The critical current of a thin superconducting strip of width $W$ much larger than the Ginzburg-Landau coherence length $ξ$ but much smaller than the Pearl length $Λ= 2 λ^2/d$ is maximized when the strip is straight with defect-free edges. When a perpendicular magnetic field is applied to a long straight strip, the critical current initially decreases linearly with $H$ but then decreases more slowly with $H$ when vortices or antivortices are forced into the strip. However, in a superconducting strip containing sharp 90-degree or 180-degree turns, the zero-field critical current at H=0 is reduced because vortices or antivortices are preferentially nucleated at the inner corners of the turns, where current crowding occurs. Using both analytic London-model calculations and time-dependent Ginzburg-Landau simulations, we predict that in such asymmetric strips the resulting critical current can be {\it increased} by applying a perpendicular magnetic field that induces a current-density contribution opposing the applied current density at the inner corners. This effect should apply to all turns that bend in the same direction.
In this paper we calculate the critical currents in thin superconducting strips with sharp right-angle turns, 180-degree turnarounds, and more complicated geometries, where all the line widths are much smaller than the Pearl length $Λ= 2 λ^2/d$. We define the critical current as the current that reduces the Gibbs free-energy barrier to zero. We show that current crowding, which occurs whenever the current rounds a sharp turn, tends to reduce the critical current, but we also show that when the radius of curvature is less than the coherence length this effect is partially compensated by a radiu…
The quantum kicked rotator can be realized in a periodically driven superconducting nanocircuit. A study of the fidelity allows the experimental investigation of exponential instability of quantum motion inside the Ehrenfest time scale, chaotic diffusion and quantum dynamical localization. The role of noise and the experimental setup to measure the fidelity is discussed as well.
We perform measurements of phase-slip-induced switching current events on different types of superconducting weak links and systematically study statistical properties of the switching current distributions. We employ two types of devices in which a weak link is formed either by a superconducting nanowire or by a graphene flake subject to proximity effect. We demonstrate that, independently on the nature of the weak link, higher moments of the distribution take universal values. In particular, the third moment (skewness) of the distribution is close to -1 both in thermal and quantum regimes. T…
We propose a scheme to generate and detect entanglement between charge states in superconducting nanocircuits. We discuss different procedures to discriminate such entanglement from classical correlations. The case of maximally entangled states of two and three coupled Josephson junctions is discussed as example.
For successful realization of a quantum computer, its building blocks (qubits) should be simultaneously scalable and sufficiently protected from environmental noise. Recently, a novel approach to the protection of superconducting qubits has been proposed. The idea is to prevent errors at the "hardware" level, by building a fault-free (topologically protected) logical qubit from "faulty" physical qubits with properly engineered interactions between them. It has been predicted that the decoupling of a protected logical qubit from local noises would grow exponentially with the number of physical …
We describe here the first experimental realization of a heat interferometer, thermal counterpart of the well-known superconducting quantum interference device (SQUID). These findings demonstrate, on the first place, the existence of phase-dependent heat transport in Josephson-based superconducting circuits and, on the second place, open the way to novel ways of mastering heat at the nanoscale. Combining the use of external magnetic fields for phase biasing and different Josephson junction architectures we show here that a number of heat interference patterns can be obtained. The experimental …
The implementation of a Lambda scheme in superconducting artificial atoms could allow detec- tion of stimulated Raman adiabatic passage (STIRAP) and other quantum manipulations in the microwave regime. However symmetries which on one hand protect the system against decoherence, yield selection rules which may cancel coupling to the pump external drive. The tradeoff between efficient coupling and decoherence due to broad-band colored Noise (BBCN), which is often the main source of decoherence is addressed, in the class of nanodevices based on the Cooper pair box (CPB) design. We study transfer …
The rapid experimental progress in the field of superconducting nanocircuits gives rise to an increasing quest for advanced quantum-control techniques for these macroscopically coherent systems. Here we demonstrate theoretically that stimulated Raman adiabatic passage (STIRAP) should be possible with the quantronium setup of a Cooper-pair box. The scheme appears to be robust against decoherence and should be realizable even with the existing technology. As an application we present a method to generate single-phonon states of a nanomechnical resonator by vacuum-stimulated adiabatic passage wit…
In this work, we review and expand recent theoretical proposals for the realization of electronic thermal diodes based on tunnel-junctions of normal metal and superconducting thin films. Starting from the basic rectifying properties of a single hybrid tunnel junction, we will show how the rectification efficiency can be largely increased by combining multiple junctions in an asymmetric chain of tunnel-coupled islands. We propose three different designs, analyzing their performance and their potential advantages. Besides being relevant from a fundamental physics point of view, this kind of devi…
The paper by G. R. Berdiyorov, M. V. Milosevic, and F. M. Peeters [Phys. Rev. B 81, 144511 (2010)] studies theoretically the dynamic properties of a superconducting loop. The authors claim that their consideration of asymmetric loop relates to our experimental results in this field. We point out that this claim is incorrect and explain shortly the true paradoxical essence of the results of our measurements of asymmetric superconducting loop.
