Vortex Tunneling Research Articles

High-Temperature Anomalous Metal States in Iron-Based Interface Superconductors.

The nature of the anomalous metal state has been a major puzzle in condensed matter physics for more than three decades. Here, we report systematic investigation and modulation of the anomalous metal states in high-temperature interface superconductor FeSe films on SrTiO_{3} substrate. Remarkably, under zero magnetic field, the anomalous metal state persists up to 20K in pristine FeSe films, an exceptionally high temperature standing out from previous observations. In stark contrast, for the FeSe films with nanohole arrays, the characteristic temperature of the anomalous metal state is considerably reduced. We demonstrate that the observed anomalous metal states originate from the quantum tunneling of vortices adjusted by the Ohmic dissipation. Our work offers a perspective for understanding the origin and modulation of the anomalous metal states in two-dimensional bosonic systems.

Fractional magnetoresistance oscillations in spin-triplet superconducting rings

Half-quantum vortices in spin-triplet superconductors are predicted to host Majorana zero modes and may provide a viable platform for topological quantum computation. Recent works also suggested that, in thin mesoscopic rings, the superconducting pairing symmetry can be probed via Little-Parks-like magnetoresistance oscillations of periodicity Φ0 = h/2e that persist below the critical temperature. Here we use the London limit of Ginzburg-Landau theory to study these magnetoresistance oscillations resulting from thermal vortex tunneling in spin-triplet superconducting rings. For a range of temperatures in the presence of disorder, we find magnetoresistance oscillations with an emergent fractional periodicity Φ0/n, where the integer n ≥ 3 is entirely determined by the ratio of the spin and charge superfluid densities. These fractional oscillations can unambiguously confirm the spin-triplet nature of superconductivity and directly reveal the tunneling of half-quantum vortices in real-world candidate materials.

Theory of the Little-Parks effect in spin-triplet superconductors

The celebrated Little-Parks effect in mesoscopic superconducting rings has recently gained great attention due to its potential to probe half-quantum vortices in spin-triplet superconductors. However, despite the large number of works reporting anomalous Little-Parks measurements attributed to unconventional superconductivity, the general signatures of spin-triplet pairing in the Little-Parks effect have been less systematically investigated. Here we use Ginzburg-Landau theory to study the Little-Parks effect in a spin-triplet superconducting ring that supports half-quantum vortices; we calculate the field-induced Little-Parks oscillations of both the critical temperature itself and the residual resistance resulting from thermal vortex tunneling below the critical temperature. We observe two separate critical temperatures with a single-spin superconducting state in between and find that due to the existence of half-quantum vortices, each minimum in the upper critical temperature splits into two minima for the lower critical temperature. From a rigorous calculation of the residual resistance, we confirm that these two minima in the lower critical temperature translate into two maxima in the residual resistance below and establish the general conditions under which the two maxima can be practically resolved. In particular, we identify a fundamental trade-off between sharpening each maximum and keeping the overall magnitude of the resistance large. Our results will guide experimental efforts in designing mesoscopic ring geometries for probing half-quantum vortices in spin-triplet candidate materials on the device scale.

Resistance of two-dimensional superconducting films

We consider the problem of finite resistance $R$ in superconducting films with geometry of a strip of width $W$ near zero temperature. The resistance is generated by vortex configurations of the phase field. In the first type of process, quantum phase slip, the vortex worldline in 2+1 dimensional space-time is space-like (i.e., the superconducting phase winds in time and space). In the second type, vortex tunneling, the worldline is time-like (i.e., the phase winds in the two spatial directions) and connects opposite edges of the film. For moderately disordered samples, processes of second type favor a train of vortices, each of which tunnels only across a fraction of the sample. Optimization with respect to the number of vortices yields a tunneling distance of the order of the coherence length $\xi$, and the train of vortices becomes equivalent to a quantum phase slip. Based on this theory, we find the resistance $\ln R \sim -g W/\xi$, where $g$ is the dimensionless normal-state conductance. Incorporation of quantum fluctuations indicates a quantum phase transition to an insulating state for $g \lesssim 1$.

Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors

Superconducting nanowire single-photon detectors have emerged as a promising technology for quantum metrology from the mid-infrared to ultraviolet frequencies. Despite recent experimental successes, a predictive model to describe the detection event in these detectors is needed to optimize the detection metrics. Here, we propose a probabilistic criterion for single-photon detection based on single-vortex (flux quanta) crossing the width of the nanowire. Our model makes a connection between the dark counts and photon counts near the detection threshold. The finite-difference calculations demonstrate that a change in the bias current distribution as a result of the photon absorption significantly increases the probability of single-vortex crossing even if the vortex potential barrier has not vanished completely. We estimate the instrument response function and show that the timing uncertainty of this vortex tunneling process corresponds to a fundamental limit in timing jitter of the click event. We demonstrate a trade-space between this intrinsic (quantum) timing jitter, quantum efficiency, and dark count rate in TaN, WSi, and NbN superconducting nanowires at different experimental conditions. Our detection model can also explain the experimental observation of exponential decrease in the quantum efficiency of SNSPDs at lower energies. This leads to a pulse-width dependency in the quantum efficiency, and it can be further used as an experimental test to compare across different detection models.

Time-Correlated Vortex Tunneling in Layered Superconductors

The nucleation and dynamics of Josephson and Abrikosov vortices determine the critical currents of layered high-Tc superconducting (HTS) thin films, grain boundaries, and coated conductors, so understanding their mechanisms is of crucial importance. Here, we treat pair creation of Josephson and Abrikosov vortices in layered superconductors as a secondary Josephson effect. Each full vortex is viewed as a composite fluid of micro-vortices, such as pancake vortices, which tunnel coherently via a tunneling matrix element. We introduce a two-terminal magnetic (Weber) blockade effect that blocks tunneling when the applied current is below a threshold value. We simulate vortex tunneling as a dynamic, time-correlated process when the current is above threshold. The model shows nearly precise agreement with voltage-current (V-I) characteristics of HTS cuprate grain boundary junctions, which become more concave rounded as temperature decreases, and also explains the piecewise linear V-I behavior observed in iron-pnictide bicrystal junctions and other HTS devices. When applied to either Abrikosov or Josephson pair creation, the model explains a plateau seen in plots of critical current vs. thickness of HTS-coated conductors. The observed correlation between theory and experiment strongly supports the proposed quantum picture of vortex nucleation and dynamics in layered superconductors.

Engineering of many-body Majorana states in a topological insulator/s-wave superconductor heterostructure

We study a vortex chain in a thin film of a topological insulator with proximity-induced superconductivity—a promising platform to realize Majorana zero modes (MZMs)—by modeling it as a two-leg Majorana ladder. While each pair of MZMs hybridizes through vortex tunneling, we hereby show that MZMs can be stabilized on the ends of the ladder with the presence of tilted external magnetic field and four-Majorana interaction. Furthermore, a fruitful phase diagram is obtained by controlling the direction of magnetic field and the thickness of the sample. We reveal many-body Majorana states and interaction-induced topological phase transitions and also identify trivial-superconducting and commensurate/incommensurate charge-density-wave states in the phase diagram.

Vortex macroscopic superpositions in ultracold bosons in a double-well potential

We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional double-well system. We show that the ensuing dynamics of $N$ interacting excited ultracold bosons, which in general requires at least eight single-particle modes and ${N+7 \choose N}$ Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magnitude faster than axisymmetric ones and are therefore more experimentally accessible. The tunneling process generates macroscopic superpositions only distinguishable by their orbital properties and within experimentally realistic times.

On the possibility of explaining the high rate of flux creep at ultra-low temperatures using the Anderson model

The nonvanishing magnetic relaxation rate and noticeable resistance in the resistive measurements in high-temperature superconductors (HTSCs) at ultra-low temperatures, which have recently been discussed as evidence of the quantum tunneling of vortices, is argued to be caused by electromagnetic noise in the framework of the modified Anderson theory. This explains the main features of this phenomenon, which cannot be described by quantum tunneling theory. Thus, the modified Anderson theory, which incorporates flux flow, the distribution of activation energies, the mutual interaction of the vortices, and the spatial variation of the pinning energy into the conventional Anderson theory, provides an explanation of the main features of magnetic flux creep in HTSCs.

