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Topological Dipole Insulator

by Ho Tat Lam, Jung Hoon Han, Yizhi You

Submission summary

Authors (as registered SciPost users): Ho Tat Lam
Submission information
Preprint Link:  (pdf)
Date submitted: 2024-05-02 10:56
Submitted by: Lam, Ho Tat
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We expand the concept of two-dimensional topological insulators to encompass a novel category known as topological dipole insulators (TDIs), characterized by conserved dipole moments along the $x$-direction in addition to charge conservation. By generalizing Laughlin's flux insertion argument, we prove a no-go theorem and predict possible edge patterns and anomalies in a TDI with both charge $U^e(1)$ and dipole $U^d(1)$ symmetries. The edge of a TDI is characterized as a quadrupolar channel that displays a dipole $U^d(1)$ anomaly. A quantized amount of dipole gets transferred between the edges under the dipolar flux insertion, manifesting as `quantized quadrupolar Hall effect' in TDIs. A microscopic coupled-wire Hamiltonian realizing the TDI is constructed by introducing a mutually commuting pair-hopping terms between wires to gap out all the bulk modes while preserving the dipole moment. The effective action at the quadrupolar edge can be derived from the wire model, with the corresponding bulk dipolar Chern-Simons response theory delineating the topological electromagnetic response in TDIs. Finally, we enrich our exploration of topological dipole insulators to the spinful case and construct a dipolar version of the quantum spin Hall effect, whose boundary evidences a mixed anomaly between spin and dipole symmetry. Effective bulk and the edge action for the dipolar quantum spin Hall insulator are constructed as well.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing

Reports on this Submission

Anonymous Report 1 on 2024-6-15 (Invited Report)


1- proposes new kinds of topological insulator and quantum spin Hall insulator protected by dipole symmetry in 2+1d.

2- constructs explicit models which realise these new (SPT) phases.


This paper proposes a new kind of topological insulator, referred to as topological dipole insular, and quantum spin Hall insulator with conserved charge and dipole moment. The anomalies at the boundary and possible edge patterns are explored. Explicit microscopic models realising these edge patterns are given. The SPT action in the bulk corresponds to a higher-rank gauge theory which has a Chern-Simons or mutual Chern-Simons (BF) like description.

I believe the paper certainly meets the criteria for publication in SciPost Physics. I have a couple of minor comments listed below.

Requested changes

1- In the introduction, the authors say "... proposing a generalized Lieb-Schultz-Mattis theorem...," but I didn't see it being discussed in the rest of the paper. Can the authors please clarify what they meant to say?

2- In Fig 1 and 3, $L$ should be $L_x$.

3- In Fig 2, I think the x and y directions in (B) are rotated by 90 degrees with respect to (A) and (C).


Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: top
  • significance: high
  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: excellent

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