No Arabic abstract
The possibility of inducing superconductivity in type-I Weyl semimetal through coupling its surface to a superconductor was investigated. A single crystal of NbP, grown by chemical vapor transport method, was carefully characterized by XRD, EDX, SEM, ARPES techniques and by electron transport measurements. The mobility spectrum of the carriers was determined. For the studies of interface transmission, the (001) surface of the crystal was covered by several hundred nm thick metallic layers of either Pb, or Nb, or In. DC current-voltage characteristics and AC differential conductance through the interfaces as a function of the DC bias were investigated. When the metals become superconducting, all three types of junctions show conductance increase, pointing out the Andreev reflection as a prevalent contribution to the subgap conductance. In the case of Pb-NbP and Nb-NbP junctions, the effect is satisfactorily described by modified Blonder-Tinkham-Klapwijk model. The absolute value of the conductance is much smaller than that for the bulk crystal, indicating that the transmission occurs through only a small part of the contact area. An opposite situation occurs in In-NbP junction, where the conductance at the peak reaches the bulk value indicating that almost whole contact area is transmitting and, additionally, a superconducting proximity phase is formed in the material. We interpret this as a result of indium diffusion into NbP, where the metal atoms penetrate the surface barrier and form very transparent superconductor-Weyl semimetal contact inside. However, further diffusion occurring already at room temperature leads to degradation of the effect, so it is observed only in the pristine structures. Despite of this, our observation directly demonstrates possibility of inducing superconductivity in a type-I Weyl semimetal.
We calculate the zero-temperature differential conductance $dI/dV$ of a voltage-biased one-dimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two representative models for the topological superconductors: (i) spinful $p$-wave and (ii) $s$-wave with spin-orbit coupling and spin splitting. We verify that in the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap $Delta_s$ is zero and there are two symmetric conductance peaks appearing at $eV = pm Delta_s$ with the quantized value $(4-pi)2e^2/h$ due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for $e|V| < Delta_s$ arising from multiple Andreev reflections. The conductance at $eV = pm Delta_s$ in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance from a zero-energy conventional Andreev bound state can be made to mimic the conductance from a true Majorana mode.
The optical properties of (001)-oriented NbP single crystals have been studied in a wide spectral range from 6 meV to 3 eV from room temperature down to 10 K. The itinerant carriers lead to a Drude-like contribution to the optical response; we can further identify two pronounced phonon modes and interband transitions starting already at rather low frequencies. By comparing our experimental findings to the calculated interband optical conductivity, we can assign the features observed in the measured conductivity to certain interband transitions. In particular, we find that transitions between the electronic bands spilt by spin-orbit coupling dominate the interband conductivity of NbP below 100 meV. At low temperatures, the momentum-relaxing scattering rate of the itinerant carriers in NbP is very small, leading to macroscopic characteristic length scales of the momentum relaxation of approximately 0.5 $mu$m.
We report on the fabrication and measurements of planar mesoscopic Josephson junctions formed by InAs nanowires coupled to superconducting Nb terminals. The use of Si-doped InAs-nanowires with different bulk carrier concentrations allowed to tune the properties of the junctions. We have studied the junction characteristics as a function of temperature, gate voltage, and magnetic field. In junctions with high doping concentrations in the nanowire Josephson supercurrent values up to 100,nA are found. Owing to the use of Nb as superconductor the Josephson coupling persists at temperatures up to 4K. In all junctions the critical current monotonously decreased with the magnetic field, which can be explained by a recently developed theoretical model for the proximity effect in ultra-small Josephson junctions. For the low-doped Josephson junctions a control of the critical current by varying the gate voltage has been demonstrated. We have studied conductance fluctuations in nanowires coupled to superconducting and normal metal terminals. The conductance fluctuation amplitude is found to be about 6 times larger in superconducting contacted nanowires. The enhancement of the conductance fluctuations is attributed to phase-coherent Andreev reflection as well as to the large number of phase-coherent channels due to the large superconducting gap of the Nb electrodes.
We fabricate superconductor-graphene-superconductor Josephson junctions with superconducting regions made of lead (Pb). The critical current through grapehene may be modulated by external magnetic field; the resulting Fraunhofer interference pattern shows several periods of oscillations, indicating that the junction is uniform. Deviations from the perfect Fraunhofer pattern are observed, and their cause is explained by a simulation that takes into account the sample design.
We calculate the tunneling conductance of a graphene normal metal-insulator-superconductor (NIS) junction with a barrier of thickness $d$ and with an arbitrary voltage $V_0$ applied across the barrier region. We demonstrate that the tunneling conductance of such a NIS junction is an oscillatory function of both $d$ and $V_0$. We also show that the periodicity and amplitude of such oscillations deviate from their universal values in the thin barrier limit as obtained in earlier work [Phys. Rev. Lett. {bf 97}, 217001 (2006)] and become a function of the applied voltage $V_0$. Our results reproduces the earlier results on tunneling conductance of such junctions in the thin [Phys. Rev. Lett. {bf 97}, 217001 (2006)] and zero [Phys. Rev. Lett. {bf 97}, 067007 (2006)] barrier limits as special limiting cases. We discuss experimental relevance of our results.