Using an exact nonequilibrium Green's function formulism, the phonon Hall effect for paramagnetic dielectrics is studied in a four-terminal device setting. The temperature difference in the transverse direction of the heat current is calculated for two-dimensional models with the magnetic field perpendicular to the plane. We find a surprising result that the square lattice does not have the phonon Hall effect while a honeycomb lattice has. This can be explained by symmetry. The temperature difference changes sign if the magnetic field is sufficiently large.
Similarly to the recently obtained result for two-terminal systems, we show that there are constraints on the full counting statistics for non-interacting fermions in multi-terminal contacts. In contrast to the two-terminal result, however, there is no factorization property in the multi-terminal case.
We study ballistic thermal transport in three-terminal atomic nanojunctions by the nonequilibrium Green's function method. We find that there is ballistic thermal rectification in asymmetric three-terminal structures because of the incoherent phonon scattering from the control terminal. With spin-phonon interaction, we also find the ballistic thermal rectification even in symmetric three-terminal paramagnetic structures.
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 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 …
We propose a thermal transistor based on a three-terminal normal-superconductor (NS) junction with superconductor terminal acting as the base. The emergence of heat amplification is due to the negative differential thermal conductance (NDTC) effect for the NS diode in which the normal side maintains a higher temperature. The temperature dependent superconducting energy gap is responsible for the NDTC. By controlling quantum dot levels and their coupling strengths to the terminals, a huge heat amplification factor can be achieved. The setup offers an alternative tuning scheme of heat amplificat…
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.
We report an observation of a new, non dissipative and non local supercurrent, carried by quartets; each consisting of four entangled electrons. The supercurrent is a result of a novel Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the DC Josephson current, exist only in equilibrium, in the present realization the ABS exists also in the strongly nonlinear regime (biased terminals). The presence of supercurrent carried by quartets was established by performing non-local conductance and cross-correlation…
We investigate the current-current correlations in a four-terminal Al-AlOx-Al tunnel junction where shot noise dominates. We demonstrate that cross-correlations in the presence of two biasing sources of the Hanbury-Brown and Twiss type are much stronger (approximately twice) than an incoherent sum of correlations generated by single sources. The difference is due to voltage fluctuations of the central island that give rise to current-current correlations in the four contacts of the junction. Our measurements are in close agreement with results obtained using a simple theoretical model based on…
We report the results of several nonequilibrium experiments performed on superconducting/normal/superconducting (S/N/S) Josephson junctions containing either one or two extra terminals that connect to normal reservoirs. Currents injected into the junctions from the normal reservoirs induce changes in the electron energy distribution function, which can change the properties of the junction. A simple experiment performed on a 3-terminal sample demonstrates that quasiparticle current and supercurrent can coexist in the normal region of the S/N/S junction. When larger voltages are applied to the …
We investigate the electronic properties of ballistic planar Josephson junctions with multiple superconducting terminals. Our devices consist of monolayer graphene encapsulated in boron nitride with molybdenum-rhenium contacts. Resistance measurements yield multiple resonant features, which are attributed to supercurrent flow among adjacent and non-adjacent Josephson junctions. In particular, we find that superconducting and dissipative currents coexist within the same region of graphene. We show that the presence of dissipative currents primarily results in electron heating and estimate the a…
We have developed a fast, yet highly reproducible method to fabricate metallic electrodes with nanometer separation using electromigration (EM). We employ four-terminal instead of two-terminal devices in combination with an analog feedback to maintain the voltage $U$ over the junction constant. After the initialization phase ($U < 0.2V), during which the temperature $T$ increases by 80-150 degs C, EM sets in shrinking the wire locally. This quickly leads to a transition from the diffusive to a quasi-ballistic regime ($0.2V < U < 0.6V). At the end of this second regime, a gap forms (U > 0.6V). …
Nonlinear electrical properties of graphene-based three-terminal nanojunctions are presented. Intrinsic rectification of voltage is observed up to room temperature. The sign and the efficiency of the rectification can be tuned by a gate. Changing the charge carrier type from holes to electrons results in a change of the rectification sign. At a bias < 20mV and at a temperature below 4.2K the sign and the efficiency of the rectification are governed by universal conductance fluctuations.
Multi-terminal Josephson junctions were recently proposed as a versatile and tunable platform to emulate topological Bloch-like Hamiltonians in arbitrary dimensions. In this perspective article, we will give a brief overview of the subject and recognize these mesoscopic devices as realizations of topological flux networks as the ones envisioned by J. E. Avron and coworkers in their seminal works on the early days of the quantum Hall effect. We summarize the current state-of-the-art theoretical and experimental research regarding these Josephson devices, highlighting recent developments and giv…
This letter introduces a micromagnetic model able to characterize the magnetization dynamics in three terminal magnetic tunnel junctions, where the effects of spin-transfer torque and spin-orbit torque are taken into account. Our results predict that the possibility to separate electrically those two torque sources is very promising from a technological point of view for both next generation of nanoscale spintronic oscillators and microwave detectors. A scalable synchronization scheme based on the parallel connection of those three terminal devices is also proposed.
