4.6 Article

Triangular lattice Majorana-Hubbard model: Mean-field theory and DMRG on a width-4 torus

Journal

PHYSICAL REVIEW B
Volume 103, Issue 11, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.103.115128

Keywords

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Funding

  1. Max Planck-UBC-UTokyo Centre for Quantum Materials
  2. Canada First Research Excellence Fund, Quantum Materials and Future Technologies Program
  3. NSERC [04033-2016]

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Majorana modes can emerge on the surface of a topological superconductor, with attractive interactions potentially driving a phase transition in the topological state. Numerical simulations can be used to study this phenomenon.
Majorana modes can arise as zero-energy bound states in a variety of solid state systems. A two-dimensional phase supporting these quasiparticles, for instance, emerges on the surface of a topological superconductor with the zero modes localized at the cores of vortices. At low energies, such a setup can be modeled by Majorana modes that interact with each other on the Abrikosov lattice. In experiments, the lattice is usually triangular. Motivated by the practical relevance, we explore the phase diagram of this Hubbard-like Majorana model using a combination of mean-field theory and numerical simulation of thin torus geometries through the density matrix renormalization group algorithm. Our analysis indicates that attractive interactions between Majoranas can drive a phase transition in an otherwise gapped topological state.

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