We investigated the pinning of flux lines in a superconducting film by a regular array of magnetic antidots. The sample consists of a Co/Pt multilayer with perpendicular magnetic anisotropy in which a regular pattern of submicron holes is introduced and which is covered by a type-II superconducting Pb film. The resulting ferromagnetic/superconducting heterostructure shows a pronounced asymmetric magnetization curve with respect to the field polarity. This asymmetry clearly demonstrates that the magnetic contribution dominates the pinning potential imposed by the magnetic antidots on the superc…
Theory of self induced resonances in asymmetric two-junction interferometer device is presented. In real devices it is impossible to have an ideal interferometer free of imperfections. Thus, we extended previous theoretical approaches introducing a model which contains several asymmetries: Josephson current $ε$, capacitances $χ$ and dissipation $ρ$ presented in an equivalent circuit. Moreover, non conventional symmetry of the order parameter in high temperature superconducting quantum interference devices forced us to include phase asymmetries. Therefore, the model has been extended to the cas…
We have investigated asymmetrically shunted Nb/Al-AlO$_x$/Nb direct current (dc) superconducting quantum interference devices (SQUIDs). While keeping the total resistance $R$ identical to a comparable symmetric SQUID with $R^{-1} = R_1^{-1} + R_2^{-1}$, we shunted only one of the two Josephson junctions with $R = R_{1,2}/2$. Simulations predict that the optimum energy resolution $ε$ and thus also the noise performance of such an asymmetric SQUID can be 3--4 times better than that of its symmetric counterpart. Experiments at a temperature of 4.2\,K yielded $ε\approx 32\,\hbar$ for an asymmetric…
The controlled motion of objects through narrow channels is important in many fields. We have fabricated asymmetric weak-pinning channels in a superconducting thin-film strip for controlling the dynamics of vortices. The lack of pinning allows the vortices to move through the channels with the dominant interaction determined by the shape of the channel walls. We present measurements of vortex dynamics in the channels and compare these with similar measurements on a set of uniform-width channels. While the uniform-width channels exhibit a symmetric response for both directions through the chann…
We examine the transmission through nonideal microwave resonant circuits. The general analytical resonance line shape is derived for both inductive and capacitive coupling with mismatched input and output transmission impedances, and it is found that for certain non-ideal conditions the line shape is asymmetric. We describe an analysis method for extracting an accurate internal quality factor ($Q_i$), the Diameter Correction Method (DCM), and compare it to the conventional method used for millikelvin resonator measurements, the $ϕ$ Rotation Method ($ϕ$RM). We analytically find that the $ϕ$RM d…
Magnetic field dependences of critical current, resistance, and rectified voltage of asymmetric (half circles of different widths) and symmetrical (half circles of equal widths) aluminum rings were measured in the temperature region close to the superconducting transition. All these dependences are periodic magnetic field functions with periods corresponding to the flux quantum in the ring. The periodic dependences of critical current measured in opposite directions were found to be close to each other for symmetrical rings and shifted with respect to each other by half the flux quantum in asy…
We present a dual cut-off, dc-tunable low-pass microwave filter on a superconducting Nb microstrip with uniaxial asymmetric nanogrooves. The frequency response of the device was measured in the range $300$\,KHz to $14$\,GHz at different temperatures, magnetic fields, and dc current values. The microwave loss is most effectively reduced when the Abrikosov vortex lattice spatially matches the underlying washboard pinning landscape. The forward transmission coefficient $S_{21}(f)$ of the microstrip has a dc-tunable cut-off frequency $f_d$ which notably changes under dc bias reversal, due to the t…
Vortex-driven superconducting diode effect in asymmetric multilayer heterostructures
Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理高等研究院）；Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control, School of Physics, Zhejiang University（浙江大学物理学院微纳量子芯片与量子控制浙江省重点实验室）；International Quantum Academy, Shenzhen（深圳国际量子研究院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer Bi-2223 and bilayer Bi-2212 cuprates. At low energies the spectroscopic maps are well described by dispersive quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a virtually non-dispersive pattern with sqrt(2)*sqrt(2) periodicity emerges. Remarkab…
Shift of the maxima of the critical currents of different polarity relative to the zero magnetic flux along the flux axis in a superconducting asymmetric aluminum ring
Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences（俄罗斯科学院微电子技术与高纯材料研究所）
The demand for low-dissipation nanoscale memory devices is as strong as ever. As Moore's Law is staggering, and the demand for a low-power-consuming supercomputer is high, the goal of making information processing circuits out of superconductors is one of the central goals of modern technology and physics. So far, digital superconducting circuits could not demonstrate their immense potential. One important reason for this is that a dense superconducting memory technology is not yet available. Miniaturization of traditional superconducting quantum interference devices is difficult below a few m…
A new type of a superconducting quantum interference device (SQUID) based on a single superconducting loop without Josephson junctions and with asymmetric link-up of current leads is proposed. This SQUID offers advantages in simplicity of fabrication and higher sensitivity of magnetic flux. Magnetic field dependence of the critical current in aluminium rings with asymmetric link-up of current leads has been measured in order to confirm the possibility of making this type of SQUID.
The asymmetric tunneling in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. By taking into account the interplay between the superconducting gap and normal-state pseudogap, the essential feature of the evolution of the asymmetric tunneling with doping and temperature is qualitatively reproduced. In particular, the asymmetry of the tunneling spectrum in the underdoped regime weakens with increasing doping, and then the symmetric tunneling spectrum recovers in the heavily overdoped regime. The theory also shows that the asymmetric tunneling is a n…
Two-dimensional (2D) transition metal dichalcogenides (TMDCs) MX2 (M=W, Mo, Nb, and X=Te, Se, S) with strong spin-orbit coupling (SOC) possess plenty of novel physics including superconductivity. Due to the Ising SOC, monolayer NbSe$_2$ and gated MoS$_2$ of 2H structure can realize the Ising superconductivity phase, which manifests itself with in-plane upper critical field far exceeding Pauli paramagnetic limit. Surprisingly, we find that a few-layer 1Td structure MoTe$_2$ also exhibits an in-plane upper critical field ($H_{c2,//}$) which goes beyond the Pauli paramagnetic limit. Importantly, …
Two-dimensional vortex dynamics in a ratchet washboard planar pinning potential (PPP) in the presence of thermal fluctuations is considered on the basis of a Fokker-Planck equation. Explicit expressions for two new nonlinear anisotropic voltages (longitudinal and transverse with respect to the current direction) are derived and analyzed. The physical origin of these odd (with respect to magnetic field or transport current direction reversal) voltages is caused by the interplay between the even effect of vortex guiding and the ratchet asymmetry. Both new voltages are going to zero in the linear…
The quantum rectification effect observed on asymmetric superconducting loops is proposed to use as a basic of a noise detector with maximum sensitivity. The measurements show that a critical amplitude of noise or ac current decreases down to zero near superconducting transition, Tc, just as superconducting critical current. Therefore any how weak noise, right down to the equilibrium one, can induce the quantum oscillations of the dc voltage near Tc. The transformation of the power of random noise into the dc power observed on asymmetric superconducting loops gives very important advantage: ev…
The current-voltage curves and magnetic dependence of the critical current of asymmetric superconducting loops are measured. It was found that sign and value of the asymmetry of the current-voltage curves changes with value of magnetic field, periodically for single loop and system of identical loops. The obtained results allow to explain the quantum oscillation of the dc voltage, observed below superconducting transition in the previous works, as rectification of ac current or noise.
