In this article we study measurement circuit effects in three-terminal electrical transport measurements arising from finite line impedances. We provide exact expressions relating the measured voltages and differential conductances to their values at the device under test, which allow for spurious voltage divider effects to be corrected. Finally, we test the implementation of these corrections with experimental measurements.
We propose a theory that treats the current, noise, and, generally, the full current statistics of electron transfer in a mesoscopic system in a unified, simple and efficient way. The theory appears to be a circuit theory of $2\times 2$ matrices associated with Keldysh Green functions. We illustrate the theory by considering the big fluctuations of currents in various three-terminal circuits.
We show that the Coulomb interaction between two circuits separated by an insulating layer leads to unconventional thermoelectric effects, such as the cooling by thermal current effect, the transverse thermoelectric effect and Maxwell's demon effect. The first refers to cooling in one circuit induced by the thermal current in the other circuit. The middle represents electric power generation in one circuit by the temperature gradient in the other circuit. The physical picture of Coulomb drag between the two circuits is first demonstrated for the case with one quantum dot in each circuits and t…
We investigate spin-dependent transport in three--terminal mesoscopic cavities with spin--orbit coupling. Focusing on the inverse spin Hall effect, we show how injecting a pure spin current or a polarized current from one terminal generates additional charge current and/or voltage across the two output terminals. This allows to extract the spin conductance of the cavity from two purely electrical measurements on the output. We use random matrix theory to show that the spin conductance of chaotic ballistic cavities fluctuates universally about zero mesoscopic average and describe experimental i…
Unlike the two-terminal device, in which the time-reversal invariant spin-orbit interaction alone cannot polarize the spins, such a polarization can be generated when electrons from one source reservoir flow into two (or more) separate drain reservoirs. We present analytical solutions for two examples. First, we demonstrate that the electrons transmitted through a "diamond" interferometer into two drains can be simultaneously fully spin-polarized along different tunable directions, even when the two arms of the interferometer are not identical. Second, we show that a single helical molecule at…
We present a generalize Landauer-Büttiker transport theory for multi-terminal spin transport in presence of spin-orbit interaction. It is pointed out that the presence of spin-orbit interaction results in {\it equilibrium spin currents}, since in presence of spin-orbit interaction spin is not a conserved quantitative. Further we illustrate the theory by applying it to a three terminal Y-shaped conductor. It is shown that when one of the terminal is a potential probe, there exist {\it nonequilibrium pure spin currents} without a n accompanying charge current. It is shown that this pure spin cur…
From the theory of quantum $LC$ circuits with discrete charge, and {\em semiclassical} considerations, we obtain approximate energy eigenvalues, depending on the parameter $q_e^2/h$. Next, we include electrical resistance for the quantum $RLC$ circuit, obtaining a relation that strongly reminds us of the Landauer formula.
A theory of spin-transport in hybrid normal metal - ferromagnetic electronic circuits is developed, taking into account non-collinear spin-accumulation. Spin-transport through resistive elements is described by 4 conductance parameters. Microscopic expression for these conductances are derived in terms of scattering matrices and explicitly calculated for simple models. The circuit theory is applied to 2-terminal and 3-terminal devices attached to ferromagnetic reservoirs.
