Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands

• URL: http://arxiv.org/abs/2407.12559v1
• Date: Wed, 17 Jul 2024 13:44:39 GMT
• Title: Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Authors: K. B. Yogendra, G. Baskaran, Tanmoy Das,
• Abstract summary: Fractional excitations offer vast potential for both fundamental physics and quantum technologies. Here, we investigate the evolution of low-energy Majorana dispersions across various crystalline phases of the pi-flux in the Kitaev spin model on a honeycomb lattice. We identify conditions under which this superexchange interaction acts as a Z2 gauge field, governing the tight-binding hopping of Majorana Wannier orbitals.
• Score: 0.19116784879310028
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fractional excitations offer vast potential for both fundamental physics and quantum technologies. However, their dynamics under the influence of gauge fields pose a significant challenge to conventional models. Here, we investigate the evolution of low-energy Majorana dispersions across various crystalline phases of the \pi-flux in the Kitaev spin model on a honeycomb lattice. We develop an effective tight-binding description for these low-energy Majorana fermions, introducing a gauge potential through a superexchange-like interaction that systematically eliminates the high-energy spectrum. We identify conditions under which this superexchange interaction acts as a Z2 gauge field, governing the tight-binding hopping of Majorana Wannier orbitals. Our study reveals an intriguing phase transition between two non-trivial topological phases characterized by gapless flat-band (extensive) degeneracy. To further explore flat band physics, we introduce a mean-field theory describing a gauge-invariant Majorana density-wave order within these bands. The resulting split Chern bands facilitate the partial filling of Chern bands, effectively leading to fractional Chern states. Our work, encompassing both the gauge-mediated tight-binding model and the mean-field theory, opens doors for future exploration of $U(1)$, $SU(N)$ gauge-mediated tight-binding approach to other fractional or entangled Wannier excitations.

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