We offer a general approach to calculation of single-electron tunneling spectra and conductance of a shuttle oscillating between two half-metallic leads with fully spin polarized carriers. In this case the spin-flip processes are completely suppressed and the problem may be solved by means of canonical transformation, where the adiabatic component of the tunnel transparency is found exactly, whereas the non-adiabatic corrections can be taken into account perturbatively. Time-dependent corrections to the tunnel conductance of moving shuttle become noticeable at finite bias in the vicinity of the even/odd occupation boundary at the Coulomb diamond diagram.
We investigate superradiant-like dynamics of the nuclear-spin bath in a single-electron quantum dot, by considering electrons cyclically shuttling on/off an isotopically enriched `nuclear-spin island'. Assuming a uniform hyperfine interaction, we discuss in detail the nuclear spin evolution under shuttling and its relation to superradiance. We derive the minimum shuttling time which allows to escape the adiabatic spin evolution. Furthermore, we discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet. Finally, by comparing our scheme to a model with stationary quantum …
We investigate theoretically a mechanically assisted Kondo effect and electric charge shuttling in nanoelectromechanical single-electron transistor (NEM-SET). It is shown that the mechanical motion of the central island (a small metallic particle) with the spin results in the time dependent tunneling width which leads to effective increase of the Kondo temperature. The time-dependent oscillating Kondo temperature T_K(t) changes the scaling behavior of the differential conductance resulting in the suppression of transport in a strong coupling- and its enhancement in a weak coupling regimes. The…
We observe transport of electrons through a metallic island on the tip of a nanomechanical pendulum. The resulting tunneling current shows distinct features corresponding to the discrete mechanical eigenfrequencies of the pendulum. We report on measurements covering the temperature range from 300 K down to 4.2 K. We explain the I-V curve, which differs from previous theoretical predictions, with model calculations based on a Master equation approach.
We demonstrate single electron shuttling through two coupled nanomechanical pendula. The pendula are realized as nanopillars etched out of the semiconductor substrate. Coulomb blockade is found at room temperature, allowing metrological applications. By controlling the mechanical shuttling frequency we are able to validate the different regimes of electron shuttling.
We consider electromechanical properties of a single-electronic device consisting of movable quantum dot attached to a vibrating cantilever, forming a tunnel contact with a non-movable source electrode. We show that the resonance Kondo tunneling of electrons amplify exponentially the strength of nanoelectromechanical (NEM) coupling in such device and makes the latter to be insensitive to mesoscopic fluctuations of electronic levels in a nano-dot. It is also shown that the study of Kondo-NEM phenomenon provides an additional (as compared with a standard conductance measurements in a non-mechani…
In this article, we report a theoretical analysis of a nanoelectromechanical shuttle based on a multiscale model that combines microscopic electronic structure data with macroscopic dynamics. The microscopic part utilizes a (static) density functional description to obtain the energy levels and orbitals of the shuttling particle together with the forces acting on the particle. The macroscopic part combines stochastic charge dynamics that incorporates the microscopically evaluated tunneling rates with a Newtonian dynamics. We have applied the multiscale model to describe the shuttling of a sing…
One core challenge of nanoelectromechanical systems (NEMS) is their efficient actuation. A promising concept superseding resonant driving is self-oscillation. Here we demonstrate voltage-sustained self-oscillation of a nanomechanical charge shuttle. Stable transport at 4.2 K is observed for billions of shuttling cycles, giving rise to ohmic current-voltage curves with a sharp dissipation threshold. With only a few nanowatts of input energy the presented scheme is suitable for operation in the millikelvin regime where Coulomb blockade-controlled single electron shuttling is anticipated.
