Evidence for an anomalous current phase relation in topological insulator Josephson junctions

Josephson junctions with topological insulator weak links can host low energy Andreev bound states giving rise to a current phase relation that deviates from sinusoidal behaviour. Of particular interest are zero energy Majorana bound states that form at a phase difference of $\pi$. Here we report on interferometry studies of Josephson junctions and superconducting quantum interference devices (SQUIDs) incorporating topological insulator weak links. We find that the nodes in single junction diffraction patterns and SQUID oscillations are lifted and independent of chemical potential. At high temperatures, the SQUID oscillations revert to conventional behaviour, ruling out asymmetry. The node lifting of the SQUID oscillations is consistent with low energy Andreev bound states exhibiting a nonsinusoidal current phase relation, coexisting with states possessing a conventional sinusoidal current phase relation. However, the finite nodal currents in the single junction diffraction pattern suggest an anomalous contribution to the supercurrent possibly carried by Majorana bound states, although we also consider the possibility of inhomogeneity.Comment: 6 pages, 4 figure

Phase Coherence and Andreev Reflection in Topological Insulator Devices

Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to non-magnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate p-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics which can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Perot oscillations in a TI sandwiched between a superconducting and normal lead. For energies below the superconducting gap, we observe a doubling in the frequency of the oscillations, arising from the additional phase accumulated from Andreev reflection. When a magnetic field is applied perpendicular to the TI surface, a number of very sharp and gate-tunable conductance peaks appear at or near zero energy, which has consequences for interpreting spectroscopic probes of Majorana fermions. Our results demonstrate that TIs are a promising platform for exploring phase-coherent transport in a solid-state system.Comment: 9 pages, 7 figure

Superconducting RF Metamaterials Made with Magnetically Active Planar Spirals

Superconducting metamaterials combine the advantages of low-loss, large inductance (with the addition of kinetic inductance), and extreme tunability compared to their normal metal counterparts. Therefore, they allow realization of compact designs operating at low frequencies. We have recently developed radio frequency (RF) metamaterials with a high loaded quality factor and an electrical size as small as $\sim$$\lambda$658, ($\lambda$ is the free space wavelength) by using Nb thin films. The RF metamaterial is composed of truly planar spirals patterned with lithographic techniques. Linear transmission characteristics of these metamaterials show robust Lorentzian resonant peaks in the sub- 100 MHz frequency range below the $T_c$ of Nb. Though Nb is a non-magnetic material, the circulating currents in the spirals generated by RF signals produce a strong magnetic response, which can be tuned sensitively either by temperature or magnetic field thanks to the superconducting nature of the design. We have also observed strong nonlinearity and meta-stable jumps in the transmission data with increasing RF input power until the Nb is driven into the normal state. We discuss the factors modifying the induced magnetic response from single and 1-D arrays of spirals in the light of numerical simulations.Comment: 4 pages, 7 figure

Dynamical Gate Tunable Supercurrents in Topological Josephson Junctions

Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has been attributed to a transition where the topologically trivial 2DEG at the surface is nearly depleted, causing a shift in the spatial location and change in nature of the helical surface states. We present measurements that support this picture by revealing qualitative changes in the temperature and magnetic field dependence of the critical current across this transition. In particular, we observe pronounced fluctuations in the critical current near total depletion of the 2DEG that demonstrate the dynamical nature of the supercurrent transport through topological low energy ABSs.Comment: 6 pages, 6 figure

Robust Fabry-Perot interference in dual-gated Bi2_2Se3_3 devices

We study Fabry-Perot interference in hybrid devices, each consisting of a mesoscopic superconducting disk deposited on the surface of a three-dimensional topological insulator. Such structures are hypothesized to contain protected zero modes known as Majorana fermions bound to vortices. The interference manifests as periodic conductance oscillations of magnitude $\sim 0.1$ $e^2/h$. These oscillations show no strong dependence on bulk carrier density or sample thickness, suggesting that they result from phase coherent transport in surface states. However, the Fabry-Perot interference can be tuned by both top and back gates, implying strong electrostatic coupling between the top and bottom surfaces of topological insulator.Comment: 5 pages, 3 figures. Accepted by Appl. Phys. Let