We present the design and implementation of a measurement system that enables parallel drive and detection of small currents and voltages at numerous electrical contacts to a multi-terminal electrical device. This system, which we term a feedback lock-in, combines digital control-loop feedback with software-defined lock-in measurements to dynamically source currents and measure small, pre-amplified potentials. The effective input impedance of each current/voltage probe can be set via software, permitting any given contact to behave as an open-circuit voltage lead or as a virtually grounded cur…
Quadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported in a series of artificial materials, such as photonic crystals, acoustic crystals, and electrical circuits. In all these cases, the underlying structures have discrete translational symmetry and thus are periodic. Here we experimentally realize two-dimensional aperiodic-quasicrystalline quadrupole-topological insulators by constructing them in electrical ci…
The energy efficiency and power of a three-terminal thermoelectric nanodevice are studied by considering elastic tunneling through a single quantum dot. Facilitated by the three-terminal geometry, the nanodevice is able to generate simultaneously two electrical powers by utilizing only one temperature bias. These two electrical powers can add up constructively or destructively, depending on their signs. It is demonstrated that the constructive addition leads to the enhancement of both energy efficiency and output power for various system parameters. In fact, such enhancement, dubbed as thermoe…
Phase sensitivity and thermal dephasing in coherent electron transport in quasi one-dimensional (1D) waveguide rings of an asymmetric four-terminal geometry are studied by magnetotransport measurements. We demonstrate the electrostatic control of the phase in Aharonov-Bohm (AB) resistance oscillations and investigate the impact of the measurement circuitry on decoherence. Phase rigidity is broken due to the ring geometry: Orthogonal waveguide cross-junctions and 1D leads minimize reflections and resonances between leads allowing for a continuous electron transmission phase shift. The measureme…
We consider transport in a three terminal device attached to one superconducting and two normal metal terminals, using the circuit theory of mesoscopic superconductivity. We compute the nonlocal conductance of the current out of the first normal metal terminal in response to a bias voltage between the second normal metal terminal and the superconducting terminal. The nonlocal conductance is given by competing contributions from crossed Andreev reflection and electron cotunneling, and we determine the contribution from each process. The nonlocal conductance vanishes when there is no resistance …
All-electrical generation and detection of pure spin currents is a promising way towards controlling the diffusive magnon transport in magnetically ordered insulators. We quantitatively compare two measurement schemes, which allow to measure the magnon spin transport in a three-terminal device based on a yttrium iron garnet thin film. We demonstrate that the dc charge current method based on the current reversal technique and the ac charge current method utilizing first and second harmonic lock-in detection can both efficiently distinguish between electrically and thermally injected magnons. I…
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.
Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased electrode restores zero-bias anomaly even for strong Majorana energy splitting. For effectively two-terminal geometry we show that electrical current through asymmetric Majorana junction is qualitatively different from the analogous current through a resonant (Breit-Wigner) level.
Using ab-initio methods we investigate the possibility of three-terminal graphene "T-junction" devices and show that these all-graphene edge contacts are energetically feasible when the 1D interface itself is free from foreign atoms. We examine the energetics of various junction structures as a function of the atomic scale geometry. Three-terminal equilibrium Green's functions are used to determine the transmission spectrum and contact resistance of the system. We find that the most symmetric structures have a significant binding energy, and we determine the contact resistances in the junction…
Spin currents are used to write information in magnetic random access memory (MRAM) devices by switching the magnetization direction of one of the ferromagnetic electrodes of a magnetic tunnel junction (MTJ) nanopillar. Different physical mechanisms of conversion of charge current to spin current can be used in 2-terminal and 3-terminal device geometries. In 2-terminal devices, charge-to-spin conversion occurs by spin filtering in the MTJ's ferromagnetic electrodes and present day MRAM devices operate near the theoretically expected maximum charge-to-spin conversion efficiency. In 3-terminal d…
Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves propagating in such networks and models of Majorana fermions hopping on a lattice. Using this analogy we propose simple electrical network architectures that realize Chern insulating phases for electromagnetic waves. Such Chern insulating networks have a bulk gap for a range of signal frequencies that is easily tunable and exhibit topologically protected chiral ed…
Charge transport measurements on flexible Mo$_{6}$S$_{3}$I$_{6}$ (MoSI) nanowires with different diameters in highly imperfect 2-terminal circuits reveal systematic power law behaviour of the conductivity $σ(T,V)$ as a function of temperature and voltage. On the basis of measurements on a number of circuits we conclude that the behaviour in \emph{thin} wires can be most convincingly described by tunneling through Tomonaga-Luttinger liquid (TLL) segments of MoSI wire, which is in some cases modified by environmental Coulomb blockade (ECB). The latter are proposed to arise from deformations or i…
Flat-band topologies and localizations in non-interacting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in interacting systems has aroused great interest. In particular, it is theoretically shown that the strong-interaction could drive the formation of nontrivial topological flat bands, even dispersive trivial bands dominate the single-particle counterparts. However, the experimental observation of those interesting phenomena is still lacking. Here, we experimentally simu…
Atomically thin two-dimensional (2D) semiconductors such as molybdenum disulphide (MoS2) hold great promise in electrical, optical, and mechanical devices and display novel physical phenomena such as coupled spin-valley physics and the valley Hall effect. However, the electron mobility of mono- and few-layer MoS2 has so far been substantially below theoretically predicted limits, particularly at low temperature (T), which has hampered efforts to observe its intrinsic quantum transport behaviors. Potential sources of disorder and scattering include both defects such as sulfur vacancies in the M…
In quantum dot circuits, screening electron clouds in strongly-coupled leads will hybridize with the states of the artificial atom. Using a three-terminal geometry, we directly probe the atomic structure of a quantum dot with Kondo coupling. Our measurements reveal that this hybrid system behaves as a non-linear entity with orbital degeneracy. Geometric distortion reduces the symmetry, lowers the energy, and lifts the degeneracy--the Jahn-Teller effect.
Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is the winding number associated with the complex energy spectrum, which is well defined for metals. We study non-Hermitian nonreciprocal systems in higher dimensions, and propose to realize them with the use of electric diode circuits. We first investigate one-dimensional interface states between two domains carrying different topological numbers, where all states are localized at the interface. They…
With recent developments in spintronics, it is now possible to envision spin-driven devices with magnets and interconnects that require a new class of transport models using generalized Fermi functions and currents, each with four components: one for charge and three for spin. The corresponding impedance elements are not pure numbers but $4\times4$ matrices. Starting from the Non-Equilibrium Green's Function (NEGF) formalism in the elastic, phase-coherent transport regime, we develop spin generalized Landauer-Büttiker formulas involving such $4\times 4$ conductances, for multi-terminal devices…
In a recent article, we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance, inductive circuit, we obtain the Stark ladder energies in yet another way; and generalize earlier results by Chandia et. al, for the circuit driven by a combination d.c. plus a.c. electromotive force (emf). As a second application, we investigate the effect of electrical resistance, together with charge discreteness, in the current amplitude, and resonance conditions of a …
A quantum circuit rule for combining quantum interference (QI) effects in the conductive properties of oligo(phenyleneethynylene) (OPE)-type molecules possessing three aromatic rings was investigated both experimentally and theoretically. Molecules were of the type X-Y-X, where X represents pyridyl anchors with para (p), meta (m) or ortho (o) connectivities and Y represents a phenyl ring with p and m connectivities. The conductances GXmX (GXpX) of molecules of the form X-m-X (X-p-X), with meta (para) connections in the central ring were predominantly lower (higher), irrespective of the meta, p…
Nonlocal currents, in devices where two normal metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev reflection and electron transfer between the two normal metal terminals, in addition to the conductance from direct Andreev reflection and quasiparticle tunneling. Dephasing and proximity effect are taken into account.