A single-electron tunneling (SET) device with a nanoscale central island that can move with respect to the bulk source- and drain electrodes allows for a nanoelectromechanical (NEM) coupling between the electrical current through the device and mechanical vibrations of the island. Although an electromechanical "shuttle" instability and the associated phenomenon of single-electron shuttling were predicted more than 15 years ago, both theoretical and experimental studies of NEM-SET structures are still carried out. New functionalities based on quantum coherence, Coulomb correlations and coherent…
We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zig-zag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin, $S$, consistent with Lieb's the…
A single-electron tunneling (SET) device with a nanoscale central island that can move with respect to the bulk source- and drain electrodes allows for a nanoelectromechanical (NEM) coupling between the electrical current through the device and mechanical vibrations of the island. Although an electromechanical "shuttle" instability and the associated phenomenon of single-electron shuttling were predicted more than 15 years ago, both theoretical and experimental studies of NEM-SET structures are still carried out. New functionalities based on quantum coherence, Coulomb correlations and coherent…
Distributing entanglement between distant semiconductor qubit registers using a shared-control shuttling link
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子纳米科学卡弗里研究所和QuTech）；QuTech and Netherlands Organisation for Applied Scientific Research (TNO)（QuTech和荷兰应用科学研究组织（TNO））
Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qub…
A new nano-lithography technique compatible with conducting oxide interfaces, which requires a single lithographic step with no additional amorphous layer deposition or etching, is presented. It is demonstrated on SrTiO3/LaAlO3 interface where a constriction is patterned in the electron liquid. We find that an additional back-gating can further confine the electron liquid into an isolated island. Conductance and differential conductance measurements show resonant tunneling through the island. The data at various temperatures and magnetic fields are analyzed and the effective island size is fou…
We formulate a theory for shot noise in quantum nanoelectromechanical systems. As a specific example, the theory is applied to a quantum shuttle, and the zero-frequency noise, measured by the Fano factor F, is computed. F reaches very low values (F~0.01) in the shuttling regime even in the quantum limit, confirming that shuttling is universally a low noise phenomenon. In approaching the semiclassical limit, the Fano factor shows a giant enhancement (F~100) at the shuttling threshold, consistent with predictions based on phase-space representations of the density matrix.
Single layer graphene islands with a typical diameter of several nanometers were grown on a Pt (111) substrate. Scanning tunneling microscopy (STM) analysis showed most of islands are hexagonally shaped and the zigzag-type edge predominates over the armchair-type edge. The apparent height at the atoms on the zigzag edge is enhanced with respect to the inside atoms for a small sample bias voltage, while such an enhancement was not observed at the atoms on the armchair edge. This result provides an experimental evidence of spatially (at the zigzag edge) and energetically (at the Fermi level) loc…
Prospects for the quantum control of electrons in the silicon quantum computer architecture are considered theoretically. In particular, we investigate the feasibility of shuttling donor-bound electrons between the impurity in the bulk and the Si-SiO2 interface by tuning an external electric field. We calculate the shuttling time to range from sub-picoseconds to nanoseconds depending on the distance (~ 10-50 nm) of the donor from the interface. Our results establish that quantum control in such nanostructure architectures could, in principle, be achieved.
High-density magnetic memories are key components in spintronics, quantum computing, and energy-efficient electronics. Reduced dimensionality and magnetic domain stability at the nanoscale are essential for the miniaturization of magnetic storage units. Yet, inducing magnetic order, and selectively tuning spin-orbital coupling at specific locations have remained challenging. Here we demonstrate the construction of switchable magnetic nano-islands in a nonmagnetic matrix based on cobaltite homo-structures. The magnetic and electronic states are laterally modified by epitaxial strain, which is r…
We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from the tunnelling to the shuttling regime, thus extending the previously found classical results to the quantum domain. Further, a new dynamical regime is discovered, where the shuttling is driven exclusively by the quantum noise.
The energetics of thin elongated ferromagnetic nano-islands is considered for some different shapes, aspect ratios, and applied magnetic field directions. These nano-island particles are important for artificial spin-ice materials. For low temperature, the magnetic internal energy of an individual particle is evaluated numerically as a function of the direction of a particle's net magnetization. This leads to estimations of effective anisotropy constants for (1) the easy axis along the particle's long direction, and (2) the hard axis along the particle's thin direction. A spin relaxation algor…
We observe field emission from an isolated nano-machined gold island. The island is able to mechanically oscillate between two facing electrodes, which provide recharging and detection of the emission current. We are able to trace and reproduce the transition from current flow through a rectangular tunneling barrier to the regime of field emission. A theoretical model via a master-equation reproduces the experimental data and shows deviation from the Fowler-Nordheim description due to the island's electric isolation.
