We investigate heat circulators where a phase coherent region is contacted by three leads that are either normal- or superconducting. A magnetic field, and potentially the superconducting phases, allow to control the preferential direction of the heat flow between the three-different temperature-biased contacts. The main goal of this study is to analyze the requirements for heat circulation in non-ideal devices, in particular focusing on sample-to-sample variations. Quite generally, we find that the circulation performance of the devices is good as long as only a few transport channels are involved. We compare the performance of circulators with normalconducting contacts to those with superconducting contacts and find that the circulation coefficient are essentially unchanged.
We theoretically propose a phase-coherent thermal circulator based on ballistic multiterminal Josephson junctions. The breaking of time-reversal symmetry by either a magnetic flux or a superconducting phase bias allows heat to flow preferentially in one direction from one terminal to the next while heat flow in the opposite direction is suppressed. We find that our device can achieve a high circulation efficiency over a wide range of parameters and that its performance is robust with respect to the presence of disorder. We provide estimates for the expected heat currents for realistic samples.
We investigate the heat transport properties of a three-level system coupled to three thermal baths, assuming a model based on superconducting circuit implementations. The system-bath coupling is mediated by resonators which serve as frequency filters for the different qutrit transitions. Taking into account the finite quality factors of the resonators, we find thermal rectification and circulation effects not expected in configurations with perfectly-filtered couplings. Heat leakage in off-resonant transitions can be exploited to make the system work as an ideal diode where heat flows in the …
In magnonics, an emerging branch of wave physics characterized by low-energy consumption, it is highly desirable to realize circuit elements within the scope of spin-wave computing. Here, based on numerical simulations, we demonstrate the functionality of the spin-wave diode and the circulator to steer and manipulate spin waves over a wide range of frequency in the GHz regime. They take advantage of the unidirectional coupling induced by the interfacial Dzyaloshinskii-Moriya interaction to transfer the spin wave between thin ferromagnetic layers in only one direction of propagation. Using the …
The electronic circulator, and its close relative the gyrator, are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies. The current implementation of these devices using the Faraday effect is satisfactory, but requires a bulky structure whose physical dimension is close to the microwave wavelength employed. The Hall effect is an alternative non-reciprocal effect that can also be used to produce desired device functionality. We review earlier efforts to use an ohmically-contact…
Magnetic fields break time-reversal symmetry, which is leveraged in many settings to enable the nonreciprocal behavior of light. This is the core physics of circulators and other elements used in a variety of microwave and optical settings. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order -- such as the XY model -- can be realize…
We find that multiple Andreev reflections mediating the transport in superconducting point contacts are strongly affected by a small amount of impurities in the area of the contact. We also argue that the model based on Zener transitions within independent conducting channels is not suitable for kinetic processes in multichannel contacts.
The dc Josephson effect in a superconducting quantum point contact, where supercurrent flows through a small number of channels, is reviewd. The central role of Andreev levels is emphasized which carry the whole supercurrent in short symmetric Josephson junctions including tunnel junctions. A simple intuitive view of the dc Josephson effect in a quantum point contact is given in terms of multiple Andreev reflections. The quantization of the critical current in superconducting quantum point contacts is briefly discussed.
We generalize the Landauer formula to describe the dissipative electron transport through a superconducting point contact. The finite-temperature, linear-in-bias, dissipative DC conductance is expressed in terms of the phase- and energy-dependent scattering matrix of the Bogoliubov quasiparticles in the quantum point contact. The derived formula is also applicable to hybrid superconducting-normal structures and normal contacts, where it agrees with the known limits of Andreev reflection and normal-state conductance, respectively.
We have studied the Josephson dynamics of resistively-shunted ballistic superconducting quantum point contacts at finite temperatures and arbitrary number of conducting modes. Compared to the classical Josephson dynamics of tunnel junctions, dynamics of quantum point contacts exhibits several new features associated with temporal fluctuations of the Josephson potential caused by fluctuations in the occupation of the current-carrying Andreev levels.
We describe and characterize a microwave setup to probe the Andreev levels of a superconducting atomic contact. The contact is part of a superconducting loop inductively coupled to a superconducting coplanar resonator. By monitoring the resonator reflection coefficient close to its resonance frequency as a function of both flux through the loop and frequency of a second tone we perform spectroscopy of the transition between two Andreev levels of highly transmitting channels of the contact. The results indicate how to perform coherent manipulation of these states.
