Abstract
We report the existence of \emph{flat bands} in a p-wave superconducting Kitaev ladder. We identify two sets of parameters for which the Kitaev ladder sustains flat bands. These flat bands are accompanied by highly localized eigenstates known as compact localized states. Invoking a Bogoliubov transformation, the Kitaev ladder can be mapped into an interlinked cross-stitch lattice. The mapping helps to reveal the compactness of the eigenstates each of which covers only two unit cells of the interlinked cross-stitch lattice. The Kitaev Hamiltonian undergoes a topological-to-trivial phase transition when certain parameters are fine-tuned. Correlation matrix techniques allow us to compute entanglement entropy of the many-body eigenstates. The study of entanglement entropy affords fresh insight into the topological phase transitions in the model. Sharp features in entanglement entropy when bands cross indicate a deep underlying relationship between entanglement entropy and dispersion.
Highlights
In the last few years, dispersionless bands, known as flat bands, have received a great deal of attention within the condensed matter physics community [1,2,3]
We report the existence of flat bands in a rather simple superconducting Kitaev ladder Hamiltonian system, which has hitherto been unexplored in this context
We report the existence of flat bands in a Kitaev ladder that includes a p-wave superconducting term
Summary
In the last few years, dispersionless bands, known as flat bands, have received a great deal of attention within the condensed matter physics community [1,2,3]. One key aspect of our work is that despite the very simple geometry of the lattice, a flat band becomes possible due to the p-wave superconducting term. The simultaneous presence of both the superconducting term and the ladder geometry leads to many rich phenomena including some exotic transport properties [25]. This system exhibits multiple topologically nontrivial phases characterized by different symmetry classes, which may be accessed by tuning different parameters. Our paper is a study of the interplay of flat bands, topological properties, and entanglement properties of the Kitaev ladder. We summarize our main findings in the last section
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