Magic-angle twisted bilayer graphene (MATBG) has recently emerged as a highly tunable two-dimensional (2D) material platform exhibiting a wide range of phases, such as metal, insulator, and superconductor states. Local electrostatic control over these phases may enable the creation of versatile quantum devices that were previously not achievable in other single material platforms. Here, we exploit the electrical tunability of MATBG to engineer Josephson junctions and tunneling transistors all within one material, defined solely by electrostatic gates. Our multi-gated device geometry offers complete control over the Josephson junction, with the ability to independently tune the weak link, barriers, and tunneling electrodes. We show that these purely 2D MATBG Josephson junctions exhibit nonlocal electrodynamics in a magnetic field, in agreement with the Pearl theory for ultrathin superconductors. Utilizing the intrinsic bandgaps of MATBG, we also demonstrate monolithic edge tunneling spectroscopy within the same MATBG devices and measure the energy spectrum of MATBG in the superconducting phase. Furthermore, by inducing a double barrier geometry, the devices can be operated as a single-electron transistor, exhibiting Coulomb blockade. These MATBG tunneling devices, with versatile functionality encompassed within a single material, may find applications in graphene-based tunable superconducting qubits, on-chip superconducting circuits, and electromagnetic sensing in next-generation quantum nanoelectronics.
We study coherent current states in the mesoscopic superconducting weak link simultaneously subjected to the order parameter phase difference on the contact and to the tangential to the junction interface superfluid velocity in the banks. The Josephson current-phase relation controlled by the external transport current is obtained. At phase difference close to pi the nonlocal nature of the Josephson phase-dependent current results in the appearance of two vortexlike states in the vicinity of the contact.
We experimentally and theoretically investigate electromagnetic cavity modes in ultra-narrow Al-AlO$_x$-Al and Nb-AlO$_x$-Nb long Josephson junctions. Experiments show that the voltage spacing between the Fiske steps on the current-voltage characteristics of sub-$μ$m wide and several hundred $μ$m long Al-AlO$_x$-Al and Nb-AlO$_x$-Nb Josephson junctions increases when decreasing the width of a junction. This effect is explained by stray magnetic fields, which become important for narrow junctions. Theoretical estimates of the Fiske step voltage based on a nonlocal wave propagation equation are …
We discuss the local and nonlocal dissipation effects on the existence of the global phase coherence transitions in two dimensional Josephson-coupled junctions. The quantum phase transitions are also examined for various lattice geometries: square, triangular and honeycomb. The T=0 superconductor-insulator phase transition is analyzed as a function of several control parameters which include self-capacitance and junction capacitance and both local and nonlocal dissipation effects. We found the critical value of the nonlocal dissipation parameter α_{1} depends on a geometry of the lattice. The …
We study temperature dependence of the critical current modulation Ic(H) for two types of planar Josephson junctions: a low-Tc Nb/CuNi/Nb and a high-Tc YBa2Cu3O7 bicrystal grain-boundary junction. At low T both junctions exhibit a conventional behavior, described by the local sine-Gordon equation. However, at elevated T the behavior becomes qualitatively different: the Ic(H) modulation field deltaH becomes almost T-independent and neither deltaH nor the critical field for penetration of Josephson vortices vanish at Tc. Such an unusual behavior is in good agreement with theoretical predictions …
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…
We study the current in a clean superconductor-normal-metal-superconductor junction of length d and width w in the presence of an applied magnetic field H. We show that both the geometrical pattern of the current density and the critical current as a function of the total flux in the junction, depend on the ratio of the Josephson vortex distance a_0 and the range r of the nonlocal electrodynamics. In particular, the critical current has the periodicity of the superconducting flux quantum only for r<a_0 and acquires, due to boundary effects, the double (pseudo-) periodicity for strong nonlocali…
In the past two years, magic-angle twisted bilayer graphene has emerged as a uniquely versatile experimental platform that combines metallic, superconducting, magnetic and insulating phases in a single crystal. In particular the ability to tune the superconducting state with a gate voltage opened up intriguing prospects for novel device functionality. Here we present the first demonstration of a device based on the interplay between two distinct phases in adjustable regions of a single magic-angle twisted bilayer graphene crystal. We electrostatically define the superconducting and insulating …
The simultaneous co-existence and gate-tuneability of the superconducting (SC), magnetic and topological orders in magic angle twisted bilayer graphene (MATBG) open up entirely new possibilities for the creation of complex hybrid Josephson junctions (JJ). Here we report on the creation of gate-defined, magnetic Josephson junctions in MATBG, where the weak link is gate-tuned close to the correlated state at a moiré filling factor of ν=-2. A highly unconventional Fraunhofer pattern emerges, which is phase-shifted and asymmetric with respect to the current and magnetic field directions, and shows…
Josephson current of spin-entangled electrons through the two branches of a SQUID-like structure with two quantum dots exhibits a magnetic-flux response different from the conventional Josephson current. Due to their interference, the period of maximum Josephson current changes from $h/2e$ to $h/e$, which can be used for detecting the Cooper-pair splitting efficiency. The nonlocal spin entanglement provides a quantum mechanical functionale for switching on and off this novel Josephson current, and explicitly a switch is formulated by including a pilot junction. It is shown that the device can …
The thermoelectric performance of a topological Josephson nonlocal heat engine is thoroughly investigated. The nonlocal response is obtained by using a normal metal probe coupled with only one of the proximized helical edges in the middle of the junction. In this configuration, we investigate how the flux bias and the phase bias trigger the nonlocal thermoelectric effects under the application of a thermal difference between the superconducting terminals. Possible experimental nonidealities such as asymmetric proximized superconducting gaps are considered showing how the nonlocal response can …
We propose the "Andreev molecule", an artificial quantum system composed of two closely spaced Josephson junctions. The coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction's "atomic" orbitals, Andreev Bound States. A striking consequence is that the supercurrent flowing through one junction depends on the superconducting phase difference across the other junction. Using the Bogolubiov-de-Gennes formalism, we derive the energy spectrum and non-local current-phase relation for arbitrary separation. We demonstrate the possibilit…
