Abstract
Semiconductor–superconductor hybrid systems are promising candidates for the realization of Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the excitation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic h/e magnetic flux periodicity in the non-trivial phase. The transition between the trivial and non-trivial phase is reflected in the closing and reopening of an excitation gap. We show that the signatures of topological order are robust against details of the geometry, electrostatic disorder and the existence of additional subbands and only rely on the topology of the nanowire and the existence of a superconducting gap. Finally, we show that the coherence length in the non-trivial phase is much longer than in the trivial phase. This opens the possibility to coat the nanowire with superconducting nanograins and thereby significantly reduce the current due to cotunnelling of Cooper pairs and to enhance the Coulomb charging energy without destroying the superconducting gap.
Highlights
Topological phases are quantum phases which cannot be described by a local order parameter
Φ0/2, as follows from the discussion above. This characteristic Φ0 flux periodicity of the excitation spectrum in the nontrivial superconducting phase is directly related to the 4π periodicity of the Josephson current between two topological SCs [10, 33, 35] which has been recently discovered in InSb/Nb nanowire junctions [26]
We have proposed a Coulomb blockade transport experiment to investigate the topological order of semiconductor-superconductor hybrid nanorings, and have shown that characteristic parity and flux periodicity effects in the excitation spectrum reflect the distinct ground-state degeneracies of trivial and nontrivial superconducting phases on manifolds with nonzero genus
Summary
Topological phases are quantum phases which cannot be described by a local order parameter. The excitation energy δE oscillates between d2/∆ and 2∆ as function of magnetic flux with period h/e which is doubled as compared to the case of a trivial SC [23] This connection between the ground-state degeneracy on manifolds with nonzero genus and the h/e flux periodicity of ring structures demonstrates that these properties are a general consequence of topological order and that nonlinear Coulomb blockade transport is a suitable tool to investigate topological order. We here propose another experiment which directly investigates consequences of topological order on a nontrivial manifold For this purpose, we use the Coulomb energy as an instrument to prescribe the parity of the hybrid system and to observe the above discussed ground-state degeneracy.
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