We review our experiments on the electronic transport properties of atomic contacts between metallic electrodes, in particular superconducting ones. Despite ignorance of the exact atomic configuration, these ultimate quantum point contacts can be manipulated and well characterized in-situ. They allow performing fundamental tests of the scattering theory of quantum transport. In particular, we discuss the case of the Josephson effect.
We demonstrate superconducting vertical interconnect access (VIA) contacts to a monolayer of molybdenum disulfide (MoS$_2$), a layered semiconductor with highly relevant electronic and optical properties. As a contact material we use MoRe, a superconductor with a high critical magnetic field and high critical temperature. The electron transport is mostly dominated by a single superconductor/normal conductor junction with a clear superconductor gap. In addition, we find MoS$_2$ regions that are strongly coupled to the superconductor, resulting in resonant Andreev tunneling and junction dependen…
We find the charge and heat currents caused by a temperature difference applied to a superconducting point contact or to a quantum point contact between a superconducting and normal conductors. The results are formulated in terms of the properties of the electron scattering matrix of the quantum point contact in its normal state, and are valid at any transmission coefficient. In the low-transmission limit, the new theory provides reliable results, setting the limits for the use of the popular method of tunnel Hamiltonian.
We have studied the relaxation and dephasing processes in a superconducting quantum point contact induced by the interaction with an electromagnetic environment. Based on a density matrix approach we obtain the rates for the dissipative dynamics as function of the transmission, the phase difference on the contact and the external impedance. Our calculation allows to determine the appropriate range of parameters for the observation of coherent oscillations in the current through the contact.
We study effects of magnetic field on the energy spectrum in a superconducting quantum point contact. The supercurrent induced by the magnetic field leads to intermode transitions between the electron waves that pass and do not pass through the constriction. The latter experience normal reflections which couple the states with opposite momenta inside the quantum channel and create a minigap in the energy spectrum that depends on the magnetic field.
We study the Giant Magnetoresistance (GMR) ratio in magnetic multiayers with a single superconducting contact in the presence of spin-mixing processes. It has been recently shown that the GMR ratio of magnetic multilayers is strongly suppressed by the presence of a superconducting contact when spin-flipping is not allowed. In this Letter we demonstrate that the GMR ratio can be dramatically enhanced by spin-orbit interaction and/or non-collinear magnetic moments. The system is described using a tight-binding model with either s-p-d or s-d atomic orbitals per site.
Amplitude of the Coulomb blockade oscillations is calculated for a single-mode Josephson junction with arbitrary electron transparency $D$. It is shown that the Coulomb blockade is suppressed in ballistic junctions with $D\to 1$. The suppression is described quantitatively as the Landau-Zener transition in imaginary time.
We present in this letter a theoretical analysis of the current-voltage (I-V) characteristics of a hybrid normal-superconducting device consisting of a quantum dot and two electrodes that can be either normal or superconducting. We show that voltage drops at two different contacts that have been regarded unimportant in literature play essential roles in the Andreev tunneling process when at least one of electrodes is superconducting. A differential-conductance-anomaly caused by the aforementioned voltage drops is predicted. We also propose a new spectroscopy method to measure the energy levels…
The dynamics of a superconducting quantum point contact biased at subgap voltages is shown to be strongly affected by a microwave electromagnetic field. Interference among a sequence of temporally localized, microwave-induced Landau-Zener transitions between current carrying Andreev levels results in energy absorption and in an increase of the subgap current by several orders of magnitude. The contact is an interferometer in the sense that the current is an oscillatory function of the inverse bias voltage. Possible applications to Andreev-level spectroscopy and microwave detection are discusse…
We discuss the general transport properties of superconducting quantum point contacts. We show how these properties can be obtained from a microscopic model using nonequilibrium Green function techniques. For the case of a one-channel contact we analyze the response under different biasing conditions: constant applied voltage, current bias and microwave-induced transport. Current fluctuations are also analyzed with particular emphasis on thermal and shot-noise. Finally, the case of superconducting transport through a resonant level is discussed. The calculated properties show a remarkable agre…
Atomic quantum point contacts accommodate a small number of conduction channels. Their number N and transmission coefficients {T_n} can be determined by analyzing the subgap structure due to multiple Andreev reflections in the current-voltage (IV) characteristics in the superconducting state. With the help of mechanically controllable break-junctions we have produced Al contacts consisting of a small number of atoms. In the smallest stable contacts, usually three channels contribute to the transport. We show here that the channel ensemble {T_n} of few atom contacts remains unchanged up to temp…
