The excitation gap above the Majorana fermion (MF) modes at the ends of 1D topological superconducting (TS) semiconductor wires scales with the bulk quasiparticle gap E_{qp}. This gap, also called minigap, facilitates experimental detection of the pr
istine TS state and MFs at experimentally accessible temperatures T << E_{qp}. Here we show that the linear scaling of minigap with E_{qp} can fail in quasi-1D wires with multiple confinement bands when the applied Zeeman field is greater than or equal to about half of the confinement-induced bandgap. TS states in such wires have an approximate chiral symmetry supporting multiple near zero energy modes at each end leading to a minigap which can effectively vanish. We show that the problem of small minigap in such wires can be resolved by forcing the system to break the approximate chirality symmetry externally with a second Zeeman field. Although experimental signatures such as zero bias peak from the wire ends is suppressed by the second Zeeman field above a critical value, such a field is required in some important parameter regimes of quasi-1D wires to isolate the topological physics of end state MFs. We also discuss the crucial difference of our minigap calculations from the previously reported minigap results appropriate for idealized spinless p-wave superconductors and explain why the clustering of fermionic subgap states around the zero energy Majorana end state with increasing chemical potential seen in the latter system does not apply to the experimental TS states in spin-orbit coupled nanowires.
Quantum ground states on the non-trivial side of a topological quantum critical point (TQCP) have unique properties that make them attractive candidates for quantum information applications. A recent example is provided by s-wave superconductivity on
a semiconductor platform, which is tuned through a TQCP to a topological superconducting (TS) state by an external Zeeman field. Despite many attractive features of TS states, TQCPs themselves do not break any symmetries, making it impossible to distinguish the TS state from a regular superconductor in conventional bulk measurements. Here we show that for the semiconductor TQCP this problem can be overcome by tracking suitable bulk transport properties across the topological quantum critical regime itself. The universal low-energy effective theory and the scaling form of the relevant susceptibilities also provide a useful theoretical framework in which to understand the topological transitions in semiconductor heterostructures. Based on our theory, specific bulk measurements are proposed here in order to characterize the novel TQCP in semiconductor heterostructures.
Josephson tunnel junctions are widely used as nonlinear elements in superconducting circuits such as low noise amplifiers and quantum bits. However, microscopic defects in the oxide tunnel barrier can produce low and high frequency noise which can po
tentially limit the coherence times and quality factors of resonant circuits. Weak link Josephson junctions are an attractive alternative provided that sufficient nonlinearity can be engineered. We compute the current phase relation for superconducting weak links, with dimensions comparable to the zero temperature coherence length, connected to two and three dimensional superconducting electrodes. Our results indicate that 50-100 nm long aluminum nanobridges connected with three dimensional banks can be used to construct nonlinear oscillators for bifurcation amplification. We also show that under static current bias, these oscillators have a sufficiently anharmonic energy level structure to form a qubit. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits.
