Tunable negative permeability in a three-dimensional superconducting metamaterial

We report on highly tunable radio frequency (rf) characteristics of a low-loss and compact three dimensional (3D) metamaterial made of superconducting thin film spiral resonators. The rf transmission spectrum of a single element of the metamaterial shows a fundamental resonance peak at $sim$24.95 MHz that shifts to a 25$%$ smaller frequency and becomes degenerate when a 3D array of such elements is created. The metamaterial shows an $emph{in-situ}$ tunable narrow frequency band in which the real part of the effective permeability is negative over a wide range of temperature, which reverts to gradually near-zero and positive values as the superconducting critical temperature is approached. This metamaterial can be used for increasing power transfer efficiency and tunability of electrically small rf-antennas.

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.

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.

Plasmonic Scaling of Superconducting Metamaterials

Superconducting metamaterials are utilized to study the approach to the plasmonic limit simply by tuning temperature to modify the superfluid density, and thus the superfluid plasma frequency. We examine the persistence of artificial magnetism in a metamaterial made with superconductors in the plasmonic limit, and compare to the electromagnetic behavior of normal metals as a function of frequency as the plasma frequency is approached from below. Spiral-shaped Nb thin film meta-atoms of scaled dimensions are employed to explore the plasmonic behavior in these superconducting metamaterials, and the scaling condition allows extraction of the temperature dependent superfluid density, which is found to be in good agreement with expectations.

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.

Rebuttal to Comment by V.M. Krasnov on Counterintuitive consequence of heating in strongly-driven intrinsic junctions of Bi2Sr2CaCu2O8+d Mesas

In our article [1], we found that with increasing dissipation there is a clear, systematic shift and sharpening of the conductance peak along with the disappearance of the higher-bias dip/hump features (DHF), for a stack of intrinsic Josephson junctions (IJJs) of intercalated Bi2Sr2CaCu2O8+{delta} (Bi2212). Our work agrees with Zhu et al [2] on unintercalated, pristine Bi2212, as both studies show the same systematic changes with dissipation. The broader peaks found with reduced dissipation [1,2] are consistent with broad peaks in the density-of-states (DOS) found among scanning tunneling spectroscopy [3] (STS), mechanical contact tunneling [4] (MCT) and inferred from angle (momentum) resolved photoemission spectroscopy [5] (ARPES); results that could not be ignored. Thus, sharp peaks are extrinsic and cannot correspond to the superconducting DOS. We suggested that the commonality of the sharp peaks in our conductance data, which is demonstrably shown to be heating-dominated, and the peaks of previous intrinsic tunneling spectroscopy (ITS) data implies that these ITS reports might need reinterpretation.

Counterintuitive Consequence of Heating in Strongly-Driven Intrinsic-Junctions of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+delta}$ Mesas

Anomalously high and sharp peaks in the conductance of intrinsic Josephson junctions in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+delta}$ (Bi2212) mesas have been universally interpreted as superconducting energy gaps, but here we show they are a result of heating. This interpretation follows from a direct comparison to the equilibrium gap, $mathit Delta$, measured in break junctions on similar Bi2212 crystals. As the dissipated power increases with a greater number of junctions in the mesa, the conductance peak abruptly sharpens and its voltage decreases to well below 2$mathit Delta$. This sharpening, found in our experimental data, defies conventional intuition of heating effects on tunneling spectra, but it can be understood as an instability into a nonequilibrium two-phase coexistent state. The measured peak positions occur accurately within the voltage range that an S-shaped backbending is found in the {it calculated} current-voltage curves for spatially {it uniform} self-heating and that S-shape implies the potential for the uniform state to be unstable.