Quantized electric multipole insulators

By M. Hirsbrunner, Wei Jia, S. Johnson, A. Khan. Science, 2016

1,850 citations recorded by the source corpus.

Corner-dwelling topological states Computing the electric polarization of a crystal is surprisingly tricky, but it can be tackled with the help of a topological concept, the so-called Berry phase. Extensions to higher multiple moments, such as quadrupole and octupole, are even trickier. Benalcazar et al. built a theoretical framework for dealing with these moments in certain types of solids. In the presence of some crystalline symmetries, the quadrupole moment is quantized, and the corners of the system play host to fractionally charged, topologically protected states. These predictions may be testable in cold atom and photonic systems. Science, this issue p. 61 Some crystalline symmetries can quantize the electric quadrupole and octupole moments of a solid. The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/e7bf494c39d70a6901a4db241196e668a345e1be

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators (2018, background): “Indeed, TCIs with quantized multipole moments are symmetry protected topological phases of matter; their quantization is robust and can change only in discrete jumps at phase transitions [12, 13] (unless the protecting symmetries are broken).”
A review on non-Hermitian skin effect (2022, methodology): “For example, taking the Benalcazar-Bernevig-Hughes model [151] as the extended Hermitian Hamiltonian, the resultant non-Hermitian model enables an interesting NHSE that hosts corner skin modes scaling with ( while accompanying H ( extended bulk modes [95].”
Observation of quadrupole transitions and edge mode topology in an LC circuit network (2018, background): “The non-zero winding number along edge bands demonstrates that the edge system is itself topological, as expected from the theory of quadrupole systems [11, 26], and also corroborates the topologicallyprotected nature of the in-gap corner states.”
Higher-order topological insulators (2017, background): “There, we also provide two further topological characterizations, one based on so-called nested Wilson loop (4) and entanglement spectra (21–23) and one applicable to systems that are in addition invariant under the product Î T̂ of inversion symmetry Î and T̂ (3).”