A three-terminal thermoelectric device based on a $p$-$i$-$n$ semiconductor junction is proposed, where the intrinsic region is mounted onto a, typically bosonic, thermal terminal. Remarkably, the figure of merit of the device is governed also by the energy distribution of the {\em bosons} participating in the transport processes, in addition to the electronic one. An enhanced figure of merit can be obtained when the relevant distribution is narrow and the electron-boson coupling is strong (such as for optical phonons). We study the conditions for which the figure of merit of the three-termina…
A theory is offered for the ballistic 4-terminal Josephson junction. The studied system consists of a mesoscopic two-dimensional normal rectangular layer which is attached in each side to the bulk superconducting banks (terminals). The relation between the currents through the different terminals, which is valid for arbitrary temperatures and junction sizes, is obtained. The nonlocal coupling of the supercurrents leads to a new effect, specific for the mesoscopic weak link between two superconducting rings; an applied magnetic flux through one of the rings produces a magnetic flux in the other…
We study multiple helical nanowires in proximity to a common mesoscopic superconducting island, where Majorana fermion bound states are formed. We show that a weak finite charging energy of the center island may dramatically affect the low-energy behavior of the system. While for strong charging interactions, the junction decouples the connecting wires, interactions lower than a non-universal threshold may trigger the flow towards an exotic Kondo fixed point. In either case, the ideally Andreev reflecting fixed point characteristic for infinite capacitance (grounded) devices gets destabilized …
We demonstrate control over heat flow in an N-terminal molecular junction. Using simple model Hamiltonians we show that the heat current through two terminals can be tuned, switched, and amplified, by the temperature and coupling parameters of external gating reservoirs. We discuss two models: A fully harmonic system, and a model incorporating anharmonic interactions. For both models the control reservoirs induce thermal fluctuations of the transition elements between molecular vibrational states. We find that a fully harmonic model does not show any controllability, while for an anharmonic sy…
Three-terminal superconductor (S) - normal metal (N) - superconductor (S) Josephson junctions are investigated. In a geometry where a T-shape normal metal is connected to three superconducting reservoirs, new sub-gap structures appear in the differential resistance for specific combinations of the superconductor chemical potentials. Those correspond to a correlated motion of Cooper pairs within the device that persist well above the Thouless energy and is consistent with the prediction of quartets formed by two entangled Cooper pairs. A simplified nonequilibrium Keldysh Green's function calcul…
The quantum Hall and longitudinal resistances in multi-terminal ferromagnetic graphene p-n junctions under a perpendicular magnetic field are investigated. In the Hall measurements, the transverse contacts are assumed to be located at p-n interface to avoid the mixing of edge states at the interface and the resulting quantized resistances are then topologically protected. According to the charge carrier type, the resistances in four-terminal p-n junction can be naturally divided into nine different regimes. The symmetric Hall and longitudinal resistances are observed, with lots of new robust q…
We study the transport properties of a four-terminal corner junction made by etching a two- dimensional topological insulator to form a quantum point contact (QPC). The QPC geometry enables inter-boundary tunneling processes allowing for the coupling among states with different helicity, while the tight confinement in the QPC region activates charging effects leading to the Coulomb blockade physics. Peculiar signatures of these effects are theoretically investigated using a scattering field theory modified to take into account the electron-electron interaction within a self- consistent mean-fi…
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 the electron transport in three terminal junctions and quantum rings looking for the classical deflection of electron trajectories in presence of intersubband scattering. We indicate that although the Aharonov-Bohm oscillations and the Lorentz force effects co-exist in the low subband transport, for higher Fermi energies a simultaneous observation of the both effects is difficult and calls for carefully formed structures. In particular, in quantum rings with channels wider than the input lead the Lorentz force is well resolved but the Aharonov-Bohm periodicity is lost in chaotic scatt…
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…
Topological surface states of three-dimensional topological insulator nanoribbons and their distinct magnetoconductance properties are promising for topoelectronic applications and topological quantum computation. A crucial building block for nanoribbon-based circuits are three-terminal junctions. While the transport of topological surface states on a planar boundary is not directly affected by an in-plane magnetic field, the orbital effect cannot be neglected when the surface states are confined to the boundary of a nanoribbon geometry. Here, we report on the magnetotransport properties of su…
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 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…
Symmetry-Induced Weyl Nodes in Interacting Multi-Terminal Josephson Junctions
Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子技术与卡弗里纳米科学研究所）；Fachbereich Physik, Universität Konstanz（康斯坦茨大学物理系）
We investigate the Josephson effect in one triple-terminal junction with embedded parallel-coupled double quantum dots. It is found that the inter-superconductor supercurrent has opportunities to oscillate in $4π$ period, with the adjustment of the phase differences among the superconductors. What is notable is that such a result is robust and independent of fermion parities, intradot Coulomb strength, and the dot-superconductor coupling manner. By introducing the concept of spinful many-particle Majorana modes, we present the analytical definition of the Majorana operator via superposing elec…
We show that direct current in a tantalum microstrip can induce steady-state magnetic oscillations in an adjacent nanomagnet through spin torque from the spin Hall effect (SHE). The oscillations are detected electrically via a magnetic tunnel junction (MTJ) contacting the nanomagnet. The oscillation frequency can be controlled using the MTJ bias to tune the magnetic anisotropy. In this 3-terminal device the SHE torque and the MTJ bias therefore provide independent controls of the oscillation amplitude and frequency, enabling new approaches for developing tunable spin torque nano-oscillators.
