The production of entangled pairs of electrons in ferromagnet-superconductor-ferromagnet or normal metal-superconductor-normal metal three-terminal structures has aroused considerable interest in the last twenty years. In these studies, the distance between the contacts is limited by the zero-energy superconducting coherence length. Here, we demonstrate nonlocality and quantum correlations in voltage-biased three-terminal Josephson junctions over the ultralong distance that exceeds the superconducting coherence length by orders of magnitude. The effect relies on} the interplay between the time-periodic Floquet-Josephson dynamics, Cooper pair splitting and long-range coupling similar to the two-terminal Tomasch effect. We find cross-over between the ``Floquet-Andreev quartets'' (if the spatial separation is smaller than the superconducting coherence length), and the ``ultralong-distance Floquet-Tomasch clusters of Cooper pairs'' if the separation exceeds the superconducting coherence length, possibly reaching the same $\simeq 30\,μ$m as in the Tomasch experiments. The effect can be detected with DC-transport and zero-frequency quantum current-noise cross-correlation experiments, and it can be used for fundamental studies of superconducting quasiparticle quantum coherence in the circuits of quantum engineering.
Control of the Josephson current by varying a gate current has recently been demonstrated in both 4-terminal and 3-terminal junctions. We show that, when the the gates are weakly coupled to the Josephson junction, the Josephson current versus gate current (or versus gate voltage) relation is the same for both the 4- and 3- terminal geometries. At low temperature, the supercurrent switches abruptly as a function of the gate voltage, but only slowly as a function of the gate current.
The Andreev bound state spectra of multi-terminal Josephson junctions form an artificial band structure, which is predicted to host tunable topological phases under certain conditions. However, the number of conductance modes between the terminals of multi-terminal Josephson junction must be few in order for this spectrum to be experimentally accessible. In this work we employ a quantum point contact geometry in three-terminal Josephson devices. We demonstrate independent control of conductance modes between each pair of terminals and access to the single-mode regime coexistent with the presen…
We calculate the electrical currents through a superconductor - insulator - superconductor junction which is also weakly coupled to a normal metal side probe. The voltage $V$ applied to the normal metal terminal controls the occupation of Andreev energy levels $E_n$, and therefore controls the Josephson current flowing through these levels. Whenever the probe voltage crosses an Andreev level, the Josephson current changes abruptly by an amount equal to the current flowing through the Andreev level. The differential conductance along the normal metal terminal permits spectroscopy of the Andreev…
Recently it has been predicted that the Andreev bound state spectrum of 4-terminal Josephson junctions may possess zero-energy Weyl singularities. Using one superconducting phase as a control parameter, these singularities are associated with topological transitions between time-reversal symmetry broken phases with different Chern numbers. Here we show that such topological transitions may also be tuned with a magnetic flux through the junction area in a 3-terminal geometry.
The macroscopic quantum interference effects in ballistic Josephson microstructures are investigated. The studied system consists of four bulk superconductors (terminals) which are weakly coupled through the mesoscopic rectangular normal metal (two dimensional electron gas). We show that nonlocal electrodynamics of ballistic systems leads to specific current-phase relations for the mesoscopic multiterminal Josephson junction. The nonlocal coupling of supercurrents produces the "dragging" effect for phases of the superconducting order parameter in different terminals. The composite Josephson ju…
Josephson junctions with three or more superconducting leads have been predicted to exhibit topological effects in the presence of few conducting modes within the interstitial normal material. Such behavior, of relevance for topologically-protected quantum bits, would lead to specific transport features measured between terminals, with topological phase transitions occurring as a function of phase and voltage bias. Although conventional, two-terminal Josephson junctions have been studied extensively, multi-terminal devices have received relatively little attention to date. Motivated in part by…
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.