We study the low temperature electrical transport behaviour of a silicon single electron transistor. The island and leads are defined by patterned phosphorus doped regions achieved by ion implantation through a polymer resist mask. In the device a 50 nm diameter island, containing ~600 donors and having a metallic density of states, is separated from source and drain leads by undoped silicon tunnel barriers. The central island and tunnel barriers are covered by a surface gate in a field effect transistor geometry allowing the coupling between the leads and island to be controlled. Coulomb bloc…
X-ray magnetic circular dichroism (XMCD) measurements of iron nano-islands grown on graphene and covered with a Au film for passivation reveal that the oxidation through defects in the Au film spontaneously leads to the formation of magnetite nano-particles (i.e, $Fe_3$$O_4$). The Fe nano-islands (20 and 75 monolayers; MLs) are grown on epitaxial graphene formed by thermally annealing 6H-SiC(0001) and subsequently covered, in the growth chamber, with nominal 20 layers of Au. Our X-ray absorption spectroscopy and XMCD measurements at applied magnetic fields show that the thin film (20 ML) is to…
We systematically address superconductivity of Pb nano-islands with different thicknesses and lateral sizes via a scanning tunneling microscopy/spectroscopy. Reduction of the superconducting gap is observed even when the island is larger than the bulk coherence length and becomes very fast below ~ 50 nm lateral size. The suppression of gap with size depends to a good approximation only on the volume of the island and is independent of its shape. Theoretical analysis indicates that the universal quenching behavior is primarily manifested by the mean number of electronic orbitals within the pair…
In the presence of Rashba spin-orbit coupling, magnetic field can drive a proximitized nanowire into a topological superconducting phase. We study transport properties of such nanowires in the Coulomb blockade regime. The associated with the topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire - a non-local signature of topological superconductivity. In this work, we focus on the case of strong hybridization of the Majorana modes with the normal leads. The induced by hybridization broadening of the Ma…
Ultrathin MgO films on Mo(100) with a thickness up to 12 ML are studied by scanning tunneling microscopy and spectroscopy at room temperature. The spatial variation of the work function within the MgO film is mapped by field emission resonance states (Gundlach oscillations) using dz/dU spectroscopy. We found circular spots with significantly reduced work function (DeltaPhi=0.6 eV), which are assigned to charged defects within the MgO film. On top of the MgO films, small Co cluster are deposited with an average contact area of 4 nm^2. These islands exhibit Coulomb oscillations in dI/dU spectra …
We consider a combined nanomechanical-supercondcuting device that allows the Cooper pair tunneling to interfere with the mechanical motion of the middle superconducting island. Coupling of mechanical oscillations of a superconducting island between two superconducting leads to the electronic tunneling generate a supercurrent which is modulated by the oscillatory motion of the island. This coupling produces alternating finite and vanishing supercurrent as function of the superconducting phases. Current peaks are sensitive to the superconducting phase shifts relative to each other. The proposed …
We consider the motion of and Josephson current through a mechanically oscillating superconducting island asymmetrically embedded in a Josephson junction. The electromechanical coupling is provided by distance dependent tunneling rates between the electrodes and the island. The system asymmetry, resulting from the geometrical configuration, leads, for weak coupling, to an equation of the mechanical motion that reduces to the well-known Duffing equation. At zero bias voltage the island motion is determined by the homogenous Duffing equation that opens up two separate regions of solutions depend…
We present controlled growth of c(2$\times$2)N islands on the (100) surface of Cu$_3$Au, which can be used as an insulating surface template for manipulation of magnetic adatoms. Compared to the commonly used Cu(100)/c(2$\times$2)N surface, where island sizes do not exceed several nanometers due to strain limitation, the current system provides better lattice matching between metal and adsorption layer, allowing larger unstrained islands to be formed. We show that we can achieve island sizes ranging from tens to hundreds of nanometers, increasing the potential building area by a factor 10$^3$.…
We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a …
We have determined the magnetic properties of epitaxially grown Dy islands on graphene/SiC(0001) that are passivated by a gold film (deposited in the ultra-high vacuum growth chamber) for {\it ex-situ} X-ray magnetic circular dichroism (XMCD). Our sum-rule analysis of the Dy $M_{4,5}$ XMCD spectra at low temperatures ($T=15$ K) as a function of magnetic field assuming Dy$^{3+}$ (spin configuration $^6H_{15/2}$) indicate that the projection of the magnetic moment along an applied magnetic field of 5 T is 3.5(3) $μ_B$. Temperature dependence of the magnetic moment (extracted from the $M_5$ XMCD …
