Multiterminal Structures Research Articles

Universality of the Spectra of Multiterminal Josephson Junction

Andreev bound states are formed in multiterminal structures based on normal metals and superconductors. Their spectrum is determined by the system parameters, in particular the scattering phases and transmission coefficients at the nodes. The article found conditions under which Andreev bound states are universal: they don’t change with any change in the reflection phases. As a consequence, the spectrum is completely determined by the transport characteristics of the system. The result was obtained for a structure in the form of a normal metal M-finite star, each of the rays (terminals) Nk of which is in contact with its superconductor Sk, 1 ≤ k ≤ M. Together they form a multiterminal Josephson junction. At the center of the structure there is a non-magnetic impurity with its some scattering matrix.

Non-Hermitian Hamiltonians and Quantum Transport in Multi-Terminal Conductors.

We study the transport properties of multi-terminal Hermitian structures within the non-equilibrium Green’s function formalism in a tight-binding approximation. We show that non-Hermitian Hamiltonians naturally appear in the description of coherent tunneling and are indispensable for the derivation of a general compact expression for the lead-to-lead transmission coefficients of an arbitrary multi-terminal system. This expression can be easily analyzed, and a robust set of conditions for finding zero and unity transmissions (even in the presence of extra electrodes) can be formulated. Using the proposed formalism, a detailed comparison between three- and two-terminal systems is performed, and it is shown, in particular, that transmission at bound states in the continuum does not change with the third electrode insertion. The main conclusions are illustratively exemplified by some three-terminal toy models. For instance, the influence of the tunneling coupling to the gate electrode is discussed for a model of quantum interference transistor. The results of this paper will be of high interest, in particular, within the field of quantum design of molecular electronic devices.

Multi-terminal Transistor-like Devices Based on Strongly Correlated Metallic Oxides for Neuromorphic Applications.

Memristive devices are attracting a great attention for memory, logic, neural networks, and sensing applications due to their simple structure, high density integration, low-power consumption, and fast operation. In particular, multi-terminal structures controlled by active gates, able to process and manipulate information in parallel, would certainly provide novel concepts for neuromorphic systems. In this way, transistor-based synaptic devices may be designed, where the synaptic weight in the postsynaptic membrane is encoded in a source-drain channel and modified by presynaptic terminals (gates). In this work, we show the potential of reversible field-induced metal-insulator transition (MIT) in strongly correlated metallic oxides for the design of robust and flexible multi-terminal memristive transistor-like devices. We have studied different structures patterned on YBa2Cu3O7−δ films, which are able to display gate modulable non-volatile volume MIT, driven by field-induced oxygen diffusion within the system. The key advantage of these materials is the possibility to homogeneously tune the oxygen diffusion not only in a confined filament or interface, as observed in widely explored binary and complex oxides, but also in the whole material volume. Another important advantage of correlated oxides with respect to devices based on conducting filaments is the significant reduction of cycle-to-cycle and device-to-device variations. In this work, we show several device configurations in which the lateral conduction between a drain-source channel (synaptic weight) is effectively controlled by active gate-tunable volume resistance changes, thus providing the basis for the design of robust and flexible transistor-based artificial synapses.

Nonlocal thermoelectric effects in high-field superconductor-ferromagnet hybrid structures

We report on the experimental observation of nonlocal spin-dependent thermoelectric effects in superconductor-ferromagnet multiterminal structures. Our samples consist of a thin superconducting aluminum wire with several ferromagnetic tunnel junctions attached to it. When a thermal excitation is applied to one of the junctions in the presence of a Zeeman splitting of the density of states of the superconductor, a thermoelectric current is observed in remote junctions at distances exceeding $10~\mathrm{\mu m}$. The results can be explained by recent theories of coupled spin and heat transport in high-field superconductors.

Scattering matrix of arbitrary tight-binding Hamiltonians

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

Strain controlled valley filtering in multi-terminal graphene structures

Valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by the deformation allows electrons from only one valley to transmit, and a current of electrons from a single valley is generated at the opposite side of the locally strained region. We show that valley filtering is most effective with bumps of a certain height and width. Despite the fact that the highest contribution to the polarized current comes from electrons from the lowest sub-band, contributions of other sub-bands are not negligible and can significantly enhance the output current.

