Abstract
We study analytically an underdamped current-biased topological Josephson junction. First, we consider a simplified model at zero temperature, where the parity of the non-local fermionic state formed by Majorana bound states (MBSs) localized on the junction is fixed, and show that a transition from insulating to conducting state in this case is governed by single-quasiparticle tunneling rather than by Cooper pair tunneling in contrast to a non-topological Josephson junction. This results in a significantly lower critical current for the transition from insulating to conducting state. We propose that, if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridization of the states with different parities as a result of the overlap of MBSs localized on the junction and at the edges of the topological nanowire forming the junction. Finally, we discuss how the appearance of MBSs can be established experimentally by measuring the critical current for an insulating regime at different values of the applied magnetic field.
Highlights
Topological superconductors have recently received much attention in the condensed-matter community as a new exotic form of quantum matter [1,2,3] and, as prospective candidates for quantum computation schemes due to the non-Abelian nature of Majorana fermions, which are formed at edges of such systems [4,5,6,7,8]
In this paper we restrict ourselves to a model of a semiconducting single-channel nanowire with strong spin-orbit interaction in the presence of a strong magnetic field applied along the nanowire axis, which results in two split subbands in the nanowire [19,30]
We introduced two regimes governed either by single-quasiparticle tunneling or by Cooper-pair tunneling, which are determined by the geometry of the sample
Summary
Topological superconductors have recently received much attention in the condensed-matter community as a new exotic form of quantum matter [1,2,3] and, as prospective candidates for quantum computation schemes due to the non-Abelian nature of Majorana fermions, which are formed at edges of such systems [4,5,6,7,8]. MBSs on the sides of the Josephson junction are described by EM cos (φ/2): can be associated with the parity of the state formed by these MBSs ( = ±1 for odd and even parity, respectively), and EM is the coupling energy between the MBSs on the junction [39] and characterizes the single-quasiparticle tunneling through the junction This HM represents an effective two-level system, where the levels correspond to the occupation of an effective nonlocal fermionic state formed by the left and right MBSs localized on the sides of the junction. It is known that at low currents a Josephson junction shunted by large impedance Re Z > ZQ = 2π /(2e) (underdamped junction) is in a zero-current Coulomb blockade state (effectively insulating) due to quantum phase fluctuations [37,40,41]. We do not consider the opposite limit of overdamped Josephson junction in this work, as strong dissipation results in phase localization and, no effectively insulating regime for a current-biased junction emerges [41]. In the Appendix, we discuss the instanton action and the fluctuation determinant for our problem
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