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Exciton Berryology

Henry Davenport1, Johannes Knolle2,3,1, and Frank Schindler1

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Phys. Rev. B 113, 045125 – Published 14 January, 2026

DOI: https://doi.org/10.1103/jtgq-vc7n

Abstract

In translationally invariant semiconductors that host exciton bound states, one can define an infinite number of possible exciton Berry connections. These correspond to the different ways in which a many-body exciton state, at fixed total momentum, can be decomposed into free electron and hole Bloch states that are entangled by an exciton envelope wave function. Inspired by the modern theory of polarization, we define an exciton projected position operator whose eigenvalues single out two unique choices of exciton Berry phase and associated Berry connection—one for electrons, and one for holes. We clarify the physical meaning of these exciton Berry phases and provide a discrete Wilson loop formulation that allows for their numerical calculation without a smooth gauge. As a corollary, we obtain a gauge-invariant expression for the exciton polarization at a given total momentum, i.e., the mean separation of the electron and hole within the exciton wave function. In the presence of crystalline inversion symmetry, the electron and hole exciton Berry phases are quantized to the same value and we derive how this value can be expressed in terms of inversion eigenvalues of the many-body exciton state. We then consider C2T symmetry, for which no symmetry eigenvalues are available as it is antiunitary, and confirm that the exciton Berry phase remains quantized and still diagnoses topologically distinct exciton bands. The notion of shift excitons, whose exciton Wannier states are displaced from those of the noninteracting bands by a quantized amount, can therefore be generalized beyond symmetry indicators.

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Outline

Information

Phys. Rev. B 113, 045125– Published 14 January, 2026
  • Received 11 August 2025
  • Revised 26 November 2025
  • Accepted 2 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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