When a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect - the phase of the junction locks to the drive frequency. As a result, the I-V curves of the junction acquire "Shapiro steps" of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multi-terminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe …
The helical state is a fundamental prerequisite for many spintronics applications and Majorana zero mode engineering in nanoscopic semiconductors. Its existence in quasi-one-dimensional nanowires was predicted to be detectable as a characteristic reentrant behavior in the conductance, which in a typical two-terminal architecture may be difficult to distinguish from other possible phenomena such as Fabry-Perot oscillations. Here we present an alternative method of helical gap detection free of the mentioned ambiguity, and based on the nonlocal conductance measurements in a three-terminal juncti…
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.
In this paper we describe a graphene p-n junction created by chemical doping. We find that chemical doping does not reduce mobility in contrast to top-gating. The preparation technique has been developed from systematic studies about influences on the initial doping of freshly prepared graphene. We investigated the removal of adsorbates by vacuum treatment, annealing and compensation doping using NH3. Hysteretic behavior is observed in the electric field effect due to dipolar adsorbates like water and NH3. Finally we demonstrate spatially selective doping of graphene using patterned PMMA. 4-te…
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…
An expression for the transmission matrix based conductance is provided for the propagation of scalar waves in certain bifurcated discrete waveguides using the paradigm of a three-terminal Landauer-Buttiker junction. It is found that the conductance across the terminals of bifurcated branches forming a sharp corner, interpreted as a controller of `leakage' flux, can be tuned by manipulating the number of channels and the type of lateral confinement. Natural applications in engineering and science arise in the context of nanoscale transport involving elastic, phononic, or electronic waves. In p…
We investigate the transport properties of three terminal carbon based nanojunctions within the scattering matrix approach. The stability of such junctions is subordinated to the presence of nonhexagonal arrangements in the molecular network. Such "defective" arrangements do influence the resulting quantum transport observables, as a consequence of the possibility of acting as pinning centers of the correspondent wavefunction. By investigating a fairly wide class of junctions we have found regular mutual dependencies between such localized states at the carbon network and a strikingly behavior…
The thermoelectric transport through a molecular bridge is discussed, with an emphasis on the effects of inelastic processes of the transport electrons caused by the coupling to the vibrational modes of the molecule. In particular it is found that when the molecule is strongly coupled to a thermal bath of its own, which may be at a temperature different from those of the electronic reservoirs, a heat current between the molecule and the electrons can be converted into electric current. Expressions for the transport coefficients governing this conversion and similar ones are derived, and a poss…
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…
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…
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 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 demonstrated that the spin injection/extraction efficiency is enhanced by an ultrathin Mg insertion layer (<= 2 nm) in Fe/Mg/MgO/n+-Si tunnel junctions. In diode-type vertical three-terminal devices fabricated on a Si substrate, we observed the narrower three-terminal Hanle (N-3TH) signals indicating true spin injection into Si, and estimated the spin polarization in Si to be 16% when the thickness of the Mg insertion layer is 1 nm, whereas no N-3TH signal was observed without Mg insertion. This means that the spin injection/extraction efficiency is enhanced by suppressing the formation of …
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…
Hall effect in SN and SNS junctions is considered. It is shown that at small temperature the Hall voltage is significantly suppressed as compared to its normal metal value. The time dependence of the Hall voltage in SNS junctions has a form of narrow pulses with the Josephson frequency.
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
We report on the current-induced magnetization switching of a three-terminal perpendicular magnetic tunnel junction by spin-orbit torque and the read-out using the tunnelling magnetoresistance (TMR) effect. The device is composed of a perpendicular Ta/FeCoB/MgO/FeCoB stack on top of a Ta current line. The magnetization of the bottom FeCoB layer can be switched reproducibly by the injection of current pulses with density $5\times10^{11}$ A/m$^2$ in the Ta layer in the presence of an in-plane bias magnetic field, leading to the full-scale change of the TMR signal. Our work demonstrates the proof…
