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Wannier-Stark Flatbands in Bravais lattices | | Arindam Mallick
; Nana Chang
; Wulayimu Maimaiti
; Sergej Flach
; Alexei Andreanov
; | | Date: |
7 Sep 2020 | | Abstract: | We systematically construct flatbands for tight-binding models on simple
Bravais lattices in space dimension $d geq 2$ in the presence of a static
uniform DC field. Commensurate DC field directions yield irreducible
Wannier-Stark bands in perpendicular dimension $d-1$ with $d$-dimensional
eigenfunctions. The irreducible bands turn into dispersionless flatbands in the
absence of nearest neighbor hoppings between lattice sites in any direction
perpendicular to the DC field one. The number of commensurate directions which
yield flatbands is of measure one. We arrive at a complete halt of transport,
with the DC field prohibiting transport along the field direction, and the
flatbands prohibiting transport in all perpendicular directions as well. The
anisotropic flatband eigenstates are localizing at least factorially (faster
than exponential). | | Source: | arXiv, 2009.02881 | | Services: | Forum | Review | PDF | Favorites | |
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