Properties of one-dimensional superconducting wires depend on physical processes with different characteristic lengths. To identify the process dominant in the critical regime we have studied trans- port properties of very narrow (9-20 nm) MoGe wires fabricated by advanced electron-beam lithography in wide range of lengths, 1-25 microns. We observed that the wires undergo a superconductor -insulator transition that is controlled by cross sectional area of a wire and possibly also by the thickness-to-width ratio. Mean-field critical temperature decreases exponentially with the inverse of the wire cross section. We observed that qualitatively similar superconductor{insulator transition can be induced by external magnetic field. Some of our long superconducting MoGe nanowires can be identified as localized superconductors, namely in these wires one-electron localization length is much shorter than the length of a wire.
We measure quantum and thermal phase-slip rates using the standard deviation of the switching current in superconducting nanowires at high bias current. Our rigorous quantitative analysis provides firm evidence for the presence of quantum phase slips (QPS) in homogeneous nanowires. We observe that as temperature is lowered, thermal fluctuations freeze at a characteristic crossover temperature Tq, below which the dispersion of the switching current saturates to a constant value, indicating the presence of QPS. The scaling of the crossover temperature Tq with the critical temperature Tc is linea…
The effects of strong magnetic field on superconducting Nb and MoGe nanowires with diameter $\sim10$ nm have been studied. We have found that the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase slips is applicable in a wide range of magnetic fields and describes well the temperature dependence of the wire resistance, over eleven orders of magnitude. The field dependence of the critical temperature, $T_{c}$, extracted from the LAMH fits is in good quantitative agreement with the theory of pair-breaking perturbations that takes into account both spin and orbital co…
We establish the superconductor-insulator phase diagram for quasi-one dimensional wires by measuring a large set of MoGe nanowires. This diagram is consistent with the Chakravarty-Schmid-Bulgadaev phase boundary, namely with the critical resistance being equal to R_Q = h/4e^2. We find that transport properties of insulating nanowires exhibit a weak Coulomb blockade behavior.
We report measurements on ultrathin (<10 nm) nanowires produced by coating carbon nanotubes with a superconducting amorphous MoGe alloy. We find that nanowires can be superconducting or insulating depending on their normal state resistance $R_{N}$ compared to $R_{q}=h/(2e)^{2}$ -- the quantum resistance for Cooper pairs. If $R_{N}< R_{q}$ the tunneling of quantum phase slips (QPS) is prohibited due to strong damping, and so the wires stay superconducting. The insulating state, observed if $R_{N}> R_{q}$, is explained in terms of proliferation of quantum phase slips and corresponding localizati…
The superconductor-insulator transition in ultrathin films of amorphous Bi was tuned by an applied magnetic field. A finite size scaling analysis has been carried out to determine the critical exponent product vz=0.7 for five films of different thicknesses and normal state resistances. This result differs from the exponents found in previous experiments on InOx and MoGe films. We discuss several possible reasons for this disagreement.
