Seminar by Jun Won Rhim (MPI-PKS) "Bulk-boundary correspondence from the intercellular Zak phase"

Seminar :

• Speaker: Jun Won Rhim, MPI-PKS, Dresden
• Title: Bulk-boundary correspondence from the intercellular Zak phase
• Date: March 2nd, 2017
• Time: 15:00-16:00
• Venue: C016, Lab1

Bulk-boundary correspondence from the intercellular Zak phase

Jun Won Rhim

The Zak phase γ, the generalization of the Berry phase to Bloch wave functions in solids, is often used to characterize inversion-symmetric 1D topological insula- tors. Due to its dependence on the real-space origin and unit cell, however, there is an ambiguity in its use in a bulk-boundary correspondence. Here, we extract an origin- independent part of γ, the so-called inter-cellular Zak phase γinter , and show that it is a bulk quantity that unambiguously predicts the number of surface modes. Specifically, a neutral finite 1D tight-binding system has ns   = γinter /π (mod 2) in-gap surface modes below the Fermi level if there exists a commensurate inversion-symmetric bulk unit cell. We demonstrate this in two steps: First, we verify that ±eγinter /2π (mod e) equals the extra charge accumulation  in the surface region in a terminated  system of a translationally invariant 1D insulator, while the remnant part of γ, the intra-cellular Zak phase γintra , corresponds to the electronic part of the bulk’s unit cell dipole moment. Second, we show that the extra charge accumulation is related to the number of sur- face modes when the unit cell is inversion symmetric.  We study several tight binding models to quantitatively check both the relation between the extra charge accumula- tion and the inter-cellular  Zak phase, and the bulk-boundary  correspondence using the inter-cellular  Zak phase.

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We look forward to seeing many of you.

Theory of Quantum Matter Unit.