SiGe islands are used to induce tensile strain in the Si channel of Field Effect Transistors to achieve larger transconductance and higher current driveabilities. We report on x-ray diffraction experiments on a single fully-processed and functional device with a TiN+Al gate stack and source, gate, and drain contacts in place. The strain fields in the Si channel were explored using an x-ray beam focused to 400 nm diameter combined with finite element simulations. A maximum in-plane tensile strain of about 1% in the Si channel was found, which is by a factor of three to four higher than achievab…
Growth of narrow-neck, epitaxial as well as non-epitaxial and nearly spherical Ge islands on air-exposed Si(111)-(7\times7) surfaces has been investigated by in-situ scanning tunnelling microscopy (STM) and ex-situ high resolution cross-sectional transmission electron microscopy (HRXTEM). A thin oxide is formed on Si(111)-(7\times7) surfaces via air exposure. Ge islands are grown on this oxide. STM measurements reveal the growth of very small (~2 nm diameter) Ge islands with a high number density of about 1.8\times10^12 cm-2. The island size has been found to depend on the amount of deposited …
Conductive ferroelectric domain walls--ultra-narrow and configurable conduction paths, have been considered as essential building blocks for future programmable domain wall electronics. For applications in high density devices, it is imperative to explore the conductive domain walls in small confined systems while earlier investigations have hitherto focused on thin films or bulk single crystals, noting that the size-confined effects will certainly modulate seriously the domain structure and wall transport. Here, we demonstrate an observation and manipulation of conductive domain walls confine…
We develop a theory for the full counting statistics (FCS) for a class of nanoelectromechanical systems (NEMS), describable by a Markovian generalized master equation. The theory is applied to two specific examples of current interest: vibrating C60 molecules and quantum shuttles. We report a numerical evaluation of the first three cumulants for the C60-setup; for the quantum shuttle we use the third cumulant to substantiate that the giant enhancement in noise observed at the shuttling transition is due to a slow switching between two competing conduction channels. Especially the last example …
We explore transport across an ultra-small Quantum Hall Island (QHI) formed by closed quan- tum Hall edge states and connected to propagating edge channels through tunnel barriers. Scanning gate microscopy and scanning gate spectroscopy are used to first localize and then study a single QHI near a quantum point contact. The presence of Coulomb diamonds in the spectroscopy con- firms that Coulomb blockade governs transport across the QHI. Varying the microscope tip bias as well as current bias across the device, we uncover the QHI discrete energy spectrum arising from electronic confinement and…
A theory of a thermally induced single-electron "shuttling" instability in a magnetic nanomechanical device subject to an external magnetic field is presented in the Coulomb blockade regime of electron transport. The model magnetic shuttle device considered comprises a movable metallic grain suspended between two magnetic leads, which are kept at different temperatures and assumed to be fully spin polarized with antiparallel magnetizations. For a given temperature difference shuttling is found to occur for a region of external magnetic fields between a lower and an upper critical field strengt…
Transmission electron microscopy (TEM) study on morphological changes in gold nanostructures deposited on Si (100) upon annealing under different vacuum conditions has been reported. Au thin films of thickness ~2.0 nm were deposited under high vacuum condition (with the native oxide at the interface of Au and Si) using thermal evaporation. In-situ, high temperature (from room temperature (RT) to 850\degreeC) real time TEM measurements showed the evaluation of gold nanoparticles into rectangular/square shaped gold silicide structures. This has been attributed to selective thermal decomposition …
We have used soft x-ray photoemission electron microscopy to image the magnetization of single domain La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ nano-islands arranged in geometrically frustrated configurations such as square ice and kagome ice geometries. Upon thermal randomization, ensembles of nano-islands with strong inter-island magnetic coupling relax towards low-energy configurations. Statistical analysis shows that the likelihood of ensembles falling into low-energy configurations depends strongly on the annealing temperature. Annealing to just below the Curie temperature of the ferromagnetic film (…
We demonstrate the proof of principle for a ternary adder using silicon metal-on-insulator single electron transistors (SET). Gate dependent rectifying behavior of a single electron transistor results in a robust three-valued output as a function of the potential of the SET island. Mapping logical, ternary inputs to the three gates controlling the potential of the SET island allows us to perform complex, inherently ternary operations, on a single transistor.