Point-contact Andreev reflection measurements of Co/ and Cu/tungsten-carbide (WC$_x$) contacts are presented. Metallic thin films were patterned by e-beam-lithography and lift-off; tungsten carbide superconducting tips were grown directly on the pre-patterned samples by decomposition of a metallo-organic vapour (tungsten hexacarbonyl) under a focused Ga$^+$-ion beam (FIB). Current-voltage measurements as a function of temperature and magnetic field clearly showed the signatures of Andreev reflection. The experimental conductance-voltage curves were analyzed within the Blonder-Tinkham-Klapwijk …
Two-dimensional (2D) transition-metal dichalcogenide superconductors have unique and desirable properties for integration with conventional superconducting circuits. However, fully superconducting contact must be made between the 2D material and three-dimensional (3D) superconductors in order to employ the standard microwave drive and readout of qubits in such circuits. Here, we present a method for creating zero-resistance contacts between 2D NbSe$_2$ and 3D aluminum that behave as Josephson junctions (JJs) with large effective areas compared to 3D-3D JJs. We present a model for the supercurr…
We present a comprehensive theoretical analysis of the dc transport properties of superconducting point contacts. We determine the full counting statistics for these junctions, which allows us to calculate not only the current or the noise, but all the cumulants of the current distribution. We show how the knowledge of the statistics of charge transfer provides an unprecedented level of understanding of the different transport properties for a great variety of situations. We illustrate our results with the analysis of junctions between BCS superconductors, contacts between superconductors with…
We have observed that the supercurrent across phase-biased, highly transmitting atomic size contacts is strongly reduced within a broad phase interval around π. We attribute this effect to quasiparticle trapping in one of the discrete sub-gap Andreev bound states formed at the contact. Trapping occurs essentially when the Andreev energy is smaller than half the superconducting gap Δ, a situation in which the lifetime of trapped quasiparticles is found to exceed 100 \mus. The origin of this sharp energy threshold is presently not understood.
We have investigated how the Andreev-reflection hole current at ballistic point contacts responds to a large bias voltage. Its strong suppression could be explained by the drag excerted by the non-equilibrium phonon wind generated by high-energy electrons flowing through the contact. The hole - phonon interaction leads to scattering lengths of the low-energetic holes down to 100\,nm, thereby destroying the coherent retracing of the electron path by the Andreev-reflected holes.
We have measured the effect of microwave irradiation on the dc current-voltage characteristics of superconducting atomic contacts. The interaction of the external field with the ac supercurrents leads to replicas of the supercurrent peak, the well known Shapiro resonances. The observation of supplementary fractional resonances for contacts containing highly transmitting conduction channels reveals their non-sinusoidal current-phase relation. The resonances sit on a background current which is itself deeply modified, as a result of photon assisted multiple Andreev reflections. The results provi…
We study the influence of classical phase diffusion on the fractional Shapiro steps in resistively shunted superconducting quantum point contacts. The problem is mapped onto a Smoluchowski equation with a time dependent potential. A numerical solution for the probability density of the phase difference between the leads gives access to the mean current and the mean voltage across the contact. Analytical solutions are derived in some limiting cases. We find that the effect of temperature is stronger on fractional than on integer steps, in accordance with preliminary experimental findings. We fu…
For certain complex superconducting systems, the superconducting properties get enhanced under mesoscopic point contacts made of elemental non-superconducting metals. However, understanding of the mechanism through which such contact induced local enhancement of superconductivity happens has been limited due to the complex nature of such compounds. In this paper we present giant enhancement of superconducting transition temperature (T$_c$) and superconducting energy gap ($Δ$) in a simple elemental superconductor Zr. While bulk Zr shows a critical temperature around 0.6\,K, superconductivity su…
We study the quantization of the supercurrent and conductance of a superconducting quantum point contact (SQPC) in a superconductor-two dimensional electrongas-superconductor (S-2DEG-S) Josephson junction with a split gate. The supercurrent and the conductance values change stepwise as a function of the gate voltage. We observe the onset of the first transport mode contributing both to the supercurrent and the conductance of the SQPC. Furthermore the steps in the supercurrent and the conductance appear at the same gate voltage values. This shows, that each transport mode in the SQPC contribute…