Recently Baselmans et al. [Nature, 397, 43 (1999)] showed that the direction of the supercurrent in a superconductor/normal/superconductor Josephson junction can be reversed by applying, perpendicularly to the supercurrent, a sufficiently large control current between two normal reservoirs. The novel behavior of their 4-terminal device (called a controllable PI-junction) arises from the nonequilibrium electron energy distribution established in the normal wire between the two superconductors. We have observed a similar supercurrent reversal in a 3-terminal device, where the control current pas…
By definition, the $p$-terminal dc-Josephson current is sensitive to the superconducting phase variables of $p$ terminals. In the paper, we establish protocol for direct detection of the $p$-terminal dc-Josephson effect with $p\ge 3$ in a device containing $N$ superconducting leads $S_1,\,S_2,\,...,\,S_N$ having the phase variables $φ_1,\,φ_2,\,...,\,φ_N$. The calculated signal $χ^{(N)}$ can be probed in microwave experiments, and it corresponds to the higher-order nonlocal inverse inductance obtained from differentiating the current $I_1$ through $S_1$ with respect to the remaining $N-2$ inde…
In a Josephson junction (JJ), Cooper pairs are transported via Andreev bound states (ABSs) between superconductors. The ABSs in the weak link of multi-terminal (MT) JJs can coherently hybridize two Cooper pairs among different superconducting electrodes, resulting in the Cooper quartet (CQ) involving four fermions entanglement. The energy spectrum of these CQ-ABS can be controlled by biasing MT-JJs due to the AC Josephson effect. Here, using gate tunable four-terminal graphene JJs complemented with a flux loop, we construct CQs with a tunable spectrum. The critical quartet supercurrent exhibit…
Establishment of phase-coherence and a non-dissipative (super)current between two weakly coupled superconductors, known as the Josephson effect, plays a foundational role in basic physics and applications to metrology, precision sensing, high-speed digital electronics, and quantum computing. The junction ranges from planar insulating oxides to single atoms, molecules, semiconductor nanowires, and generally to any finite-size coherent conductor. Recently, junctions of more than two superconducting terminals gained broad attention in the context of braiding of Majorana fermions in the solid stat…
We investigate nonlocal coherent transport in ballistic four-terminal Josephson structures (where bulk superconductors (terminals) are connected through a clean normal layer, e.g., a two-dimensional electron gas). Coherent anisotropic superposition of macroscopic wave functions of the superconductors in the normal region produces phase slip lines (2D analogs to phase slip centres) and time-reversal symmetry breaking 2D vortex states in it, as well as such effects as phase dragging and magnetic flux transfer. The tunneling density of local Andreev states in the normal layer was shown to contain…
Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to $\leq3$ dimensions. Here we demonstrate that $n$-terminal Josephson junctions with conventional superconductors may provide a straightforward realization of tunable topological materials in $n-1$ dimensions. For $n\geq 4$, the Andreev subgap spectrum of the junction can accommodate Weyl singularit…
Recently we predicted that the Andreev bound state spectrum of 4-terminal Josephson junctions may possess topologically protected zero-energy Weyl singularities, which manifest themselves in a quantized transconductance in units of $4e^2/h$ when two of the terminals are voltage biased [R.-P. Riwar et al., Nature Commun. 7, 11167 (2016)]. Here, using the Landauer-Büttiker scattering theory, we compute numerically the currents flowing through such a structure in order to assess the conditions for observing this effect. We show that the voltage below which the transconductance becomes quantized i…
We study the evolution of averaged transconductances in three-terminal Josephson junctions when the superconducting leads are led throughout a topological phase transition from an $s$-wave to a $p$-wave (Majorana) phase by an in-plane magnetic field $B_x$. We provide a complete description of this transition as a function of $B_x$ and a magnetic flux $Φ$ threading the junction. For that we use a spinful model within a formalism that allows to treat on equal footing the contribution to the transconductance from both the Andreev subgap levels and the continuum spectrum. We unveil a fractionaliza…
We study the emergent band topology of subgap Andreev bound states in the three-terminal Josephson junctions. We scrutinize the symmetry constraints of the scattering matrix in the normal region connecting superconducting leads that enable the topological nodal points in the spectrum of Andreev states. When the scattering matrix possesses time-reversal symmetry, the gap closing occurs at special stationary points that are topologically trivial as they carry vanishing Berry fluxes. In contrast, for the time-reversal broken case we find topological monopoles of the Berry curvature and correspond…