Artificial nets from superconducting nanogranules

We show that a large transport current can flow through superconducting nets composed of nano-clusters. Although thermal and quantum fluctuations lead to a finite value of dissipation, this value can be very small in one- and two-dimensional systems for realistic parameters of the nanoclusters and distances between them. The value of the action for vortex tunneling at zero temperature can be made sufficiently large to make the dissipation negligibly small. We estimate the temperature T0 of the transition from the thermal activation to quantum tunneling.

Anisotropic vortex lattice structures in the FeSe superconductor

In the recent work by Song et al. [Science 332, 1410 (2011)], the scanning tunneling spectroscopy experiment in the stoichiometric FeSe reveals evidence for nodal superconductivity and strong anisotropy. The nodal structure can be explained with the extended s-wave pairing structure with the mixture of the $s_{x^2+y^2}$ and $s_{x^2y^2}$ pairing symmetries. We calculate the anisotropic vortex structure by using the self-consistent Bogoliubov-de Gennes mean-field theory. In considering the absence of magnetic ordering in the FeSe at the ambient pressure, orbital ordering is introduced, which breaks the $C_4$ lattice symmetry down to $C_2$, to explain the anisotropy in the vortex tunneling spectra.

MAGNETIC RELAXATION OF SUPERCONDUCTING QUANTUM DOT AND TUNNELING OF ELECTRON IN A MAGNETIC FIELD

Quantum tunneling of vortices had been found to be an important novel phenomena for description of low temperature creep in high temperature superconductors (HTSCs). We speculate that quantum tunneling may be also exhibited in mesoscopic superconductors due to vortices trapped by the Bean-Livingston barrier. The London approximation and method of images is used to estimate the shape of the potential well in superconducting HTSC quantum dot. To calculate the escape rate we use the instanton technique. We model the vortex by a quantum particle tunneling from a two-dimensional ground state under magnetic field applied in the transverse direction. The resulting decay rates obtained by the instanton approach and conventional WKB are compared revealing complete coincidence with each other.

Quantum tunneling of vortices in two-dimensional superfluids

We examine the problem of quantum vortex tunneling in the Gross-Pitaevskii model. The effect of gapless phonons is to produce a super-Ohmic quantum dissipation that renormalizes the effective tunneling parameters but does not destroy quantum coherence. The renormalization of the instanton frequency is computed within a specific model tunneling potential.

Quantum phase slips in a confined geometry

We consider tunneling of vortices across a superconducting film that is both narrow and short (and connected to bulk superconducting leads at the ends). We find that in the superconducting state the resistance, at low values of the temperature $(T)$ and current, does not follow the power-law dependence on $T$ characteristic of longer samples but is exponential in $1∕T$. The coefficient of $1∕T$ in the exponent depends on the length or, equivalently, the total normal-state resistance of the sample. These conclusions persist in the one-dimensional limit, which is similar to the problem of quantum phase slips in an ultranarrow short wire.

Quantum vortex tunneling inYBa2Cu3O7−δthin films

Cuprate films offer a unique opportunity to observe vortex tunneling effects due to their unusually low superfluid density and short coherence length. Here, we measure the magnetoresistance (MR) due to vortex motion of a long meander line of a superconducting film made of underdoped $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$. At low temperatures $(T)$, the MR shows a significant deviation from Arrhenius activation. The data are consistent with two dimensional variable range hopping (VRH) of single vortices, i.e., $\mathrm{MR}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{({T}_{0}∕T)}^{1∕3}]$. The VRH temperature scale ${T}_{0}$ depends on the vortex tunneling rates between pinning sites. We discuss its magnitude with respect to estimated parameters of the meander thin film.

