Multiple zero-energy Majorana fermions (MFs) with spatially overlapping wave functions can survive only if their splitting is prevented by an underlying symmetry. Here we show that, in quasi-one-dimensional (Q1D) time reversal invariant topological s
uperconductors (class DIII), a realistic model for superconducting lithium molybdenum purple bronze and certain families of organic superconductors, multiple Majorana-Kramers pairs with strongly overlapping wave functions persist at zero energy even in the absence of an easily identifiable symmetry. We find that similar results hold in the case of Q1D semiconductor-superconductor heterostructures (class D) with transverse hopping t_{perp} much smaller than longitudinal hopping t_x. Our results, explained in terms of special properties of the Hamiltonian and wave functions, underscore the importance of hidden accidental symmetries in topological superconductors.
We have investigated the growth of BaTiO3 thin films deposited on pure and 1% Nb-doped SrTiO3(001) single crystals using atomic oxygen assisted molecular beam epitaxy (AO-MBE) and dedicated Ba and Ti Knudsen cells. Thicknesses up to 30 nm were invest
igated for various layer compositions. We demonstrate 2D growth and epitaxial single crystalline BaTiO3 layers up to 10 nm before additional 3D features appear; lattice parameter relaxation occurs during the first few nanometers and is completed at {guillemotright}10 nm. The presence of a Ba oxide rich top layer that probably favors 2D growth is evidenced for well crystallized layers. We show that the Ba oxide rich top layer can be removed by chemical etching. The present work stresses the importance of stoichiometry and surface composition of BaTiO3 layers, especially in view of their integration in devices.
Recent observations of a zero bias conductance peak in tunneling transport measurements in superconductor--semiconductor nanowire devices provide evidence for the predicted zero--energy Majorana modes, but not the conclusive proof for their existence
. We establish that direct observation of a splitting of the zero bias conductance peak can serve as the smoking gun evidence for the existence of the Majorana mode. We show that the splitting has an oscillatory dependence on the Zeeman field (chemical potential) at fixed chemical potential (Zeeman field). By contrast, when the density is constant rather than the chemical potential -- the likely situation in the current experimental set-ups -- the splitting oscillations are generically suppressed. Our theory predicts the conditions under which the splitting oscillations can serve as the smoking gun for the experimental confirmation of the elusive Majorana mode.
Majorana fermions (MFs) are predicted to occur as zero-energy bound states in semiconductor nanowire-superconductor structures. However, in the presence of disorder or smooth confining potentials, these structures can also host non-topological nearly
-zero energy states. Here, we demonstrate that the MFs and the nearly-zero topologically-trivial states have different characteristic signatures in a tunneling conductance measurement, which allows to clearly discriminate between them. We also show that low-energy non-topological states can strongly hybridize with metallic states from the leads, which generates the smooth background that characterizes the soft superconducting gap measured in tunneling experiments and produces an additional decoherence mechanism for the Majorana mode. Our results pave the way for the conclusive identification of MFs in a solid state system and provide directions for minimizing quantum decoherence in Majorana wires.
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.
We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a d
isordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological state. We find that the effective impurity scattering rate involves higher-order tunneling processes and is suppressed due to the destructive quantum interference of quasi-particle and quasi-hole trajectories. We show that, despite the fact that both the proximity-induced gap and the effective impurity scattering rate depend on interface transparency, there is a large parameter regime where the topological superconducting phase is robust against disorder in the superconductor. Thus, we establish that the static disorder in the superconductor does not suppress the proximity induced topological superconductivity in the semiconductor.