Magnetic field-bias current interplay in HgTe-based three-terminal Josephson junctions
University of Regensburg（雷根斯堡大学）；Julius-Maximilians-Universität Würzburg（维尔茨堡朱利叶斯-马克西米利安大学）；Instituto de Ciencia de Materiales de Madrid ICMM-CSIC（马德里材料科学研究所 ICMM-CSIC）；A. V. Rzhanov Institute of Semiconductor Physics（A.V.扎哈诺夫半导体物理研究所）
We propose a protocol to locally detect the Berry curvature of a three terminal Josephson junction with a quantum dot based on a synchronic detection when an AC modulation is applied in the device. This local gauge invariant quantity is expressed in terms of the instantaneous Green function of the Bogoliubov-de Gennes Hamiltonian. We analyze the contribution to the Berry curvature from both the quasi-particle excitations and the Andreev bound state levels by introducing an effective low-energy model. In addition, we propose to induce topological properties in the junction by breaking time-reve…
We investigate the transport properties of a bilayer exciton condensate that is contacted by four superconducting leads. We focus on the equilibrium regime and investigate how the Josephson currents induced in the bilayer by phase biases applied to the superconducting electrodes are affected by the presence of an exciton condensate in the bulk of the system. As long as the distance between the superconducting electrodes is much larger than the exciton coherence length, the Josephson current depends only on the difference between the phase biases in the two layers. This result holds true in bot…
A theory is offered for a novel device, mesoscopic four-terminal SQUID. The studied system consists of a mesoscopic four-terminal junction, one pair of terminals of which is incorporated in a superconducting ring and the other one is connected with a transport circuit. The nonlocal weak coupling between the terminals leads to effects of phase dragging and magnetic flux transfer. The behaviour of a four-terminal SQUID, controlled by the external parameters, the applied magnetic flux and the transport current is investigated. The critical current and the current voltage characteristics as functi…
The dynamical properties of multi-terminal Josephson junctions have recently attracted interest, driven by the promise of new insights into synthetic topological phases of matter and Floquet states. This effort has culminated in the discovery of Cooper multiplets, in which the splitting of a Cooper pair is enabled via a series of Andreev reflections that entangle four (or more) electrons. In this text, we show conclusively that multiplet resonances can also emerge as a consequence of the three terminal circuit model. The supercurrent appears due to the correlated phase dynamics at values that …
We analyze the Andreev spectrum in a four-terminal Josephson junction between one-dimensional topological superconductors in class D. We find that a topologically protected crossing in the space of three superconducting phase differences can occur between the two lowest Andreev bound states. This crossing can be detected through the transconductance quantization, in units of $2e^2/h$, between two voltage-biased terminals. Our prediction provides yet another example of topology in multi-terminal Josephson junctions. We discuss possible realizations of such junctions with semiconducting crossed …
In an in-situ prepared three-terminal Josephson junction based on the topological insulator Bi$_4$Te$_3$ and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the d…
On the basis of the Usadel equation we study a multi-terminal Josephson junction. This junction is composed by "magnetic" superconductors S$_{\text{m}}$ which have singlet pairing and are separated from the normal n~wire by spin filters so that the Josephson coupling is caused only by fully polarized triplet components. We show that there is no interaction between triplet Cooper pairs with antiparallel total spin orientations. The presence of an additional singlet superconductor S attached to the n wire leads to a finite Josephson current $I_{\text{Q}}$ with an unusual current--phase relation.…
A three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction $(S_a,S_b,S_c)$ biased with voltages $(V,-V,0)$ is considered, but the conclusions hold more generally for resonant semi-conducting quantum wire set-ups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for $V=0$) evolve into nonequilibrium Floquet-Wann…
In a transparent three-terminal Josephson junction, modeling nonequilibrium transport is numerically challenging, owing to the interplay between multiple Andreev reflection (MAR) thresholds and multipair resonances in the pair current. An approximate method, coined as "partially resummed perturbation theory in the number of nonlocal Green's functions", is presented that can be operational on a standard computer and demonstrates compatibility with results existing in the literature. In a linear structure made of two neighboring interfaces (with intermediate transparency) connected by a central …
Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries. A key goal is to accurately determine when the system makes a transition from a gapped to non-gapped state as a function of the phase differences in the system, the latter effectively playing the role of quasiparticle momenta in conventional topological matter. We here determine the proximity gap phase diagram of diffusive …
We study diffusive magnetic Josephson junctions with four superconducting terminals in the weak proximity limit where the leads are arranged in cross form. Employing the linearized Keldysh-Usadel technique, the anomalous Green's function and Josephson current are analytically obtained based on a quasiclassical theory using the Fourier series method. The derived results may be reduced to non-magnetic junctions by setting the exchange field equal to zero. We find that increments of the magnetic barrier thickness may cause a reversal of the supercurrent direction flowing into some of the leads, w…
We investigate the proximity effect in junctions between $N=3$ superconductors under commensurate voltage bias. The bias is chosen to highlight the role of transport processes that exchange multiple Cooper pairs coherently between more than two superconductors. Such non-local processes can be studied in the dc response, where local transport processes do not contribute. We focus on the proximity-induced normal density of states that we investigate in a wide parameter space. We reveal the presence of deep and highly tunable pseudogaps and other rich structures. These are due to a static proximi…
We investigate the Andreev-bound-state (ABS) spectra of three-terminal Josephson junctions which consist of 1D topological superconductors (TSCs) harboring multiple zero-energy edge Majorana bound states (MBSs) protected by chiral symmetry. Our theoretical analysis relies on the exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian describing the three interfaced TSCs, complemented by an effective low-energy description solely based on the coupling of the interfacial MBSs arising before the leads get contacted. Considering the 2D synthetic space spanned by the two indep…
We present an exhaustive theoretical analysis of a double-loop Josephson proximity interferometer, as the one recently realized by Strambini et al. for the control of the Andreev spectrum via an external magnetic field. This system, called $ω$-SQUIPT, consists of a T-shaped diffusive normal metal (N) attached to three superconductors (S) forming a double loop configuration. By using the quasiclassical Green function formalism, we calculate the local normalized density of states, the Josephson currents through the device and the dependence of the former on the length of the junction arms, the a…
We study the dc Josephson effect and the density of states in a multiterminal structure of cross-type geometry which consists of four superconducting electrodes connected by one-dimensional normal or ferromagnetic wires. We find that the Josephson current $I_{Jz}$ has a sinusoidal dependence on the phase difference $ϕ_z$ between the superconductors in the horizontal wire with a critical current $I_c$ that can be varied by changing the phase difference $ϕ_y$ between the superconductors in the vertical wire. The period of the function $I_{Jz}(ϕ_z)$ depends on the ratio of the interface resistanc…
We study the subgap spectrum of the interacting single-level quantum dot coupled between two superconducting reservoirs, forming the Josephson-type circuit, and additionally hybridized with a metallic normal lead. This system allows for the phase-tunable interplay between the correlation effects and the proximity-induced electron pairing resulting in the singlet-doublet (0-$π$) crossover and the phase-dependent Kondo effect. We investigate the spectral function, induced local pairing, Josephson supercurrent, and Andreev conductance in a wide range of system parameters by the numerically exact …
A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dc-current carrying three-body static phase coherence, known as the "quartet current". We calculate the zero-frequency current noise cross-correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy $ε_0$ is connected to three superconductors $S_a$, $S_b$ and $S_c$ with gap $Δ$, biased at $V_a=V$, $V_b=-V$ and $V_c=0$, and wit…
We report on the fabrication and measurements of planar mesoscopic Josephson junctions formed by InAs nanowires coupled to superconducting Nb terminals. The use of Si-doped InAs-nanowires with different bulk carrier concentrations allowed to tune the properties of the junctions. We have studied the junction characteristics as a function of temperature, gate voltage, and magnetic field. In junctions with high doping concentrations in the nanowire Josephson supercurrent values up to 100\,nA are found. Owing to the use of Nb as superconductor the Josephson coupling persists at temperatures up to …