Suppression of tunneling of superconducting vortices caused by a remote gate: Example of an extended object tunneling

We discuss a recent experiment in which the resistance of a superconducting film has been measured in magnetic field. A strong decrease of the superconducting film resistance has been observed when a metallic gate is placed above the film. We study how the magnetic coupling between vortices in a thin superconducting film and electrons in a remote unbiased gate suppresses the rate of the vortices. We examine two general approaches to analyze in the presence of slow low-energy degrees of freedom: the functional-integral and scattering formalisms. In the first one, the response of the electrons inside the metallic gate to a change in the vortex position is described by the tunneling with dissipation. We consider the Eddy current induced in the gate by the magnetic flux of the vortex as a result of tunneling. In the second approach, the response is given in terms of scattering of the electrons by the magnetic flux of the vortex in a way similar to the Aharonov-Bohm scattering. A sudden change in the vortex position leads to the Orthogonality Catastrophe that opposes the vortex tunneling. We show that the magnetic coupling between the vortices and the electrons inside the gate can lead to a dramatic suppression of the vortex tunneling, restoring the superconducting property in accord with the experiment.

Tunneling of an extended object in a dissipative environment: Suppression of tunneling of superconducting vortices caused by a remote gate

We discuss a recent experiment in which the resistance of a superconducting film has been measured in magnetic field. A strong decrease of the superconducting film resistance has been observed when a metallic gate is placed above the film. We study how the magnetic coupling between vortices in a thin superconducting film and electrons in a remote unbiased gate affects the tunneling rate of the vortices. We show that the response of electrons inside the gate to a change in the vortex position can lead to a dramatic suppression of the vortex tunneling, restoring the superconducting property in accord with the experiment. We interpret the change in the resistance of the film as a transition from “metallic” to “insulating” phases in the system of tunneling vortices caused by the gate. We examine two general approaches to analyze tunneling in the presence of slow low-energy degrees of freedom: the functional–integral and scattering formalisms. In the first one, the response of the electrons inside the metallic gate to a change in the vortex position is described by the “tunneling with dissipation”. We consider the Eddy current induced in the gate by the magnetic flux of the vortex as a result of tunneling. In the second approach, the response is given in terms of scattering of the electrons by the magnetic flux of the vortex in a way similar to the Aharonov–Bohm scattering. The response of the electrons to a sudden change in the vortex position leads to the Orthogonality Catastrophe that opposes the vortex tunneling. We conclude that adding a gate to superconducting films can be an effective tool for studying the dynamics of vortices at low temperatures.

Edge states and tunneling of non-Abelian quasiparticles in theν=5∕2quantum Hall state andp+ipsuperconductors

We study quasiparticle tunneling between the edges of a non-Abelian topological state. The simplest examples are a p+ip superconductor and the Moore-Read Pfaffian non-Abelian fractional quantum Hall state; the latter state may have been observed at Landau-level filling fraction nu=5/2. Formulating the problem is conceptually and technically non-trivial: edge quasiparticle correlation functions are elements of a vector space, and transform into each other as the quasiparticle coordinates are braided. We show in general how to resolve this difficulty and uniquely define the quasiparticle tunneling Hamiltonian. The tunneling operators in the simplest examples can then be rewritten in terms of a free boson. One key consequence of this bosonization is an emergent spin-1/2 degree of freedom. We show that vortex tunneling across a p+ip superconductor is equivalent to the single-channel Kondo problem, while quasiparticle tunneling across the Moore-Read state is analogous to the two-channel Kondo effect. Temperature and voltage dependences of the tunneling conductivity are given in the low- and high-temperature limits.

Quantum and Classical Relaxation in the Proton Glass

The hydrogen-bond network formed from a crystalline solution of ferroelectric RbH2PO4 and antiferroelectric NH4H2PO4 demonstrates glassy behavior, with proton tunneling the dominant mechanism for relaxation at low temperature. We characterize the dielectric response over seven decades of frequency and quantitatively fit the long-time relaxation by directly measuring the local potential energy landscape via neutron Compton scattering. The collective motion of protons rearranges the hydrogen bonds in the network. By analogy with vortex tunneling in superconductors, we relate the logarithmic decay of the polarization to the quantum-mechanical action.

Metal-Insulator Transition in a System of Superconducting Vortices Caused by a Metallic Gate

We address a recent experiment in which a strong decrease of the resistance of a superconducting film has been observed when a remote unbiased gate was placed above the film. Here we explain the experimental finding as a suppression of the vortex tunneling due to the orthogonality catastrophe of the electrons inside the gate. We interpret the change in the resistance of the film as a "metal-insulator" transition in the system of vortices induced by the gate.