Microwave Fabry-Perot resonators containing nonlinear mesoscopic elements (such as superconducting nanowires) can be used to explore many-body circuit QED. Here, we report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involve MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, are achieved when the steady-state amplitude of the current in the driven resonato…
We study the effect of morphology on the low temperature behavior of superconducting nanowires of length $\approx$100 nm. A well-defined superconductor-insulator transition (SIT) is observed only in homogenous wires, in which case the transition occurs when the normal resistance is close to $h/4e^2$. Inhomogeneous wires, on the other hand, exhibit a mixed behavior, such that signatures of the superconducting and insulating regimes can be observed in the same sample. The resistance versus temperature curves of inhomogeneous wires show multiple steps, each corresponding to a weak link constricti…
Superconducting nanowires are the dual elements to Josephson junctions, with quantum phase-slip processes replacing the tunneling of Cooper pairs. When the quantum phase-slip amplitude ES is much smaller than the inductive energy EL, the nanowire responds as a superconducting inductor. When the inductive energy is small, the response is capacitive. The crossover at low temperatures as a function of ES/EL is discussed and compared with earlier experimental results. For one-dimensional and two-dimensional arrays of nanowires quantum phase transitions are expected as a function of ES/EL. They can…
We study the tunneling effect in an AIII-class insulator proximity coupled with a spin-singlet $s$-wave superconductor, in which three phases are characterized by the integer topological invariant $\mathcal{N}$. By solving the Bogoliubov-de Gennes equation explicitly, we analytically obtain a normal reflection coefficient $R_{σσ'}$ and an Andreev reflection coefficient $A_{σσ'}$, and derive a charge conductance formula,where $σ(σ')$ is the spin index of a reflected (injected) wave. The resulting conductance indicates a wide variety of line shapes: (i)gap structure without coherence peaks for $…
Developing a gate-tunable, scalable, and topologically-protectable supercurrent qubit and integrating it into a quantum circuit are crucial for applications in the fields of quantum information technology and topological phenomena. Here we propose that the nano-hybrid supercurrent transistors, a superconducting quantum analogue of a transistor, made of topological insulator nanowire would be a promising platform for unprecedented control of both the supercurrent magnitude and the current-phase relation by applying a voltage on a gate electrode. We believe that our experimental design will help…
We report on the fabrication and electrical transport properties of superconducting junctions made of β-Ag$_{2}$Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to …
The critical current of a superconductor can depend on the direction of current flow due to magnetochiral anisotropy when both inversion and time-reversal symmetry are broken, an effect known as the superconducting (SC) diode effect. Here, we consider one-dimensional (1D) systems in which superconductivity is induced via the proximity effect. In both topological insulator and Rashba nanowires, the SC diode effect due to a magnetic field applied along the spin-polarization axis and perpendicular to the nanowire provides a measure of inversion symmetry breaking in the presence of a superconducto…
We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model sys…
A topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, is shown to realize a one-dimensional topological superconductor with unpaired Majorana fermions localized at both ends. This situation occurs under a wide range of conditions and constitutes what is possibly the most easily accessible physical realization of the elusive Majorana particles in a solid-state system.
Topological insulator (TI) nanowires in proximity with conventional superconductors have been proposed as a tunable platform to realize topological superconductivity and Majorana zero modes (MZM). The tuning is done using an axial magnetic flux $Φ$ which allows transforming the system from trivial at $Φ=0$ to topologically nontrivial when half a magnetic flux quantum $Φ_0/2$ threads the wire's cross-section. Here we explore the expected topological transition in TI-wire-based Josephson junctions as a function of magnetic flux by probing the $4π$-periodic fraction of the supercurrent, which is …
A heterostructure consisting of a topological insulator (TI) nanowire brought into proximity with a superconducting layer provides a promising route to achieve topological superconductivity and associated Majorana bound states (MBSs). Here, we study effects caused by such a coupling between a thin layer of an $s$-wave superconductor and a TI nanowire. We show that there is a distinct phenomenology arising from the metallization of states in the TI nanowire by the superconductor. In the strong coupling limit, required to induce a large superconducting pairing potential, we find that metallizati…