We analyze the shot noise in a voltage biased superconducting quantum point-contact. Results are presented for the single channel case with arbitrary transmission. In the limit of very low transmission it is found that the effective charge, defined from the noise-current ratio, exhibits a step-like behavior as a function of voltage with well defined plateaus at integer values of the electronic charge. This multiple charge corresponds to the transmitted charge in a Multiple Andreev Reflection (MAR) process. This effect gradually disappears for increasing transmission due to interference between…
Pre-Patterned Superconducting Contacts for Clean Superconductor-Topological Material Interfaces Enabling Long-Range Josephson Coupling
Pohang University of Science and Technology（浦项科技大学）；Max Planck POSTECH Center for Complex Phase of Materials（马普POSTECH复杂物相中心）；Columbia University（哥伦比亚大学）；National Institute for Materials Science（国家材料研究所）；Institute for Basic Science (IBS)（基础科学研究院）
Contacts between high critical field superconductors and semiconductor nanowires are important in the context of topological quantum circuits in which superconductivity must be sustained to high magnetic fields. Here we demonstrate gate-tunable supercurrent in NbTiN-Ge/Si core/shell nanowire-NbTiN junctions. We observe supercurrents up to magnetic fields of 800 mT. The induced soft superconducting gap measured by co-tunneling through a quantum dot is 220 μeV. To improve contact transparency, we deposit an aluminum interlayer prior to NbTiN and observe a systematic change in the device pinch-of…
We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with adiabatic coupling to Andreev bound states. Near $π$ phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. We identify features consistent with the presence of single Andreev bound…
Nonreciprocal devices such as circulators and isolators belong to an important class of microwave components employed in applications like the measurement of mesoscopic circuits at cryogenic temperatures. The measurement protocols usually involve an amplification chain which relies on circulators to separate input and output channels and to suppress backaction from different stages on the sample under test. In these devices the usual reciprocal symmetry of circuits is broken by the phenomenon of Faraday rotation based on magnetic materials and fields. However, magnets are averse to on-chip int…
We predict that current perpendicular to the plane (CPP) giant magnetoresistance (GMR) in a phase-coherent magnetic multilayer is suppressed when one of the contacts is superconducting. This is a consequence of a superconductivity-induced magneto-resistive (SMR) effect, whereby the conductance of the ferromagnetically aligned state is drastically reduced by superconductivity. To demonstrate this effect, we compute the GMR ratio of clean (Cu/Co)_nCu and (Cu/Co)_nPb multilayers, described by an ab-initio spd tight binding Hamiltonian. By analyzing a simpler model with two orbitals per site, we a…
We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n) \hbar ω_r/2e, where n,m are integer numbers and ω_r is the radiation frequency. The subharmonic steps (n different from 1) are a consequence of the ocurrence of multiple Andreev reflections (MAR) and provide an unambiguous signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due…
We show how to calculate the charge noise spectrum in a normal mesoscopic conductor, which is capacitively coupled to a macroscopic gate, when this conductor is attached to L normal leads and M superconducting leads, the only restriction being that the superconducting leads must be at the same chemical potential. We then proceed to examine results for a quantum point contact (QPC) in a normal lead connecting to a superconductor. Of interest is the fluctuating current in a gate capacitively coupled to a QPC. The results are compared with the case when all leads are normal. We find a doubling of…
We investigate the properties of complex mesoscopic superconducting-normal hybrid devices, Andreev-Interferometers in the case, where the current is proped through a superconducting tunneling contact whereas the proximity effect is generated by a transparent SN-interface. We show within the quasiclassical Green's functions technique, how the fundamental SNIS-element of the such structures can be mapped onto an effective S$^\prime$IS-junction, where S$^\prime$ is the proximised material with an effective energy gap $E_g<Δ$. We propose the Andreev-Interferometer, where $E_g$ can be tuned by an e…
We generalize the representation of the real time Green's functions introduced by Langreth and Nordlander [Phys. Rev. B 43 2541 (1991)] and Meir and Wingreen [Phys. Rev. Lett. 68 2512 (1992)] in stationary quantum transport in order to study problems with hybrid structures containing normal (N) and superconducting (S) pieces. We illustrate the treatment in a S-N junction under a stationary bias and investigate in detail the behavior of the equilibrium currents in a normal ring threaded by a magnetic flux with attached superconducting wires at equilibrium. We analyze the flux sensitivity of the…
The Josephson effect describes the flow of supercurrent in a weak link, such as a tunnel junction, nanowire, or molecule, between two superconductors. It is the basis for a variety of circuits and devices, with applications ranging from medicine to quantum information. Currently, experiments using Josephson circuits that behave like artificial atoms are revolutionizing the way we probe and exploit the laws of quantum physics. Microscopically, the supercurrent is carried by Andreev pair states, which are localized at the weak link. These states come in doublets and have energies inside the supe…
We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field.
