In this work we present a detailed theoretical analysis for the spectral properties of Andreev bound states in the multiterminal Josephson junctions by employing a symmetry-constrained scattering matrix approach. We find that in the synthetic multidimensional space of superconducting phases, crossings of Andreev bands may support non-Abelian SU(2) monopoles with a topological charge characterized by the second class Chern number. We propose that these topological defects can be detected via a nonlinear response measurement of the current autocorrelations. In addition, multiterminal Josephson junction devices can be tested as a hardware platform for realizing holonomic quantum computation.
In the presence of an AC drive, multiterminal Josephson junctions exhibit the inverse AC Josephson effect, where the oscillations of the superconducting phase of each junction can lock onto one another or onto the external drive. The competition between these different phase locked states results in a complex array of quantized voltage plateaus whose stability strongly depend on the circuit parameters of the shunted junctions. This phase diagram cannot be explored with low temperature transport experiments alone, given the breadth of the parameter space, so we present an easily tunable analog …
We present a detailed study of nonequilibrium Josephson currents and conductance in ballistic multiterminal SNS-devices. Nonequilibrium is created by means of quasiparticle injection from a normal reservoir connected to the normal part of the junction. By applying a voltage at the normal reservoir the Josephson current can be suppressed or the direction of the current can be reversed. For a junction longer than the thermal length, $L\ggξ_T$, the nonequilibrium current increases linearly with applied voltage, saturating at a value equal to the equilibrium current of a short junction. The conduc…
We study the nonequilibrium Josephson current in a long two-dimensional ballistic SNS-junction with a normal reservoir coupled to the normal part of the junction. The current for a given superconducting phase difference $ϕ$ oscillates as a function of voltage applied between the normal reservoir and the SNS-junction. The period of the oscillations is $π\hbar v_F/L$, with $L$ the length of the junction, and the amplitude of the oscillations decays as $V^{-3/2}$ for $eV \gg \hbar v_{F}/L$ and zero temperature. The critical current $I_c$ shows a similar oscillating, decaying behavior as a functio…
Nonlocal supercurrent was observed in mesoscopic planar SNS Josephson junction with additional normal metal electrodes when nonequilibrium quasiparticles were injected from the normal metal electrode in one of the superconducting banks of the Josephson junction in the absence of net transport current through the junction. We claim that the effect observed is due to a supercurrent counterflow appearing to compensate the quasiparticle flow in the SNS weak link. We have measured SNS junction response for different distances from the quasiparticle injector to the SNS junction at temperatures far b…
In this report we analyse three effects which may arise in a mesoscopic multiterminal S/N structure (two normal and two superconducting reservoirs). We show that the Josephson critical current is a non-monotonic function of a voltage between the normal reservoirs. The influence of the spin-polarized electrons on the Josephson critical current was also studied. We show that if there is a temperature difference between the normal reservoirs, a voltage between the superconductors and normal conductors arises which oscillates as the phase difference varies. Its magnitude is much greater than the t…
We study the Josephson effect in the multiterminal junction of topological superconductors. We use the symmetry-constrained scattering matrix approach to derive band dispersions of emergent sub-gap Andreev bound states in a multidimensional parameter space of superconducting phase differences. We find distinct topologically protected band crossings that serve as monopoles of finite Berry curvature. Particularly, in a four-terminal junction the admixture of $2π$ and $4π$ periodic levels leads to the appearance of finite energy Majorana-Weyl nodes. This topological regime in the junction can be …
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…
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The correspondin…
Revisiting the adiabatic limit in ballistic multiterminal Josephson junctions
Université Grenoble-Alpes, CNRS, Grenoble INP, Institut NEEL（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、NEEL研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
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 energy of an Andreev bound state in a clean normal metal in contact with two superconductors disperses with the difference $Δϕ$ in the superconducting phase between the superconductors in much the same way as the energies of electrons in a one-dimensional crystal disperse with the crystal momentum $k$ of the electrons. A normal metal with $n$ superconductors maps on to a $n-1$ dimensional crystal, each dimension corresponding to the phase difference $ϕ_i$ between a specific pair of superconductors. The resulting band structure as a function of the phase differences $\{Δϕ_i\}$ has been prop…
We consider a Josephson junction consisting of superconductor/ferromagnetic insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron gas. By starting from a generic Josephson hybrid planar setup we present an exhaustive analysis of the the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a non-trivial topological phase. We address the 2D bound state problem using a general transfer matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for straightforward…
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…
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…
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.
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 …
In $N$-band superconductors, the $U(1)^N$ phase invariance is spontaneously broken. We propose a model for $N$-band superconductors where the phase differences between gaps are represented by abelian gauge fields. This model corresponds to an $SU(N)$ gauge theory with the abelian projection. We show that there are massless modes as well as massive modes when the number of gaps $N$ is greater than 3. There are $N-3$ massless modes and two massive modes near a minimum of the Josephson potential when $N$ bands are equivalent and Josephson couplings are frustrated. The global symmetry $U(1)^{N-1}$…
The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates providing a highly scalable and in-situ variation of the device properties. In addition, semiconductors with large $g$-factor and spin-orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as $φ_0$ Josephson jun…
Employing quasiclassical theory of superconductivity combined with Keldysh technique we investigate large thermoelectric effect in multiterminal ballistic normal-superconducting (NS) hybrid structures. We argue that this effect is caused by electron-hole asymmetry generated by coherent Andreev reflection of quasiparticles at interfaces of two different superconductors with non-zero phase difference. Within our model we derive a general expression for thermoelectric voltages $V_{T1,2}$ induced in two different normal terminals exposed to a thermal gradient. Our results apply at any temperature …
In this article we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single level Anderson type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of π-j…
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…