The quantum oscillations in magnetic field of the critical current of asymmetric superconducting rings with different widths of the half-rings are shifted to opposite sides for measurement in the opposite direction. The value of this shift found before equal half of the flux quantum for single ring with radius 2 μm has smaller value at lower critical current and for system of the rings with smaller radius.
A possibility to observe the persistent voltage in a superconducting ring of different widths of the arms is experimentally investigated. It was earlier found that switching of the arms between superconducting and normal states by ac current induces the dc voltage oscillation in magnetic field with a period corresponding to the flux quantum inside the ring. We use systems with a large number of asymmetric rings connected in series in order to investigate the possibility to observe this quantum phenomenon near the superconducting transition where thermal fluctuations switch ring segments withou…
We discuss the phase coherence which emanates from the ladder-like proximity effect between a ``weak superconductor'' with preformed bosonic pairs (here, a single-chain Luther-Emery liquid with superconducting correlations that decay approximately as $x^{-1}$) and a Fermi gas with unpaired fermions. Carefully studying tunneling mechanism(s), we show that the boson-mediated Cooper pairing between remaining unpaired electrons results in a quasi long-range superconductivity: Superconducting correlations decay very slowly as $x^{-η}$ with $η\approx 1/2$. This process is reminiscent of the coupling…
We report the non-equilibrium behavior of disordered superconducting Al films in high Zeeman fields. We have measured the tunneling density of states of the films through the first-order Zeeman critical field transition. We find that films with sheet resistances of a few hundred ohms exhibit large avalanche-like collapses of the condensate on the superheating branch of the critical field hysteresis loop. In contrast, the transition back into the superconducting phase (i.e., along the supercooling branch) is always continuous. The fact that the condensate follows an unstable trajectory to the n…
The influence of the spatial asymmetry of the pinning potential on the spectral composition of the voltage, induced in perforated superconducting Al bridges by the injection of a sinusoidal bias current, was investigated. The loss of the mirror symmetry of the pinning potential leads to the appearance of even Fourier components in the induced voltage in the vicinity of the superconducting phase transition line on the H-T diagram (H is the external magnetic field, T is temperature). Artificially-introduced asymmetry for vortex motion makes it possible to create low-resistive materials, in which…
A vortex lattice ratchet effect has been investigated in Nb films grown on arrays of nanometric Ni triangles, which induce periodic asymmetric pinning potentials. The vortex lattice motion yields a net dc-voltage when an ac driving current is applied to the sample and the vortex lattice moves through the field of asymmetric potentials. This ratchet effect is studied taking into account the array geometry, the temperature, the number of vortices per unit cell of the array and the applied ac currents.
