E. Strambini, A. Iorio, O. Durante, R. Citro, C. Sanz-Fernández, C. Guarcello, I. V. Tokatly, A. Braggio, M. Rocci, N. Ligato, V. Zannier, L. Sorba, F. S. Bergeret, F. Giazotto
A battery is a classical apparatus which converts a chemical reaction into a persistent voltage bias able to power electronic circuits. Similarly, a phase battery is a quantum equipment which provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on quantum coherence. Unlike the voltage batteries, a phase battery has not been implemented so far, mainly because of the natural rigidity of the quantum phase that, in typical quantum circuits, is imposed by the parity and time-reversal symmetry constrains. Here we report on the first experimental realization of a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states and proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias $φ_0$ across the wire, leading to the anomalous Josephson effect. By applying an external in-plane magnetic field a continuous tuning of $φ_0$ is achieved. This allows the charging and discharging of the quantum phase battery and reveals the symmetries of the anomalous Josephson effect predicted by our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction breaks the phase rigidity of the system inducing a strong coupling between charge, spin and superconducting phase. This interplay opens avenues for topological quantum technologies, superconducting circuitry and advanced schemes of circuit quantum electrodynamics.}
We theoretically study the macroscopic quantum tunneling (MQT) in a hetero Josephson junction formed by a conventional single-gap superconductor and a multi-gap one such as ${MgB}_{2}$ and iron-based superconductors. In such a Josephson junction more than one phase differences are defined. We clarify the quantum dynamics of the phase differences and construct a theory for the MQT in the multi-gap Josephson junctions. The dynamics of the phase differences are strongly affected by the Josephson-Leggett mode, which is the out-of-phase oscillation mode of the phase differences. The escape rate is …
We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov-de Gennes equations we find the ground-state phase difference $φ_0$ between the superconducting leads tuned by the spin splitting field $h$ driving the system from the topologically trivial to the nontrivial superconducting state. The phase $φ_0$ vanishes for rather small $h$, grows in a certain field range around the topological transition, and then saturates at large $h$ in the Kitaev regime. Both the sub…
We investigate the Josephson transport through a ferromagnetic oxide film, e.g., La$_2$BaCuO$_5$, theoretically. Using the recursive Green's function technique, we found the formation of a pi-junction in such systems. Moreover the 0-pi phase transition is induced by increasing the temperature. Such ferromagnetic-oxide based Josephson junctions may become an element in the architecture of future quantum computers.
We study the thermodynamic properties of a superconductor/normal metal/superconductor Josephson junction {in the short limit}. Owing to the proximity effect, such a junction constitutes a thermodynamic system where {phase difference}, supercurrent, temperature and entropy are thermodynamical variables connected by equations of state. These allow conceiving quasi-static processes that we characterize in terms of heat and work exchanged. Finally, we combine such processes to construct a Josephson-based Otto and Stirling cycles. We study the related performance in both engine and refrigerator ope…
I present a theoretical study of current-voltage characteristics ($I$-$V$ curves ) of small Josephson junctions. In the limit of a small Josephson coupling energy $E_J \ll k_B T$ the thermal fluctuations result in a stochastic dependence of the Josephson phase $φ$ on time, i.e the Josephson phase diffusion. These thermal fluctuations destroy the superconducting state, and the low-voltage resistive state is characterized by a nonlinear $I$-$V$ curve. Such $I$-$V$ curve is determined by the resonant interaction of ac Josephson current with the Josephson phase oscillations excited in the junction…
We theoretically investigate the magnetization inside a normal metal containing the Rashba spin-orbit interaction (RSOI) induced by the proximity effect in an s-wave superconductor/normal metal/ferromagnetic metal/s-wave superconductor (S/N/F/S) Josephson junction. By solving the linearized Usadel equation taking account of the RSOI,we find that the direction of the magnetization induced by the proximity effect in N can be reversed by tuning the RSOI.Moreover, we also find that the direction of the magnetization inside N can be reversed by changing the superconducting phase difference, i.e., J…