We develop a theory for the three-terminal nonlocal conductance in Majorana nanowires as existing in the superconductor-semiconductor hybrid structures in the presence of superconducting proximity, spin-orbit coupling, and Zeeman splitting. The key question addressed is whether such nonlocal conductance can decisively distinguish between trivial and topological Majorana scenarios in the presence of chemical potential inhomogeneity and random impurity disorder. We calculate the local electrical as well as nonlocal electrical and thermal conductance of the pristine nanowire (good zero-bias condu…
Custodial symmetries are common in the Standard Model of particle physics. They arise when quantum corrections to a parameter are proportional to the parameter itself. Here, we show that a custodial symmetry of the chiral type is also present in a classical Su-Schrieffer-Heeger (SSH) electrical circuit with memory (memcircuit). In the absence of memory, the SSH circuit supports a symmetry-protected topological edge state. Memory induces nonlinearities that break chiral symmetry explicitly and spreads the state across the circuit. However, the resulting state is still protected against perturba…
We investigate current fluctuations in a three-terminal quantum dot in the sequential tunneling regime. In the voltage-bias configuration chosen here, the circuit is operated like a beam splitter, i.e. one lead is used as an input and the other two as outputs. In the limit where a double occupancy of the dot is not possible, a super-Poissonian Fano factor of the current in the input lead and positive cross-correlations between the current fluctuations in the two output leads can be obtained, due to dynamical channel-blockade. When a single orbital of the dot transports current, this effect can…
We build on the study of single-photon heat conduction in electronic circuits taking into account the back-action of the superconductor--insulator--normal-metal thermometers. In addition, we show that placing capacitors, resistors, and superconducting quantum interference devices (SQUIDs) into a microwave cavity can severely distort the spatial current profile which, in general, should be accounted for in circuit design. The introduction of SQUIDs also allows for in situ tuning of the photonic power transfer which could be utilized in experiments on superconducting quantum bits.
Controllable writing and deleting of nanoscale magnetic skyrmions are key requirements for their use as information carriers for next-generation memory and computing technologies. While several schemes have been proposed, they require complex fabrication techniques or precisely tailored electrical inputs, which limits their long-term scalability. Here we demonstrate an alternative approach for writing and deleting skyrmions using conventional electrical pulses within a simple, two-terminal wire geometry. X-ray microscopy experiments and micromagnetic simulations establish the observed skyrmion…
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…
Quantum heat transport devices are currently intensively studied in theory. Experimental realization of quantum heat transport devices is a challenging task. So far, they have been mostly investigated in experiments with ultra-cold atoms and single atomic traps. Experiments with superconducting qubits have also been carried out and heat transport and heat rectification has been studied in two terminal devices. The structures with three independent terminals offer additional opportunities for realization of heat transistors, heat switches, on-chip masers and even more complicated devices. Here …
We treat the spin injection and extraction via a ferromagnetic metal/semiconductor Schottky barrier as a quantum scattering problem. This enables the theory to explain a number of phenomena involving spin-dependent current through the Schottky barrier, especially the counter-intuitive spin polarization direction in the semiconductor due to current extraction seen in recent experiments. A possible explanation of this phenomenon involves taking into account the spin-dependent inelastic scattering via the bound states in the interface region. The quantum-mechanical treatment of spin transport thr…
The recent design of a nanoscale device with a memristive characteristic has had a great impact in nonlinear circuit theory. Such a device, whose existence was predicted by Leon Chua in 1971, is governed by a charge-dependent voltage-current relation of the form $v=M(q)i$. In this paper we show that allowing for a fully nonlinear characteristic $v=η(q, i)$ in memristive devices provides a general framework for modeling and analyzing a very broad family of electrical and electronic circuits; Chua's memristors are particular instances in which $η(q,i)$ is linear in $i$. We examine several dynami…
We present a tutorial on the properties of the new ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux $ϕ$ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated just this year. We present the properties of a single m…
We have designed and operated a superconducting tunnel junction circuit that behaves as a two-level atom: the ``quantronium''. An arbitrary evolution of its quantum state can be programmed with a series of microwave pulses, and a projective measurement of the state can be performed by a pulsed readout sub-circuit. The measured quality factor of quantum coherence Qphi=25000 is sufficiently high that a solid-state quantum processor based on this type of circuit can be envisioned.
We propose the non-accelerator non-low-temperature simulator of quantum-field effects which is based on the feeder circuits with the special feedback. By means of it one can study the field models which contain fundamental concepts in the modern field theory but do not exist in nature in a separate form. Besides, several field phenomena might find technological applications by virtue of the electrical analogy.
