological insulator in an acoustical metamaterial with a breathing kagome lattice, supporting one-dimensional edge states and zero-dimensional corner states is demonstrated, and shape dependence allows corner states to act as topologically protected but reconfigurable local resonances.

Quantized electric multipole insulators

This work introduces a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked and opens a venue for the expansion of the classification of topological phases of matter.

A quantized microwave quadrupole insulator with topologically protected corner states

This work demonstrates experimentally a member of this predicted class of materials—a quantized quadrupole topological insulator—produced using a gigahertz-frequency reconfigurable microwave circuit, and provides conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topologicalinsulators.

Observation of second-order topological insulators in sonic crystals

Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological

Higher-Order Topology in Bismuth

It is established that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes.

Observation of a phononic quadrupole topological insulator

Measurements of a phononic quadrupole topological insulator are reported and topological corner states are found that are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.

Topolectrical-circuit realization of topological corner modes

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological

Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains

The demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

Evidence for higher order topology in Bi and Bi0.92Sb0.08

It is shown that the (110) facets of Bi and BiSb alloys can be used to unequivocally establish the topology of these systems, and raises questions about the topological classification of the full family of BixSb1−x alloys.