A quantum mechanical analysis of the Josephson phase escape in the presence of both dc and ac bias currents is presented. We find that the potential barrier for the escape of the phase is effectively suppressed as the resonant condition occurs, i.e. when the frequency $ω$ of the ac bias matches the Josephson junction energy level separation. This effect manifests itself by a pronounced drop in the dependence of the switching current $I_s$ on the power $W$ of the applied microwave radiation and by a peculiar double-peak structure in the switching current distribution $P(I_s)$. The developed the…
Josephson-Phase Reversal of Non-Bloch Andreev Propagation
College of Physics and Materials Science, Tianjin Normal University（天津师范大学物理与材料科学学院）；Interdisciplinary Center, Tianjin Normal University（天津师范大学交叉研究中心）；Center for Joint Quantum Studies & Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系量子联合研究中心及天津市低维材料物理与制备技术重点实验室）
The Josephson equations predict remarkable effects concerning the phase state of a superconducting junction with an oscillating current induced by a static voltage. Whether the paradigm can be twisted by yielding an oscillating voltage without making use of harmonic drives is a fundamentally relevant problem yet not fully settled. Here, we demonstrate that a dynamical regime with an oscillating phase evolution is a general hallmark of driven Josephson systems exhibiting sign competition in the Josephson couplings. We show that in frustrated Josephson systems an oscillating phase dynamics gets …
This is a detailed derivation of the equation for the voltage noise of a resistively shunted Josephson junction with non-sinusoidal current-phase relation, which was presented in Sov. Phys. JETP {\bf 67}, 579 (1988).
An extended Josephson junction intrinsically couples the superconducting current to the microwave cavity in the insulating barrier. We demonstrate that this coupling produces sidebands in the microwave cavity resonances of the junction. By measuring the switching current distribution, we show that microwave radiation at sidebands brings the Josephson phase out of equilibrium. In particular, the effective phase temperature is reduced or enhanced through anti-Stokes and Stokes scattering, respectively. Phase cooling and heating both increase with microwave power.
We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between th…
We perform extensive analysis of graphene Josephson junctions embedded in microwave circuits. By comparing a diffusive junction at 15 mK with a ballistic one at 15 mK and 1 K, we are able to reconstruct the current-phase relation.
We investigate experimentally the physics of quantum phase slips in one-dimensional Josephson Junction chains. These quantum phase-slips are induced by quantum phase fluctuations occurring on single junctions of the chain. In our experiment we can tune the strength of these fluctuations as each chain junction is realized in form of a SQUID leading to tunable Josephson coupling. We determine the ground state of the chain via switching current measurements of the chain shunted by a large Josephson junction. Our results can be well fitted with a tight binding Hamiltonian taking into account quant…
Josephson tunnel junctions are proposed as efficient phase-tunable thermal rectifiers. The latter exploit the strong temperature dependence of the superconducting density of states and phase-dependence of heat currents flowing through Josephson junctions to operate. Remarkably, large heat rectification coefficients up to 800% can potentially be achieved using conventional materials and standard fabrication methods. In addition, these devices allow for the in-situ fine tuning of the thermal rectification magnitude and direction.
We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase relationships (I$Φ$). We present results for a three-junction system in the vicinity of charge degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I$Φ$ at phase $π$ persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.
We have investigated the Josephson inductance $L_J$ of a Superconducting Cooper Pair Transistor (SCPT). We traced the inductance using microwave reflection measurements on a tuned resonance circuit in which a SCPT was mounted in parallel to a $ \sim 200$ pH strip line inductance. When the inverse of the Josephson inductance, determined on the charge-phase bias plane for a SCPT with a Josephson to Coulomb energy ratio of $E_J/E_C =1.75$, is integrated over the phase, we obtain a current-phase relation, which is strongly non-sinusoidal near the charge degeneracy point.