We investigate instability and dynamical properties of nanoelectromechanical systems represented by a single-electron device containing movable quantum dot attached to a vibrating cantilever via asymmetric tunnel contact. The Kondo resonance in electron tunneling between source and shuttle facilitates self-sustained oscillations originated from strong coupling of mechanical and electronic/spin degrees of freedom. We analyze stability diagram for two-channel Kondo shuttling regime due to limitations given by the electromotive force acting on a moving shuttle and find that the saturation amplitu…
We report the absorption/transmission properties of thin copper films slightly below the percolation limit produced by laser ablation; these samples show randomly positioned islands. Two types of films are grown: in the first type, copper is deposited on glass, and it is shown that as the amount of deposited copper approaches the percolation limit, the samples show enhanced light transmission; in the second set of samples, made of TiO$_2$/Cu/TiO$_2$ layers, the presence of titanium oxide inhibits light transmission enhancement, even though the same amount of copper has been deposited compared …
Using scanning tunneling microscopy and spectroscopy, we demonstrate that the adsorption of a minute amount of Cs on a Pb mesa grown in the quantum regime can induce dramatic morphological changes of the mesa, characterized by the appearance of populous monatomic-layer-high Pb nano-islands on top of the mesa. The edges of the Pb nano-islands are decorated with Cs adatoms, and the nano-islands preferentially nucleate and grow on the quantum mechanically unstable regions of the mesa. Furthermore, first-principles calculations within density functional theory show that the Pb atoms forming these …
We investigate electron shuttling in three-terminal nanoelectromechanocal device built on a movable metallic rod oscillating between two drains. The device shows a double-well shaped electromechanical potential tunable by a source-drain bias voltage. Four stationary regimes controllable by the bias are found for this device: (i) single stable fixed point, (ii) two stable fixed points, (iii) two limiting cycles, and (iv) single limiting cycle. In the presence of perpendicular magnetic field the Lorentz force makes possible switching from one electromechanical state to another. The mechanism of …
C$_3$N is a recently discovered 2D layered material structurally similar to graphene, which has demonstrated immense prospect for future nanoelectronics. In this work, we have designed and investigated the operation and performance of a C$_3$N island single electron transistor (SET) for the first time. Using First-principles based calculations, we investigated the effect of various molecular adsorptions on the electronic and conduction behaviour of the SET. C$_3$N was found to be the perfect host material for capturing CO$_2$. The charge stability diagram carries the signature of different mol…
Electrical contacts between nano-engineered systems are expected to constitute the basic building blocks of future nano-scale electronics. However, the accurate characterization and understanding of electrical contacts at the nano-scale is an experimentally challenging task. Here we employ low-temperature scanning tunneling spectroscopy to investigate the conductance of individual nano-contacts formed between flat Pb islands and their supporting substrates. We observe a suppression of the differential tunnel conductance at small bias voltages due to dynamical Coulomb blockade effects. The diff…
Dispersive charge sensing is realized in hybrid semiconductor-superconductor nanowires in gate-defined single- and double-island device geometries. Signal-to-noise ratios (SNRs) were measured both in the frequency and time domain. Frequency-domain measurements were carried out as a function of frequency and power and yield a charge sensitivity of $1 \times 10^{-3} e/\sqrt{\rm Hz}$ for an 11 MHz measurement bandwidth. Time-domain measurements yield SNR > 1 for 20 $μ$s integration time. At zero magnetic field, photon-assisted tunneling was detected dispersively in a double-island geometry, indic…
We have employed spin-polarized scanning tunneling microscopy and Monte-Carlo simulations to investigate the effect of lateral confinement onto the nanoskyrmion lattice in Fe/Ir(111). We find a strong coupling of one diagonal of the square magnetic unit cell to the close-packed edges of Fe nanostructures. In triangular islands this coupling in combination with the mismatching symmetries of the islands and of the square nanoskyrmion lattice leads to frustration and triple-domain states. In direct vicinity to ferromagnetic NiFe islands, the surrounding skyrmion lattice forms additional domains. …
