Flatbands in tight-binding lattices with anisotropic potentials

• URL: http://arxiv.org/abs/2409.11336v1
• Date: Tue, 17 Sep 2024 16:37:35 GMT
• Title: Flatbands in tight-binding lattices with anisotropic potentials
• Authors: Arindam Mallick, Alexei Andreanov,
• Abstract summary: We consider tight-binding models on Bravais lattices with anisotropic onsite potentials that vary along a given direction and are constant along the transverse one. Inspired by our previous work on flatbands in anti-$mathcalPT$ symmetric Hamiltonians, we construct an anti-$mathcalPT$ flatband by tuning the hoppings and the shapes of potentials.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider tight-binding models on Bravais lattices with anisotropic onsite potentials that vary along a given direction and are constant along the transverse one. Inspired by our previous work on flatbands in anti-$\mathcal{PT}$ symmetric Hamiltonians [Phys. Rev. A 105, L021305 (2022)], we construct an anti-$\mathcal{PT}$ symmetric Hamiltonians with an $E=0$ flatband by tuning the hoppings and the shapes of potentials. This construction is illustrated for the square lattice with bounded and unbounded potentials. Unlike flatbands in short-ranged translationally invariant Hamiltonians, we conjecture that the considered $E=0$ flatbands do not host compact localized states. Instead the flatband eigenstates exhibit a localization transition along the potential direction upon increasing the potential strength for bounded potentials. For unbounded potentials flatband eigenstates are always localized irrespective of the potential strength.

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