Edge Majoranas on locally flat surfaces : The cone and the Möbius band

• In this paper, we investigate the edge Majorana modes in the simplest possible p(x) + ip(y) superconductor defined on surfaces with different geometries, the annulus, the cylinder, the Mobius band, and a cone (by cone we mean a cone with the tip cut away so it is topologically equivalent to the annulus and cylinder), and with different configurations of magnetic fluxes threading holes in these surfaces. In particular, we shall address two questions: Given that, in the absence of any flux, the ground state on the annulus does not support Majorana modes while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two? Given that in finite geometries edge Majorana modes have to come in pairs, how can a p(x) + ip(y) state be defined on a Mobius band, which has only one edge? We show that the key to answering these questions is that the ground state depends on the geometry, even though all the surfaces are locally flat. In the case of the truncated cone, there is a nontrivial holonomy, while the nonorientable Mobius band must necessarily support a domain wall.

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NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

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Theoretical Physics

teoretisk fysik

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