We study the ratchet effect in a narrow pinning-free superconductive ring based on time-dependent Ginzburg-Landau (TDGL) equations. Voltage responses to external dc an ac currents at various magnetic fields are studied. Due to asymmetric barriers for flux penetration and flux exit in the ring-shaped superconductor, the critical current above which the flux-flow state is reached, as well as the critical current for the transition to the normal state, are different for the two directions of applied current. These effects cooperatively cause ratchet signal reversal at high magnetic fields, which …
The response of a mesoscopic homogeneous superconducting wire, connected with bulk normal metal reservoirs, is theoretically investigated as function of the applied voltage. The finite relaxation length of the nonequilibrium quasiparticle distribution function $\bar{L_E}$ is included where we assumed that our wire is in the dirty limit. We found that {\it both} symmetric and asymmetric states can exist which are characterized by a stationary symmetric and asymmetric distribution of the order parameter with respect to the center of the wire. Current voltage characteristics of the wire with leng…
The quantum oscillations of the dc voltage are induced on segments of asymmetric superconducting loops by an external ac current or noise. The dependencies of the amplitude of the quantum oscillations on amplitude of inducing ac current are measured at different temperatures below superconducting transition Tc on aluminum asymmetric loops and systems of the loops connected in series. The measured values of the maximum amplitude of the quantum oscillations, the amplitude of the ac current inducing this maximum dc voltage and the critical amplitude of the ac current decrease with temperature inc…
The observations the dc voltage on asymmetric superconducting ring testify that one of the ring segments is a dc power source. The persistent current flows against the total electric field in this segment. This paradoxical phenomenon is observed when the ring or its segments are switched between superconducting and normal state by non-equilibrium noises. We demonstrate that the dc voltage and the power increase with the number of the identical rings connected in series. Large voltage and power sufficient for practical application can be obtained in a system with a sufficiently large number of …
We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/de-exciting vibrational quanta in the bus. This is a superconducting analog of …
We have measured periodic oscillations of rectified dc voltage versus magnetic field V_{dc}(B) in a superconducting aluminum thin-film circular-asymmetric figure-of-eight microstructure threaded by a magnetic flux and biased with a sinusoidal alternating current (without a dc component) near the critical temperature. The Fourier spectra of these V_{dc}(B) functions contain fundamental frequencies representing periodic responses of the larger and smaller asymmetric circular loops, composing the microstructure, to the magnetic field. The higher harmonics of the obtained fundamental frequencies r…
Magnetic quantum periodicity in the dc voltage is observed when asymmetric rings are switched between superconducting and normal state by a noise or ac current. This quantum effect is used for detection of a non-equilibrium noise with the help of a system of 667 asymmetric aluminum rings of $1 \ μm$ in diameter connected in series. Any noise down to the equilibrium one can be detected with the help of such system with enough great number of asymmetric rings.
We show that in the presence of a pseudogap, the spectral function in the superconducting state of the underdoped cuprates exhibits additional Bogoliubov quasiparticle peaks at both positive and negative energy which are revealed by the particle-hole asymmetry of the pseudogapped energy bands. This provides direct information on the unoccupied band via measurement of the occupied states. When sufficiently close, these Bogoliubov peaks will appear to merge with existing peaks leading to the anomalous observation, seen in experiment, that the carrier spectral density broadens with reduced temper…
Enhanced Superconducting Diode Effect in the Asymmetric Hatsugai-Kohmoto Model
School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院）；Department of Physics and Texas Center for Superconductivity, University of Houston（休斯顿大学物理系及德克萨斯超导中心）
The obtained periodic magnetic-field dependencies of the critical current, measured in opposite directions on asymmetric superconducting aluminum rings, allow to explain observed earlier quantum oscillations of a dc voltage as a result of alternating current rectification. It is found, that the high efficiency of the rectification of both individual rings and ring systems is connected to a hysteresis of the current-voltage characteristics. The asymmetry of the current-voltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependencies of the cr…