The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the stron…
Coupling of Josephson-phase and spin-waves is theoretically studied in a superconductor/ferromagnetic insulator/superconductor (S/FI/S) junction. Electromagnetic (EM) field inside the junction and the Josephson current coupled with spin-waves in FI are calculated by combining Maxwell and Landau-Lifshitz-Gilbert equations. In the S/FI/S junction, it is found that the current-voltage (I-V) characteristic shows two resonant peaks. Voltages at the resonant peaks are obtained as a function of the normal modes of EM field, which indicates a composite excitation of the EM field and spin-waves in the …
The current-phase relation (CPR) of a Josephson junction reveals valuable information about the microscopic processes and symmetries that influence the supercurrent. In this Letter, we present direct measurements of the CPR for Josephson junctions with a graphene barrier, obtained by a phase-sensitive SQUID interferometry technique. We find that the CPR is skewed with respect to the commonly observed sinusoidal behavior. The amount of skewness varies linearly with critical current (Ic) regardless of whether Ic is tuned by the carrier density or temperature.
Josephson junctions fabricated on the surface of three-dimensional topological insulators (TI) show a few unusual properties distinct from conventional Josephson junctions. In these devices, the Josephson coupling and the supercurrent are mediated by helical metal, the two-dimensional surface of the TI. A line junction of this kind is known to support Andreev bound states at zero energy for phase bias π, and consequently the so-called fractional ac Josephson effect. Motivated by recent experiments on TI-based Josephson junctions, here we describe a convenient algorithm to compute the bound sta…
The $4π$-periodic Josephson effect is an indicator of Majorana zero modes and a ground-state degeneracy which are central to topological quantum computation. However, the observability of a $4π$-periodic Josephson current-phase relation (CPR) is hindered by the necessity to fix the fermionic parity. As an alternative to a $4π$-periodic CPR, this paper proposes a chiral CPR for the $4π$-periodic Josephson effect. This is a CPR of the form $J(ϕ) \propto C \, |\sin(ϕ/2)|$, describing a unidirectional supercurrent with the chirality $C= \pm 1$. Its non-analytic dependence on the Josephson phase di…
Non-Abelian geometric phases can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the holonomies are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.
Quantum-phase transitions in two layers of ultrasmall Josephson junctions, coupled capacitively with each other, are investigated. As the interlayer capacitance is increased, the system at zero temperature is found to exhibit an insulator-to-superconductor transition. It is shown that, unlike one-dimensional arrays with a similar coupling configuration, the transition cannot be accounted for exclusively by particle-hole pairs.
We consider a long topological Josephson junction formed on a conducting 2D surface of a 3D topological insulator (TI). The superconducting correlations are proximity-induced by s-wave superconductors covering the surface. The 1D spacing between the coverings is either unfilled or filled by a magnetic insulator. Generally, the Josephson current mediated by the TI surface is determined by scattering modes as well as by the states localized around the junction (Andreev bound states or Andreev bands). We find out that it is crucial to take into account both contributions to determine the current-…
We consider two chains of ultrasmall Josephson junctions, coupled capacitively with each other, and investigate the transport of particle-hole pairs and the quantum phase transitions at zero temperature. For appropriate parameter ranges, the particle-hole pairs are found to play major roles in transport phenomena; condensation of such pairs leads to the superconducting state, displaying perfect drag of supercurrents along the two chains.