In this work we study the effect of engineered disorder on the local magnetic response of proximity coupled superconducting island arrays by comparing scanning Superconducting Quantum Interference Device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low l…
Nano-magnetic systems of artificially shaped ferromagnetic islands, recently became a popular subject due to their current and potential applications in spintronics, magneto-photonics and superconductivity. When the island size is close to the exchange length of magnetic material (around 15 nm), its magnetic structure becomes markedly different. It determines both static and dynamic magnetic properties of elements, but strongly depends on their shape and size. Here we map this dependence for circular cylindrical islands of a few exchange lengths in size. We outline the region of metastability …
The local spin polarisation (LSP) of electrons in two typical semiconductor nanowires under the modulation of Rashba spin-orbit interaction (SOI) is investigated theoretically. The influence of both the SOI- and structure-induced bound states on the LSP is taken into account via the spin-resolved lattice Green function method. It is discovered that high spin-density islands with alternative signs of polarisation are formed inside the nanowires due to the interaction between the bound states and the Rashba effective magnetic field. Further study shows that the spin-density islands caused by the…
We consider a single electron transistor where the central island can oscillate. It has been shown that for weak coupling of the elastic and electric degrees of freedom the position of the island fluctuates with a small variation of the current through the device. In this paper we consider the strong coupling limit. We show that the system undergoes a static mechanical instability that is responsible for the opening of a gap in the current voltage characteristics even at the degeneracy point. We provide an analytical description of the transition point. We also discuss how the mechanical natur…
A quantum shuttle is an archetypical nanoelectromechanical device, where the mechanical degree of freedom is quantized. Using a full-scale numerical solution of the generalized master equation describing the shuttle, we have recently shown [Novotný {\it et al.}, Phys. Rev. Lett. {\bf 92}, 248302 (2004)] that for certain limits of the shuttle parameters one can distinguish three distinct charge transport mechanisms: (i) an incoherent tunneling regime, (ii) a shuttling regime, where the charge transport is synchronous with the mechanical motion, and (iii) a coexistence regime, where the device s…
The discretization of the electronic structure of nanometer-size solid systems due to quantum confinement and the concomitant modification of their physical properties is one of the cornerstones for the development of Nanoscience and Nanotechnology. In this letter we demonstrate that Bragg scattering of Cu(111) surface state electrons by the periodic arrangement of tetracyanoquinodimethane (TCNQ) molecules at the edges of self-assembled molecular islands, discretizes the possible values of the electron momentum parallel to the island edge. The electronic structure consists thus of a discrete n…
An in situ measurement of spin transport in a graphene nonlocal spin valve is used to quantify the spin current absorbed by a small (250 nm $\times$ 750 nm) metallic island. The experiment allows for successive depositions of either Fe or Cu without breaking vacuum, so that the thickness of the island is the only parameter that is varied. Furthermore, by measuring the effect of the island using separate contacts for injection and detection, we isolate the effect of spin absorption from any change in the spin injection and detection mechanisms. As inferred from the thickness dependence, the eff…
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known relaxation algorithm for solving the Poisson equation in two dimensions is generalized to 3D. In addition,all charges on the system, free as well as induced charges,are determined accurately and self-consistently to satisfy the desired boundary conditions. This allows the straightforward calculation of the potential on the outer boundary using the free space electr…
Richardson model with complex level structure and spin-orbit coupling for hybrid superconducting islands: stepwise suppression of pairing and magnetic pinning