There have been considerable efforts devoted to the study of topological phases in certain non-Hermitian systems that possess real eigenfrequencies in the presence of gain and loss. However, it is challenging to experimentally realize such non-Hermitian topological insulators in either quantum or photonic systems, due to the difficulties in introducing controlled gain and loss. On the other hand, the wide choices of active circuit components provide us with unprecedented convenience and flexibility in engineering non-Hermitian topological insulators in electrical circuits. Here, we report expe…
We present a superconducting tunnel junction circuit which behaves as a controllable atom, and whose ground and first excited state form an effective spin 1/2. By applying microwave pulses, we have performed on this circuit experiments demonstrating the controlled manipulation of the spin : Rabi precession, Ramsey interferences, and spin echoes.
We study photonic heat conduction between two resistors coupled weakly to a single superconducting microwave cavity. At low enough temperature, the dominating part of the heat exchanged between the resistors is transmitted by single-photon excitations of the fundamental mode of the cavity. This manifestation of single-photon heat conduction should be experimentally observable with the current state of the art. Our scheme can possibly be utilized in remote interference-free temperature control of electric components and environment engineering for superconducting qubits coupled to cavities.
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.
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 propose a realizable architecture using one-dimensional transmission line resonators to reach the strong coupling limit of cavity quantum electrodynamics in superconducting electrical circuits. The vacuum Rabi frequency for the coupling of cavity photons to quantized excitations of an adjacent electrical circuit (qubit) can easily exceed the damping rates of both the cavity and the qubit. This architecture is attractive both as a macroscopic analog of atomic physics experiments and for quantum computing and control, since it provides strong inhibition of spontaneous emission, potentially le…
The efficiency of a thermal engine working in linear response regime in a multi-terminals configuration is discussed. For the generic three-terminal case, we provide a general definition of local and non-local transport coefficients: electrical and thermal conductances, and thermoelectric powers. Within the Onsager formalism, we derive analytical expressions for the efficiency at maximum power, which can be written in terms of generalized figures of merit. Also, using two examples, we investigate numerically how a third terminal could improve the performance of a quantum system, and under whic…
We present a physics-based circuit-compatible model for double-gated two-dimensional semiconductor based field effect transistors, which provides explicit expressions for the drain current, terminal charges and intrinsic capacitances. The drain current model is based on the drift-diffusion mechanism for the carrier transport and considers Fermi-Dirac statistics coupled with an appropriate field-effect approach. The terminal charge and intrinsic capacitance models are calculated adopting a Ward-Dutton linear charge partition scheme that guarantees charge-conservation. It has been implemented in…
Current-induced spin-transfer torques (STT) and spin-orbit torques (SOT) enable the electrical switching of magnetic tunnel junctions (MTJs) in nonvolatile magnetic random access memories. In order to develop faster memory devices, an improvement of the timescales underlying the current driven magnetization dynamics is required. Here we report all-electrical time-resolved measurements of magnetization reversal driven by SOT in a three-terminal MTJ device. Single-shot measurements of the MTJ resistance during current injection reveal that SOT switching involves a stochastic two-step process con…
We report the fabrication and performance of all-metallic three-terminal devices with tantalum diselenide thin-film conducting channels. For this proof-of-concept demonstration, the layers of 2H-TaSe2 were exfoliated mechanically from single crystals grown by the chemical vapor transport method. Devices with nanometer-scale thicknesses exhibit strongly non-linear current-voltage characteristics, unusual optical response, and electrical gating at room temperature. We have found that the drain-source current in thin-film 2H-TaSe2-Ti/Au devices reproducibly shows an abrupt transition from a highl…
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.
Two-dimensional materials offer a novel platform for the development of future quantum technologies. However, the electrical characterisation of topological insulating states, non-local resistance and bandgap tuning in atomically-thin materials, can be strongly affected by spurious signals arising from the measuring electronics. Common-mode voltages, dielectric leakage in the coaxial cables and the limited input impedance of alternate-current amplifiers can mask the true nature of such high-impedance states. Here, we present an optical isolator circuit which grants access to such states by ele…