Enhancement of Shapiro-like steps in multiterminal Josephson structures

The distinctive features of current–voltage characteristics are studied for mesoscopic multiterminal structures effected by external irradiation. Considering a simple model of applied dc+ac voltage, we calculate Shapiro-like steps in Josephson systems with several weakly coupled superconducting electrodes. Owing to the action of an external alternating signal, the dc current is found to be rather increased than it appears in the same multiterminal Josephson node without the radiation. The possible applications of our results for the experimental observation of the Shapiro-like steps in such Josephson structures are discussed.

Conductance matrix of multiterminal semiconductor devices with edge channels

A method for determining the conductance matrix of multiterminal semiconductor structures with edge channels is proposed. The method is based on the solution of a system of linear algebraic equations based on Kirchhoff equations, made up of potential differences U ij measured at stabilized currents I kl , where i, j, k, l are terminal numbers. The matrix obtained by solving the system of equations completely describes the structure under study, reflecting its configuration and homogeneity. This method can find wide application when using the known Landauer-Buttiker formalism to analyze carrier transport in the quantum Hall effect and quantum spin Hall effect modes. Within the proposed method, the contribution of the contact area resistances R c to the formation of conductance matrix elements is taken into account. The possibilities of practical application of the results obtained in developing analog cryptographic devices are considered.

High-Quality Multiterminal Suspended Graphene Devices

We introduce a new scheme to realize suspended, multiterminal graphene structures that can be current annealed successfully to obtain uniform, very high quality devices. A key aspect is that the bulky metallic contacts are not connected directly to the part of graphene probed by transport measurements, but only through etched constriction, which prevents the contacts from acting invasively. The device high quality and uniformity is demonstrated by a reproducibly narrow (δn ~ 10(9) cm(-2)) resistance peak around charge neutrality, by carrier mobility values exceeding 10(6) cm(2) V(-1) s(-1), by the observation of integer quantum Hall plateaus starting at 30 mT and of symmetry broken states at about 200 mT, and by the occurrence of a negative multiterminal resistance directly proving the occurrence of ballistic transport. As these multiterminal devices enable measurements that cannot be done in a simpler two-terminal configuration, we anticipate that their use in future studies of graphene-based systems will be particularly relevant.

Long-Range Spin-Polarized Quasiparticle Transport in Mesoscopic Al Superconductors with a Zeeman Splitting

We report on nonlocal transport in multiterminal superconductor-ferromagnet structures, which were fabricated by means of e-beam lithography and shadow evaporation techniques. In the presence of a significant Zeeman splitting of the quasiparticle states, we find signatures of spin transport over distances of several μm, exceeding other length scales such as the coherence length, the normal-state spin-diffusion length, and the charge-imbalance length. The relaxation length of the spin signal shows a nearly linear increase with magnetic field, hinting at a freeze-out of relaxation by the Zeeman splitting. We propose that the relaxation length is given by the recombination length of the quasiparticles rather than a renormalized spin-diffusion length.

Electronic transport in the multi-terminal graphene nanodevices

We examined the ac transport attribute of the multi-terminal structures in the absence and presence of magnetic field. We found that the ac response depends on the structural configurations and that the admittance varies with the features of the attached nanoribbons. In the vicinity of Dirac point the dc conductance manifests a dip or peak and the imaginary part (emittance) vanishes or not, depending on whether the attached ribbon is semiconductive or metallic. In the presence of magnetic field, the emittance becomes asymmetric reflecting the dynamic behaviors of electron and hole.

Charge imbalance in superconductors in the low-temperature limit

We explore charge imbalance in mesoscopic normal-metal/superconductor multiterminal structures at very low temperatures. The investigated samples, fabricated by e-beam lithography and shadow evaporation, consist of a superconducting aluminum bar with several copper wires forming tunnel contacts at different distances from each other. We have measured in detail the local and nonlocal conductance of these structures as a function of the applied bias voltage $V$, the applied magnetic field $B$, the temperature $T$, and the contact distance $d$. From these data the charge-imbalance relaxation length ${\ensuremath{\lambda}}_{{Q}^{\ensuremath{\ast}}}$ is derived. The bias-resolved measurements show a transition from dominant elastic scattering close to the energy gap to an inelastic two-stage relaxation at higher bias. We observe a strong suppression of charge imbalance with magnetic field, which can be directly linked to the pair-breaking parameter. In contrast, practically no temperature dependence of the charge-imbalance signal was observed below 0.5 K. These results are relevant for the investigation of other nonlocal effects such as crossed Andreev reflection and spin diffusion.

Optimal block-tridiagonalization of matrices for coherent charge transport

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.