Microscopic examination of hot spots giving rise to nonlinearity in superconducting resonators

We investigate the microscopic origins of nonlinear rf response in superconducting electromagnetic resonators. Strong nonlinearity appearing in the transmission spectra at high input powers manifests itself through the emergence of jumplike features near the resonant frequency that evolve toward lower quality factor with higher insertion loss as the rf input power is increased. We directly relate these characteristics to the dynamics of localized normal regions (hot spots) caused by microscopic features in the superconducting material making up the resonator. A clear observation of hot-spot formation inside a Nb thin film self-resonant structure is presented by employing the microwave laser scanning microscope, and a direct link between microscopic and macroscopic manifestations of nonlinearity is established.Comment: 5 pages, 4 figure

On the correct formula for the lifetime broadened superconducting density of states

We argue that the well known Dynes formula [Dynes R C {\it et al.} 1978 {\it Phys. Rev. Lett.} {\bf 41} 1509] for the superconducting quasiparticle density of states, which tries to incorporate the lifetime broadening in an approximate way, cannot be justified microscopically for conventional superconductors. Instead, we propose a new simple formula in which the energy gap has a finite imaginary part $-\Delta_2$ and the quasiparticle energy is real. We prove that in the quasiparticle approximation 2$\Delta_2$ gives the quasiparticle decay rate at the gap edge for conventional superconductors. This conclusion does not depend on the nature of interactions that cause the quasiparticle decay. The new formula is tested on the case of a strong coupling superconductor Pb$_{0.9}$Bi$_{0.1}$ and an excellent agreement with theoretical predictions is obtained. While both the Dynes formula and the one proposed in this work give good fits and fit parameters for Pb$_{0.9}$Bi$_{0.1}$, only the latter formula can be justified microscopically.Comment: 6 pages, 4 figure

A superconducting-nanowire 3-terminal electronic device

In existing superconducting electronic systems, Josephson junctions play a central role in processing and transmitting small-amplitude electrical signals. However, Josephson-junction-based devices have a number of limitations including: (1) sensitivity to magnetic fields, (2) limited gain, (3) inability to drive large impedances, and (4) difficulty in controlling the junction critical current (which depends sensitively on sub-Angstrom-scale thickness variation of the tunneling barrier). Here we present a nanowire-based superconducting electronic device, which we call the nanocryotron (nTron), that does not rely on Josephson junctions and can be patterned from a single thin film of superconducting material with conventional electron-beam lithography. The nTron is a 3-terminal, T-shaped planar device with a gain of ~20 that is capable of driving impedances of more than 100 k{\Omega}, and operates in typical ambient magnetic fields at temperatures of 4.2K. The device uses a localized, Joule-heated hotspot formed in the gate to modulate current flow in a perpendicular superconducting channel. We have characterized the nTron, matched it to a theoretical framework, and applied it both as a digital logic element in a half-adder circuit, and as a digital amplifier for superconducting nanowire single-photon detectors pulses. The nTron has immediate applications in classical and quantum communications, photon sensing and astronomy, and its performance characteristics make it compatible with existing superconducting technologies. Furthermore, because the hotspot effect occurs in all known superconductors, we expect the design to be extensible to other materials, providing a path to digital logic, switching, and amplification in high-temperature superconductors

Imaging the Anisotropic Nonlinear Meissner Effect in Nodal YBa ₂Cu₃O\u3csub\u3e7-δ\u3c/sub\u3e Thin-Film Superconductors

We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states associated with these nodes, on the Fermi surface of the superconductor. The method is demonstrated on the nodal superconductor YBa2Cu3O7-δ and the results are consistent with theoretical predictions for the bulk and surface contributions

Imaging the Anisotropic Nonlinear Meissner Effect in Nodal YBa2_{2}Cu3_{3}O7−δ_{7-\delta} Thin-Film Superconductors

We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states associated with these nodes, on the Fermi surface of the superconductor. The method is demonstrated on the nodal superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ and the results are consistent with theoretical predictions for the bulk and surface contributions.Comment: 5 pages, 3 figures, Phys. Rev. Lett. (in press