The work reported in my doctoral thesis is an experimental study of vortex dynamics and phase transitions in thin films of type II superconductors using scanning tunneling spectroscopy, low frequency ac susceptibility measurements and complimentary transport measurements. Chapter I and II cover basics of superconductivity and methodologies used in the thesis. Chapter III discusses the effect of periodic pinning centers on the geometry and dynamics of vortex lattice in NbN thin films. Consequent study of dynamic transition of vortex Mott-like to vortex metal-like state is described. In Chapter …
It has been shown previously that a finite-length topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, realizes a one-dimensional topological superconductor with an unpaired Majorana fermion (MF) localized at each end of the nanowire. Here, we study the stability of these MFs with respect to various perturbations that are likely to occur in a physical realization of the proposed device. We show that the unpaired Majorana fermions persist in this system for any value of the chemical potential inside the…
Finding a clear signature of topological superconductivity in transport experiments remains an outstanding challenge. In this work, we propose exploiting the unique properties of three-dimensional topological insulator nanowires to generate a normal-superconductor junction in the single-mode regime where an exactly quantized $2e^2/h$ zero-bias conductance can be observed over a wide range of realistic system parameters. This is achieved by inducing superconductivity in half of the wire, which can be tuned at will from trivial to topological with a parallel magnetic field, while a perpendicular…
Quantum phase slip (QPS) is the particular manifestation of quantum fluctuations of the order parameter of a current-biased quasi-1D superconductor. The QPS event(s) can be considered a dynamic equivalent of tunneling through conventional Josephson junction containing static in space and time weak link(s). At low temperatures T<<Tc the QPS effect leads to finite resistivity of narrow superconducting channels and suppresses persistent currents in tiny nanorings. Here we demonstrate that the quantum tunneling of phase may result in Coulomb blockade: superconducting nanowire, imbedded in high-Ohm…
Among the different platforms to engineer Majorana fermions in one-dimensional topological superconductors, topological insulator nanowires remain a promising option. Threading an odd number of flux quanta through these wires induces an odd number of surface channels, which can then be gapped with proximity induced pairing. Because of the flux and depending on energetics, the phase of this surface pairing may or may not wind around the wire in the form of a vortex. Here we show that for wires with discrete rotational symmetry, this vortex is necessary to produce a fully gapped topological supe…
Finite-size scaling analysis is a well-accepted method for identification and characterization of quantum phase transitions (QPTs) in superconducting, magnetic and insulating systems. We formally apply this analysis in the form suitable for QPTs in 2-dimensional superconducting films to magnetic-field driven superconductor-metal transition in 1-dimensional MoGe nanowires. Despite being obviously inapplicable to nanowires, the 2d scaling equation leads to a high-quality scaling collapse of the nanowire resistance in the temperature and resistance ranges comparable or better to what is accepted …
When a topological insulator is made into a nanowire, the interplay between topology and size quantization gives rise to peculiar one-dimensional states whose energy dispersion can be manipulated by external fields. In the presence of proximity-induced superconductivity, these 1D states offer a tunable platform for Majorana zero modes. While the existence of such peculiar 1D states has been experimentally confirmed, the realization of robust proximity-induced superconductivity in topological-insulator nanowires remains a challenge. Here, we report the realization of superconducting topological…
Spin-split superconductivity in spin-orbit coupled hybrid nanowires with ferromagnetic barriers
University of Copenhagen（哥本哈根大学）；Centro de Física de Materiales Centro Mixto CSIC-UPV/EHU（CSIC-UPV/EHU联合材料物理中心）；NNF Quantum Computing Programme, Niels Bohr Institute（尼尔斯·玻尔研究所NNF量子计算项目）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
Rapid miniaturization of electronic devices and circuits demands profound understanding of fluctuation phenomena at the nanoscale. Superconducting nanowires -- serving as important building blocks for such devices -- may seriously suffer from fluctuations which tend to destroy long-range order and suppress superconductivity. In particular, quantum phase slips (QPS) proliferating at low temperatures may turn a quasi-one-dimensional superconductor into a resistor or an insulator. Here, we introduce a physical concept of QPS-controlled localization of Cooper pairs that may occur even in uniform n…
Recent experiments on short MoGe nanowires show a sharp superconductor-insulator transition tuned by the normal state resistance of the wire, with a critical resistance of $R_c\approx R_Q= h/(4e^2)$. These results are at odds with a broad range of theoretical work on Josephson-like systems that predicts a smooth transition, tuned by the value of the resistance that shunts the junction. We develop a self-consistent renormalization group treatment of interacting phase-slips and their dual counterparts, correlated cooper pair tunneling, beyond the dilute approximation. This analysis leads to a ve…