We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [Deacon, R. S. et al., Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tu…
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…
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 study arrays of planar Nb Josephson junctions with contacts to intermediate electrodes, which allow measurements of individual junctions and, thus, provide an insight into intricate array dynamics. We observe a robust phase-locking of arrays, despite a significant inter-junction separation. Several unusual phenomena are reported, such as a bi-stable critical current with re-entrant superconductivity upon switching of nearby junctions; and incorrect Shapiro steps, occurring at mixing frequencies between the external RF radiation and the internal Josephson frequency in nearby junctions. Our r…
The Cooper pair box qubit of SQUID configuration enables the readout of the qubit states by probing the effective Josephson inductance of the SQUID. This is realized by coupling the qubit to a tank circuit which induces a small alternating supercurrent in the SQUID loop. The effect of a small (but finite) geometrical inductance of the loop on the eigenstates of the system is figured out. The effect of qubit dephasing due to quadratic coupling to the tank circuit is evaluated. It is shown that the rate of dephasing in the vicinity of the magic points is relatively low unless the Josephson junct…
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 present theoretical and numerical investigations of vortices driven by strong dc and ac currents in long Josephson junctions described by a nonlinear integro-differential equation which takes into account nonlocal electrodynamics of films, vortex bremsstrahlung and Cherenkov radiation amplified by the attraction of vortices to the edges of the junction. The work focuses on the dynamics of vortices in Josephson junctions in thin films where the effects of Josephson nonlocality dominate but London screening is negligible. We obtained an exact solution for a vortex driven by an arbitrary time-…
We study the field dependence of the maximum supercurrent in narrow edge-type thin-film Josephson junctions. It is assumed that the junction extends across thin-film strip of width W that is much less than the Pearl length; the film thickness is much less than the London penetration depth. We calculate the maximum supercurrent within nonlocal Josephson electrodynamics, which takes into account the stray fields affecting tunneling currents. In the case when W is much less than the thin-film Josephson length, the phase difference along the junction depends only on the junction geometry and the a…
We study Andreev reflection and Josephson currents in topological bilayer exciton condensates (TEC). These systems can create 100% spin entangled nonlocal currents with high amplitudes due to perfect nonlocal Andreev reflection. This Andreev reflection process can be gate tuned from a regime of purely retro reflection to purely specular reflection. We have studied the bound states in TEC-TI-TEC Josephson junctions and find a gapless dispersion for perpendicular incidence. The presence of a sharp transition in the supercurrent-phase relationship when the system is in equilibrium is a signature …
In this paper, the nonlocal mixing of coherent current states in d-wave superconducting banks is investigated. The superconducting banks are connected via a ballistic point contact. The banks have a mis-orientation and a phase difference. Furthermore, they are subjected to a tangential transport current along the $ab$-plane of d-wave crystals and parallel with interface between superconductors. The effects of mis-orientation and external transport current on the current-phase relations and current distributions are subjects of this paper. It observed that, at values of phase difference close t…
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 multi-terminal Josephson effect allows DC supercurrent to flow at finite commensurate voltages. Existing proposals to realize this effect rely on nonlocal Andreev processes in superconductor-normal-superconductor junctions. However, this approach requires precise control over microscopic states and is obscured by dissipative current. We show that standard tunnel Josephson circuits also support multiplet supercurrent mediated only by local tunneling processes. Furtheremore, we observe that the supercurrents persist even in the high charging energy regime in which only sequential Cooper tran…
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 …
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…
We study the magnetic and superconducting proximity effects in a semiconducting nanowire (NW) attached to superconducting leads and a ferromagnetic insulator (FI). We show that a sizable equilibrium spin polarization arises in the NW due to the interplay between the superconducting correlations and the exchange field in the FI. The resulting magnetization has a nonlocal contribution that spreads in the NW over the superconducting coherence length and is opposite in sign to the local spin polarization induced by the magnetic proximity effect in the normal state. For a Josephson-junction setup, …
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…
We propose an all-superconducting three-terminal setup consisting in a carbon nanotube (or semiconducting nanowire) contacted to three superconducting leads. The resulting device, referred to as a "biSQUID", is made of four quantum dots arranged in two loops of different surface area. We show how this biSQUID can prove a useful tool to probe nonlocal quantum phenomena in an interferometry setup. We study the measured critical current as a function of the applied magnetic field, which shows peaks in its Fourier spectrum, providing clear signatures of multipair Josephson processes. The device do…
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 …
Despite the robustness of the chiral edge modes of quantum Hall systems against the superconducting proximity effect, Cooper pairs can penetrate into the chiral edge channels and carry the Josephson current in an appropriate setup. In our work, the Josephson junction of a spin-polarized quantum anomalous Hall insulator (QAHI) with a Chern number $ν=1$ connecting conventional superconductors is studied from the perspective of pairing symmetry consistent with the chiral edge mode. Induced pairing states are equal-spin triplet, a combination of the even- and odd-frequency components, nonlocally e…
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…
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…
Many-body Josephson diode effect in superconducting quantum interferometers
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics and Institute for Quantum Science and Technology, Shanghai University（上海大学物理系与量子科学技术研究院）；Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University（上海大学高温超导上海市重点实验室）
Occupation-Driven Josephson Diode in a Symmetric Junction
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学理学院）
