Journal
PHYSICAL REVIEW B
Volume 93, Issue 15, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.93.155425
Keywords
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Funding
- ERC [256965]
- European Research Council (ERC) [256965] Funding Source: European Research Council (ERC)
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We study the formation of Majorana states in quasi-one-dimensional (quasi-1D) and two-dimensional square lattices with open boundary conditions, with general anisotropic Rashba coupling, in the presence of an applied Zeeman field and in the proximity of a superconductor. For systems in which the length of the system is very large (quasi-1D) we calculate analytically the exact topological invariant, and we find a rich corresponding phase diagram which is strongly dependent on the width of the system. We compare our results with previous results based on a few-band approximation. We also investigate numerically open two-dimensional systems of finite length in both directions. We use the recently introduced generalized Majorana polarization, which can locally evaluate the Majorana character of a given state. We find that the formation of Majoranas depends strongly on the geometry of the system: for a very elongated wire the finite-size numerical phase diagram reproduces the analytical phase diagram for infinite systems, while if the length and the width are comparable, no Majorana states can form; however, one can show the formation of quasi-Majorana states that have a local Majorana character but no global Majorana symmetry.
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