Motivated by recent experiments searching for Majorana zero modes in tripartite semiconductor nanowires with epitaxial superconductor and ferromagnetic-insulator layers, we explore the emergence of topological superconductivity in such devices for paradigmatic arrangements of the three constituents. Accounting for the competition between magnetism and superconductivity, we treat superconductivity self consistently and describe the electronic properties, including the superconducting and ferromagnetic proximity effects, within a direct wave-function approach. We conclude that the most viable me…
We studied the electrical transport on $β$-Fe$_{4+δ}$Se$_{5}$ single-crystal nanowires, exhibiting $\sqrt{5}\times\sqrt{5}$ Fe-vacancy order and mixed valence of Fe. We observed a first-order metal-insulator transition of the transition temperature at $\sim$28~K at zero magnetic field. The dielectric relaxation reveals that the transition is related to an energy gap expansion of $\sim$12~meV, involving the charge-orbital ordering. At nearly 28~K, colossal positive magnetoresistance emerges, resulting from the magnetic-field dependent shift of the transition temperature. Through the transition,…
We study theoretically the effect of interactions between quantum phase slips in a short superconducting wire beyond the dilute phase slip approximation. In contrast to the smooth transition in dissipative Josephson junctions, our analysis shows that treating these interactions in a self consistent manner leads to a very sharp transition with a critical resistance of $R_Q= h/(4e^2)$. The addition of the quasi-particles resistance at finite temperature leads to a quantitative agreement with recent experiments on short MoGe nanowires. Our treatment is complementary to the theory of the thermal a…
We consider Josephson junctions on surfaces of three dimensional topological insulator nanowires. We find that in the presence of a parallel magnetic field, short junctions on nanowires show signatures of a perfectly transmitted mode capable of supporting Majorana fermions. Such signatures appear in the current-phase relation in the presence or absence of the fermion parity anomaly, and are most striking when considering the critical current as a function of flux Φ, which exhibits a peak at Φ=h/2e. The peak sharpens in the presence of disorder at low but finite chemical potentials, and can be …
An unusual enhancement of resistance (i.e., superresistivity) below a certain characteristic temperature Tsr was observed in granular Bi nanowires. This superresistive state was found to be dependent on the applied magnetic field (H) as well as the excitation current (I). The suppression of Tsr by magnetic field resembles that of a superconductor. The observed superresistivity appears to be related to the nucleation of local superconductivity inside the granular nanowire without long-range phase coherence. The phenomenon is reminiscent of the Bose-insulator observed previously in ultra thin tw…
Reply to the Comment by Tikhonov and Khrapai on "Long-range crossed Andreev reflection in a topological insulator nanowire proximitized by a superconductor"
In a short superconducting nanowire connected to bulk superconducting leads, quantum phase slips behave as a system of linearly (as opposed to logarithmically) interacting charges. This system maps onto quantum mechanics of a particle in a periodic potential. We show that, while the state with a high density of phase slips is not a true insulator (a consequence of Josephson tunneling between the leads), for a range of parameters it behaves as such down to unobservably small temperatures. We also show that quantum phase slips give rise to multiple branches (bands) in the energy-current relation…
A dc voltage drop develops along amorphous indium oxide nanowires that are exposed to an ac bias source. This voltage is anti-symmetric with magnetic field and is characterized by sample specific quasi-periodic magneto-voltage oscillations. The voltage magnitude increases with decreasing temperature below $T_{C}$ but saturates at low T. As the disorder of the sample is decreased, the dc voltage is suppressed. We suggest that this rectification is a manifestation of the superconducting ratchet effect in which disorder and geometrical confinement play the role of asymmetric pinning centers. This…
We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.
We study the magnetic and superconducting proximity effects in a semiconducting nanowire (NW) attached to superconducting leads and a ferromagnetic insulator (FI). We show that a sizable equilibrium spin polarization arises in the NW due to the interplay between the superconducting correlations and the exchange field in the FI. The resulting magnetization has a nonlocal contribution that spreads in the NW over the superconducting coherence length and is opposite in sign to the local spin polarization induced by the magnetic proximity effect in the normal state. For a Josephson-junction setup, …
We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted external magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor is able to restore the topological phase and therefore the Majorana end-states. Using Abelian bosonization, we further confirm this result in the presence of electron-electron interactions and show a profound connection of this phenomenon to the physics of a one-dimensional doped Mott-insulator. The present results have important applications in e.g., realizi…
