Tunable hybridization of Majorana bound states at the quantum spin Hall edge

Confinement at the helical edge of a topological insulator is possible in the presence of proximity-induced magnetic (F) or superconducting (S) order. The interplay of both phenomena leads to the formation of localized Majorana bound states (MBS) or likewise (under certain resonance conditions) the formation of ordinary Andreev bound states (ABS). We investigate the properties of bound states in junctions composed of alternating regions of F or S barriers. Interestingly, the direction of magnetization in F regions and the relative superconducting phase between S regions can be exploited to hybridize MBS or ABS at will. We show that the local properties of MBS translate into a particular nonlocal superconducting pairing amplitude. Remarkably, the symmetry of the pairing amplitude contains information about the nature of the bound state that it stems from. Hence, this symmetry can in principle be used to distinguish MBS from ABS, owing to the strong connection between local density of states and nonlocal pairing in our setup.Comment: 10 pages, 6 figure

Creation of spin-triplet Cooper pairs in the absence of magnetic ordering

In superconducting spintronics, it is essential to generate spin-triplet Cooper pairs on demand. Up to now, proposals to do so concentrate on hybrid structures in which a superconductor (SC) is combined with a magnetically ordered material (or an external magnetic field). We, instead, identify a novel way to create and isolate spin-triplet Cooper pairs in the absence of any magnetic ordering. This achievement is only possible because we drive a system with strong spin-orbit interaction--the Dirac surface states of a strong topological insulator (TI)--out of equilibrium. In particular, we consider a bipolar TI-SC-TI junction, where the electrochemical potentials in the outer leads differ in their overall sign. As a result, we find that nonlocal singlet pairing across the junction is completely suppressed for any excitation energy. Hence, this junction acts as a perfect spin triplet filter across the SC generating equal-spin Cooper pairs via crossed Andreev reflection.Comment: 12 pages, 8 figure

Entanglement detection from conductance measurements in carbon nanotube Cooper pair splitters

Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through the Bell inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell inequality is within the reach of current experimental setups.Comment: 8 pages, 5 figure

Confinement-induced zero-bias peaks in conventional superconductor hybrids

Majorana bound states in topological superconductors have been predicted to appear in the form of zero-bias conductance peaks of height 2e2/h, which represents one of the most studied signatures so far. Here, we show that quasi-zero-energy states, similar to Majorana bound states, can naturally form in any superconducting hybrid junction due to confinement effects, in the absence of spin fields and, thus, without relation to topology. Remarkably, these topologically trivial quasi-zero-energy states produce zero-bias conductance peaks, that could be similar to Majorana signatures, but develop a different peak height ((4e2/h) and are less stable under gating or depletion of the confined region. Our results put forward confinement as an alternative mechanism to explain the ubiquitous presence of trivial zero-bias peaks and quasi-zero-energy states in superconductor hybrid

Phase-tunable multiple Andreev reflections in a quantum spin Hall strip

A quantum spin Hall strip where different edges are contacted by $s$-wave superconductors with a phase difference $\phi$ supports Majorana Kramers pairs (MKPs). We study the transport properties of this setup in a four-terminal normal metal (N)/insulator (I)/superconductor (S) and S/I/S junction. The tunneling spectroscopy for the N/I/S junction reveals that the signature of MKPs is that the conductance is quantized by $4e^2/h$ at zero bias and suppressed at the gap edges. In the S/I/S junction, the subharmonic gap structure displays a phase-tuned even-odd effect, where all odd spikes disappear in the presence of MKPs and the remaining even spikes split when superconductors forming the junction have different gaps. We explain these features by showing that midgap bound states enhance the transmission of the even order multiple Andreev reflections, while the reduced density of states at the gap edges suppresses the odd order ones.Comment: 9 pages, 5 figure