We present measurements of the current-phase relation (CPR) of Superconductor-Ferromagnet-Superconductor (SFS) Josephson junctions as a function of temperature. The CPR is determined by incorporating the junction into a superconducting loop coupled to a dc SQUID, allowing measurement of the junction phase difference. Junctions fabricated with a thin (~ 22 nm) barrier of Cu0.47Ni0.53 sandwiched between Nb electrodes exhibit a re-entrant critical current with temperature, vanishing at T =T_pi ~ 2-4 K. We find that the critical current is negative for T < T_pi, indicating that the junction is a p…
Since its recent foundation, phase-coherent caloritronics has sparkled continuous interest giving rise to numerous concrete applications. This research field deals with the coherent manipulation of heat currents in mesoscopic superconducting devices by mastering the Josephson phase difference. Here, we introduce a new generation of devices for fast caloritronics able to control local heat power and temperature through manipulation of Josephson vortices, i.e., solitons. Although most salient features concerning Josephson vortices in long Josephson junctions were comprehensively hitherto explore…
We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-$π$ junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, non-vanishing supercurrent and half-integer Shapiro steps at the 0-$π$ transition self-consistently point to an intrinsic second harmonic term, making it possible to rule out common alternative orig…
The charge-phase Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the qubit in magic points producing minimum decoherence are given.
We provide a brief and comprehensive overview over recent developments in the field of phase-coherent caloritronics in ordinary and topological Josephson junctions. We start from the simple case of a short, one-dimensional superconductor-normal metal-superconductor (S-N-S) Josephson junction and derive the phase-dependent thermal conductance within the Bogoliubov-de Gennes formalism. Then, we review the key experimental breakthroughs that have triggered the recent growing interest into phase-coherent heat transport. They include the realization of thermal interferometers, diffractors, modulato…
We have investigated the dynamics of underdamped Josephson junctions. In addition to the usual crossover between macroscopic quantum tunnelling and thermally activated (TA) behaviour we observe in our samples with relatively small Josephson coupling E_J, for the first time, the transition from TA behaviour to underdamped phase diffusion. Above the crossover temperature the threshold for switching into the finite voltage state becomes extremely sharp. We propose a (T,E_J) phase-diagram with various regimes and show that for a proper description of it dissipation and level quantization in a meta…
We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in t…
In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current-voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.
We study coherent quantum phase-slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Schön modes). These, in turn, are affected by spatial inhomogeneities in the ring. We analyze the case of weak periodic modulations of the system parameters and calculate the corresponding modification of the quantum phase-slip amplitude.
The transmission of Cooper pairs between two weakly coupled superconductors produces a superfluid current and a phase difference; the celebrated Josephson effect. Because of time-reversal and parity symmetries, there is no Josephson current without a phase difference between two superconductors. Reciprocally, when those two symmetries are broken, an anomalous supercurrent can exist in the absence of phase bias or, equivalently, an anomalous phase shift $φ_0$ can exist in the absence of a superfluid current. We report on the observation of an anomalous phase shift $φ_0$ in hybrid Josephson junc…
We propose a heat valve based on the interplay between thermal transport and proximity-induced exchange splitting in Josephson tunnel junctions. We demonstrate that the junction heat conductance strongly depends on the relative alignment of the exchange fields induced in the superconductors. Colossal magneto-heat resistance ratios as large as 10^7% are predicted to occur under proper temperature and phase conditions, as well as suitable ferromagnet-superconductor combinations. Moreover, the quantum phase tailoring, intrinsic to the Josephson coupling, offers an additional degree of freedom for…
We investigate phase-coherent thermal transport in Josephson junctions made from unconventional superconductors or superfluids. The thermal conductance is evaluated for one- and two-dimensional junctions within the Bogoliubov-de Gennes formalism. We analyze three different scenarios of junctions between two triplet superconductors with (i) helical pairing, (ii) unitary chiral and (iii) nonunitary chiral pairing. We find that the phase-dependent thermal conductance allows us to distinguish the different pairings and provides insight into the formation of topologically nontrivial Andreev bound s…
The anomalous ground state phase shift in S/AF/S Josephson junctions in the presence of the Rashba SO-coupling is predicted and numerically investigated. It is found to be a consequence of the uncompensated magnetic moment at the S/AF interfaces. The anomalous phase shift exhibits a strong dependence on the value of the SO-coupling and the sublattice magnetization with the simultaneous existence of stable and metastable branches. It depends strongly on the orientation of the Neel vector with respect to the S/AF interfaces via the dependence on the orientation of the interface uncompensated mag…
In the presence of phase fluctuations the dc Josephson effect is modified and the supercurrent at zero voltage is replaced by a peak at small but finite voltages. It is shown that at zero temperature this peak is determined by two complementary expansions of finite radius of convergence. The leading order expressions are related to results known from the regimes of Coulomb blockade and of macroscopic quantum tunneling. The peak positions and the suppression of the critical current by quantum fluctuations are discussed.
