Electric polarization in Chern insulators: Unifying many-body and single-particle approaches

• URL: http://arxiv.org/abs/2503.05864v1
• Date: Fri, 07 Mar 2025 19:00:00 GMT
• Title: Electric polarization in Chern insulators: Unifying many-body and single-particle approaches
• Authors: Yuxuan Zhang, Maissam Barkeshli,
• Abstract summary: Chern insulators possess an intrinsic two-dimensional electric polarization, despite having gapless edge states and non-localizable Wannier orbitals.<n>This paper shows that when the real-space origin $texto$ and momentum-space point $veck_0$ are appropriately chosen in relation to each other, the Berry phase and many-body definitions of polarization are equal.
• Score: 7.694970944345054
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, it has been established that Chern insulators possess an intrinsic two-dimensional electric polarization, despite having gapless edge states and non-localizable Wannier orbitals. This polarization, $\vec{P}_{\text{o}}$, can be defined in a many-body setting from various physical quantities, including dislocation charges, boundary charge distributions, and linear momentum. Importantly, there is a dependence on a choice of real-space origin $\text{o}$ within the unit cell. In contrast, Coh and Vanderbilt extended the single-particle Berry phase definition of polarization to Chern insulators by choosing an arbitrary point in momentum space, $\vec{k}_0$. In this paper, we unify these two approaches and show that when the real-space origin $\text{o}$ and momentum-space point $\vec{k}_0$ are appropriately chosen in relation to each other, the Berry phase and many-body definitions of polarization are equal.

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