Bulk and surfaces of topological insulators: What can we learn from relativistic many-body calculations?

Irene Aguilera, Christoph Friedrich, Stefan Blügel

F. Manghi

We study the effects of electron-electron interaction in a three-dimensional crystalline topological insulator by adding on-site repulsion to the single-particle Hamiltonian and solving the many-body problem within cluster perturbation theory. The goal is to clarify how many-body effects modify the topological phase that stems from the crystal symmetries. Tuning the strength of the on-site interaction, we show that band inversion disappears in the bulk and surface states lose their metallic character.

Arjun Dey, David F. Mross

We study the entanglement spectra of surface states of symmetry-protected topological phases. The topological bulk imprints the surface with an anomaly that does not permit it to form a trivial “vacuum” state that is gapped, unfractionalized, and symmetry preserving. Any surface wave function encodes the topology of the underlying bulk in addition to a specific surface phase. We show that the real-space entanglement spectrum of such surface wave functions are dominated by the bulk topology and do not readily permit identifying the surface phase. We thus use a modified form of entanglement spectra that incorporates the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons. Published by the American Physical Society 2024

Xiao-Liang Qi

Shoucheng Zhang

Kuang-Ting Chen, Patrick A. Lee

In this paper, we investigate in general how thermodynamic quantities such as the polarization, magnetization, and the magnetoelectric tensor are affected by the boundaries. We show that when the calculation with periodic boundary conditions does not involve a Berry's phase, the quantity in question is determined unambiguously by the bulk, even in the presence of gapless surface states. When the calculation involves a Berry's phase, the bulk can only determine the quantity up to some quantized value, given that (i) there are no gapless surface states, (ii) the surfaces do not break the symmetries preserved by the bulk, and (iii) the system is kept at charge neutrality. If any of the above conditions is violated, the quantity is then determined entirely by the details at the boundary. Due to the strong dependence on the boundary, this kind of thermodynamic quantity, such as the isotropic magnetoelectric coefficient, cannot be measured in the bulk without careful control at the boundary. One thus cannot distinguish between a topological insulator and a trivial insulator in three dimensions by any local measurement in the bulk.