Multiterminal multimode spin-dependent scattering matrix formalism: Electron and hole quantum spin transport in multiterminal junctions

We present a derivation of a scattering matrix method providing an exact multimode solution to spin-dependent quantum transport in multiterminal structures. The method is formulated in a general language such that it can readily be applied to any spin-S system with spin interactions. We apply the formalism to spin-1/2 electron and spin-3/2 hole transport in three- and four-terminal structures. It is shown that the existence of a third lead lifts constraints on the flux polarization of two-terminal electron transport. A spin-rectification property in a three-terminal system with Rashba spin-orbit interaction is demonstrated. We furthermore find that a four-terminal structure can partition a fully spin-polarized electron flux into two oppositely polarized fluxes. For holes, we calculate the polarization vector of both the injected states as well as the outgoing states in a three-terminal structure. Close to the onset of propagating channels, the hole polarization exhibits peak-dip structures attributed to the angular-momentum dependent Fano resonances in the three-terminal junction. We rigorously show that when the outgoing state is restricted to a single channel, the polarization is uniquely determined by the outgoing lead state, independent of the scattering details of the structure. (Less)

Spin Current and Spin Hall Effect in Metallic Nano-Structures

Laterally configured ferromagnetic/nonmagnetic multiterminal structures have great potential for developing future spintronic devices. We demonstrate two kinds of novel spintronic devices. One is a lateral spin valve with noncollinear dual spin injectors by which the direction of the spin accumulation in a nonmagnetic metal can be changed by varying the currents injected by two spin injectors. The other is a transformer between spin and charge currents using the spin Hall effect. A large spin Hall conductivity of 260 S/cm at room temperature, which is 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> times larger than that in semiconductor systems, is found in the Pt wire. We also demonstrate the reciprocal relation between the spin and charge currents. Temperature dependence of the spin Hall conductivity is also discussed.

Observation of Andreev–Saint-James reflections in nano-scale planar superconductor to ferromagnet contacts

We fabricated nanoscale ferromagnetic (F) Nickel/superconducting (S) indium junctions which show that spin polarization effects on the contact conductance can be observed in a planar geometry. The data demonstrate that the Andreev–Saint-James [Sov. Phys. JETP 19, 1228 (1964) and J. Phys. (Paris) 25, 899 (1964)] electron-hole reflections at the F∕S interface, which are sensitive to the polarization of the F side, dominate the conductance of the contact at low bias. The simplicity of fabrication makes these junctions appealing for use in multiterminal SF structures.

Crossed Andreev reflection in diffusive contacts: Quasiclassical Keldysh-Usadel formalism

Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal-metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to contribute equally to the nonlocal current, which is of relevance to the use of normal-metal--superconducting heterostructures as sources of entanglement.

Direct Study of the Proximity Effect in the Normal Layer inside of the Stacked SINIS Device

We have observed a striking anisotropy in the electrical transport of layered multiterminal SINIS structures [where S, I, and N denote a superconductor (Nb), an insulator (AlOx), and a normal metal (Al), respectively]. We find that the lateral conductivity of the N layer is dissipative, but a superconducting current can flow normal to the structure, suggesting a direct Josephson coupling between the external S electrodes. A small coherent contribution to the lateral conductivity of the N layer is observed near zero voltage.

A simple way to CN x/carbon nanotube intramolecular junctions and branches

Large quantities of CN x /carbon nanotube intramolecular junctions were successfully synthesized on a silicon substrate via the chemical vapor deposition method by pyrolysis of ferrocene and melamine. The nanotubes have two apparently different sections, one made of carbon with an empty hollow cylinder structure, and the other made of carbon nitride with a bamboo-like structure. Three- and four-terminal CN x /carbon nanotube intramolecular branches were also observed, and such multi-terminal structures offer potential applications for future nanodevices. A simple model is suggested for the synthesis of these CN x /carbon nanotube intramolecular junctions and branches.

Integration Of Carbon Nanotubes Into Device Structures

ABSTRACTCarbon nanotubes have shown promising properties for applications in electronic circuits and other device structures. Several device structures have been demonstrated in recent years by manual manipulation of single nanotubes. The integration of large numbers of nanotubes on wafer size substrates, however, has been a challenge.Our approach addressing this issue utilizes nano-patterning methods in combination with plasma enhanced chemical vapor deposition to directly assemble carbon nanotubes on wafer structures. A secondary formation step is used to actually form device structures connecting the nanotubes to electrode structures. We present first results demonstrating the feasibility of our approach. Electrode structures were prepared using multi-step electron beam lithography processes. Carbon nanotubes were grown in pre-defined locations, and contact formation procedures were carried out to establish multi-terminal contact structures.