We study the patterns at which the current flow stabilizes in a 1D superconducting wire, for various experimentally reasonable boundary conditions, for small fixed current densities and temperatures close to $T_c$. We pay special attention to the possible existence of a stationary regime. If the contacts are superconducting, truly stationary or normal regimes do not exist, but can be approached as a limit. In the case of weak superconducting contacts, a rich phase diagram is found, with several periodic regimes that involve two phase slip centers. For some of these regimes, the density of Coop…
Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here, we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasiparticle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup we perform single-shot readout of this "Andreev qubit". We determine its excited state lifetime and coherence time to be in the…
Manipulating individual vortices in a deterministic way is challenging, ideally, manipulation should be effective, local, and tunable in strength and location. Here, we show that vortices interact with strain fields generated by mechanical stress. We utilized this interaction to move individual vortices in thin superconducting films via local mechanical contact, without magnetic field or current. We used a scanning superconducting quantum interference device (SQUID) to image vortices and to apply local vertical stress with the tip of our sensor. Vortices were attracted to the contact point, re…
We present a theoretical analysis for photon-assisted electron tunneling through a hybrid superconducting-normal quantum point contact (QPC) consisting of a superconducting lead (S), a normal two-level quantum dot (N), and a normal lead (N). Using single particle non-equilibrium Green's function formalism, we incorporate Floquet basis in the Nambu space and solve the Green's function with finite matrix truncation to obtain the transport properties numerically. Based on the proposed method, we studied the effects of photon-induced single-level oscillations and quantum transition between two lev…
We investigate the Josephson effect in the graphene nanoribbons of length $L$ smaller than the superconducting coherence length and an arbitrary width $W$. We find that in contrast to an ordinary superconducting quantum point contact (SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons with smooth and armchair edges. For a low concentration of the carriers $I_c$ decreases monotonically with lowering $W/L$ and tends to a constant minimum for a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the smooth edges but $eΔ_{0}/\hbar$ for the armchair edges. At…
Transparent contact interfaces in superconductor-graphene hybrid systems are critical for realizing superconducting quantum applications. Here, we examine the effect of the edge-contact fabrication process on the transparency of the superconducting aluminum-graphene junction. We show significant improvement in the transparency of our superconductor-graphene junctions by promoting the chemical component of the edge contact etch process. Our results compare favorably with state-of-the-art graphene Josephson junctions. The findings of our study contribute to advancing the fabrication knowledge of…
The supercurrent of a quantum point contact coupled to a nanomagnet strongly depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic model to calculate the transport properties of a junction coupled to a spin whose dynamics is modeled as Larmor precession brought about by an external magnetic field and find that the dynamics affects the charge and spin currents by inducing transitions between the continuum states below the superconducting gap edge and the Andreev levels. This redistribution of the quasiparticles leads to a non-equilibrium population of the Andreev level…
The Andreev reflection of narrow ferromagnet/superconductor point contacts is theoretically studied. We show that the conductance quantization depends on whether the contact region is superconducting or ferromagnetic as well as on the strength of the exchange field in the ferromagnet. The Andreev reflection of the ferromagnetic contact is more suppressed than that of the superconducting contact. We also show that the conductance-voltage curve has a bump at zero bias-voltage if there is no interfacial-scattering. On the contrary, the conductance-voltage curve shows a dip if the system has an in…
We present here an extensive theoretical analysis of the supercurrent of a superconducting point contact of arbitrary transparency in the presence of a microwave field. Our study is mainly based on two different approaches: a two-level model that describes the dynamics of the Andreev bound states in these systems and a fully microscopic method based on the Keldysh-Green function technique. This combination provides both a deep insight into the physics of irradiated Josephson junctions and quantitative predictions for arbitrary range of parameters. The main predictions of our analysis are: (i) …
We study Andreev reflection in a ballistic one-dimensional channel coupled in parallel to a superconductor via a tunnel barrier of finite length $L$. The dependence of the low-energy Andreev reflection probability $R_A$ on $L$ reveals the existence of a characteristic length scale $ξ_N$ beyond which $R_A(L)$ is enhanced up to unity despite the low interfacial transparency. The Andreev reflection enhancement is due to the strong mixing of particle and hole states that builds up in contacts exceeding the coherence length $ξ_N$, leading to a small energy gap (minigap) in the density of states of …
We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound-states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission $D$ of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic (D=1) limit. It is shown tha…