Superconducting films in perpendicular magnetic field are found to rectify alternating currents. The effect has been observed both in plain and nanostructured superconducting films (niobium and lead). The rectified voltage appears both along and transverse to alternating current and strongly depends on the magnetic field. Rectification phenomena is based on the property of superconductors to have permanent circulating currents in magnetic field (vortices) and to develop electric fields at high enough currents. In contrast to previous findings, at higher current frequencies no asymmetric pinnin…
Trapping magnetic flux quanta in superconducting 3D caps
Technische Universität Braunschweig（布伦瑞克工业大学）；Leibniz IFW Dresden（德累斯顿莱布尼茨固体与材料研究所）；Moldova State University（摩尔多瓦国立大学）；FLUXONICS—The European Foundry for Superconducting Electronics e.V.（FLUXONICS——欧洲超导电子制造协会）
Little-Parks oscillations are observed in a system of 110 series-connected aluminum rings 2000 nm in diameter with the use of measuring currents from 10 nA to 1000 nA. The measurements show that the amplitude and character of the oscillations are independent of the relation between the measuring current and the amplitude of the persistent current. By using asymmetric rings, it is demonstrated that the persistent current has clockwise or contra-clockwise direction. This means that the total current in one of the semi-rings may be directed against the electric field at measurement of the Little-…
In submicron superconducting squares in a homogeneous magnetic field, Ginzburg-Landau theory may admit solutions of the vortex-antivortex type, conforming with the symmetry of the sample [Chibotaru et al., Nature 408, 833 (2000)]. Here we show that these fascinating, but never experimentally observed states, can be enforced by artificial fourfold pinning, with their diagnostic features enhanced by orders of magnitude. The second-order nucleation of vortex-antivortex molecules can be driven either by temperature or applied magnetic field, with stable asymmetric vortex-antivortex equilibria foun…
The magnetic dependencies of the critical current of aluminum ring with asymmetric link-up of current leads have been measured in order to clear up the essence of the paradoxical absence of the jump of the critical current at the quantum number change revealed before at the measurements of asymmetric superconducting ring. The measurements have shown that the experimental and theoretical dependencies agree in the region of magnetic field corresponding to integer numbers of the flux quantum and disagree at the half of the flux quantum. The jump is not observed as well as in the asymmetric rings.
We measured both quantum oscillations of a rectified time-averaged direct voltage V_{rec}(B) and a dc voltage V_{dc}(B) as a function of normal magnetic field B, in a thin-film aluminum structure of two asymmetric circular loops in series at temperatures below the superconducting critical temperature T_{c}. The V_{rec}(B) and V_{dc}(B) voltages were observed in the structure biased only with an alternating current (without a dc component) and only with a direct current (without an ac component), respectively. The aim of the measurements was to find whether interaction (nonlinear coupling) exis…
The electrical transport properties of corner-shaped Al superconducting microstrips have been investigated. We demonstrate that the sharp turns lead to asymmetric vortex dynamics, allowing for easier penetration from the inner concave angle than from the outer convex angle. This effect is evidenced by a strong rectification of the voltage signal otherwise absent in straight superconducting strips. At low magnetic fields, an enhancement of the critical current with increasing magnetic field is observed for a particular combination of field and current polarity, confirming a recently theoretical…
We present data on the modulation of the critical current with applied magnetic field in UPt_3-Cu-Pb Josephson junctions and SQUIDs. The junctions were fabricated on polished surfaces of UPt_3 single crystals. The shape of the resulting diffraction patterns provides phase sensitive information on the superconducting order parameter. Our corner junction data show asymmetric patterns with respect to magnetic field, indicating a complex order parameter, and both our junction and SQUID measurements point to a phase shift of Pi, supporting the E_2u representation of the order parameter.
Designing the spatial profile of the superconducting gap -- gap engineering -- has long been recognized as an effective way of controlling quasiparticles in superconducting devices. In aluminum films, their thickness modulates the gap; therefore, standard fabrication of Al/AlOx/Al Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices. Here we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction. We find that di…
A scaling relation of vortex-induced rectification effects in a superconducting thin-film heterostructure
Osaka University（大阪大学）；Institute for Open and Transdisciplinary Research Initiatives, Osaka University（大阪大学开放跨学科研究倡议研究所）；Institute for Materials Research, Tohoku University（东北大学材料科学研究所）