In this work, we systematically study two phases, called Andreev $π$-phase and orbital-phase, and their influence on the Josephson effect. When the system is time-reversal invariant and centrosymmetric, these two phases only appear in the odd-parity pairings. The Andreev $π$-phase has nothing to do with the specific form of the odd-parity pairings and means an intrinsic $π$-phase between the spin-triplet Cooper pairs entering and leaving CTSCs in the Andreev reflections. The orbital-phase corresponds to the phase difference between the spin-triplet Cooper pairs with opposite spin polarization …
We experimentally study electron transport between two superconducting indium leads, coupled to a single WTe$_2$ crystal, which is a three-dimensional Weyl semimetal. We demonstrate Josephson current in long 5~$μ$m In-WTe$_2$-In junctions, as confirmed by the observation of integer (1,2,3) and fractional (1/3, 1/2, 2/3) Shapiro steps under microwave irradiation. Demonstration of fractional a.c. Josephson effect indicates multivalued character of the current-phase relationship, which we connect with Weyl topological surface states contribution to Josephson current. In contrast to topological in…
We present low temperature transport measurements in one dimensional Josephson junctions rhombi chains. We have measured the current phase relation of a chain of 8 rhombi. The junctions are either in the classical phase regime with the Josephson energy much larger than the charging energy, $E_{J}\gg E_{C}$, or in the quantum phase regime where $E_{J}/E_{C}\approx 2$. In the strong Josephson coupling regime ($E_{J}\gg E_{C} \gg k_{B}T$) we observe a sawtooth-like supercurrent as a function of the phase difference over the chain. The period of the supercurrent oscillations changes abruptly from …
Dynamics of stacked intrinsic Josephson junctions (IJJ) in the high-Tc superconductors is theoretically investigated. We calculate the current-voltage characteristics (CVC) of IJJ and study the breakpoint region on the outermost branch of the CVC for the stacks with 9 IJJ. A method for investigation of the fine structure in CVC of IJJ based on the recording the "phase-charge" diagrams is suggested. It is demonstrated that this method reflects the main features of the breakpoint region.
We propose and analyze a mesoscopic Josephson junction consisting of two ferromagnetic insulator-superconductors (FI-Ss) coupled through a normal metal (N) layer. The Josephson current of the junction is non-trivially affected by the spin-splitting field induced by the FIs in the two superconductors. In particular, it shows sizeable enhancement by increasing the amplitude of the exchange field ($h_{ex}$) and displays a switchable current-phase relation which depends on the relative orientation of $h_{ex}$ in the FIs. In a realistic EuS/Al-based setup this junction can be exploited as a high-re…
The quantum Josephson Hamiltonian of two weakly linked Bose-Einstein condensates is written in an overcomplete phase representation, thus avoiding the problem of defining a Hermitian phase operator. We discuss the limit of validity of the standard, non-rigorous Mathieu equation, due to the onset of a higher order $\cos 2 ϕ$ term in the Josephson potential, and also to the overcompleteness of the representation (the phase $ϕ$ being the relative phase between the two condensates). We thereby unify the Boson Hubbard and Quantum Phase models.
The investigation of the switching current probability distribution of a Josephson junction is a conventional tool to gain information on the phase slips dynamics as a function of the temperature. Here we adopt this well-established technique to probe the impact of an external static electric field on the occurrence of phase slips in gated all-metallic titanium (Ti) Josephson weak links. We show, in a temperature range between 20 mK and 420 mK, that the evolution of the phase slips dynamics as a function of the electrostatic field starkly differs from that observed as a function of the tempera…
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.
