We extend quantum models of nanowire surface scattering to incorporate bulk resistivity and extract an expression for the increased resistivity due to surface roughness. To learn how to improve conductivity, we calculate conductivity degradation from individual wavelengths of surface roughness, and show how these can be convolved to give resistivity for arbitrary surfaces. We review measurements from Cu films and conclude that roughness at short wavelengths (less than 100 nm) dominates scattering, and that primarily specular scattering should be achievable for RMS roughness below about 0.7 nm.
The low-temperature electrical resistivity of corrugated semiconductor films is theoretically considered. Nanoscale corrugation enhances the electron-electron scattering contribution to the resistivity, resulting in a stepwise resistivity development with increasing corrugation amplitude. The enhanced electron scattering is attributed to the curvature-induced potential energy that affects the motion of electrons confined to a thin curved film. Geometric conditions and microscopic mechanism of the stepwise resistivity are discussed in detail.
We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, non-uniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.
We study the interaction between two closely spaced but electrically isolated quasi-one-dimensional electrical wires by a drag experiment. In this work we experimentally demonstrate the generation of current in an unbiased (drag) wire, which results from the interactions with a neighboring biased (drive) wire. The direction of the drag current depends on the length of the one-dimensional wire with respect to the position of the barrier in the drag wire. When we additionally form a potential barrier in the drive wire, the direction of the drag current is determined by the relative position of t…
The effect of domain walls on electron transport has been investigated in microfabricated Fe wires (0.65 to 20 $μm$ linewidths) with controlled stripe domains. Magnetoresistance (MR) measurements as a function of domain wall density, temperature and the angle of the applied field are used to determine the low field MR contributions due to conventional sources in ferromagnetic materials and that due to the erasure of domain walls. A negative domain wall contribution to the resistivity is found. This result is discussed in light of a recent theoretical study of the effect of domain walls on quan…
We consider a honeycomb network built of quantum wires, with each node of the network having a Y-junction of three wires with a ring through which flux can be inserted. The junctions are the basic circuit elements for the network, and they are characterized by 3 x 3 conductance tensors. The low energy stable fixed point tensor conductances result from quantum effects, and are determined by the strength of the interactions in each wire and the magnetic flux through the ring. We consider the limit where there is decoherence in the wires between any two nodes, and study the array as a network of …
We describe a field-theoretic approach to calculate quantum shot noise in nanoscale conductors from first principles. Our starting point is the second-quantization field operator to calculate shot noise in terms of single quasi-particle wavefunctions obtained self-consistently within density functional theory. The approach is valid in both linear and nonlinear response and is particularly suitable in studying shot noise in atomic-scale conductors. As an example we study shot noise in Si atomic wires between metal electrodes. We find that shot noise is strongly nonlinear as a function of bias a…
We study the transport properties of a long non-uniform quantum wire where the electron-electron interactions and the density vary smoothly at large length scales. We show that these inhomogeneities lead to a finite resistivity of the wire, due to a weak violation of momentum conservation in the collisions between electrons. Estimating the rate of change of momentum associated with non-momentum-conserving scattering processes, we derive the expression for the resistivity of the wire in the regime of weakly interacting electrons and find a contribution linear in temperature for a broad range of…
The temperature dependence of the thermal boundary resistivity is investigated in glass-embedded Ag particles of radius 4.5 nm, in the temperature range from 300 to 70 K, using all-optical time-resolved nanocalorimetry. The present results provide a benchmark for theories aiming at explaining the thermal boundary resistivity at the interface between metal nanoparticles and their environment, a topic of great relevance when tailoring thermal energy delivery from nanoparticles as for applications in nanomedicine and thermal management at the nanoscale
Resistivity augmentation in nanoscale metal interconnects is a performance limiting factor in integrated circuits. Here we present calculations of electron scattering and transmission at the interface between Cu interconnects and their barrier layers, in this case Ta. We also present a semiclassical model to predict the technological impact of this scattering and find that a barrier layer can significantly decrease conductivity, consistent with previously published measurements.
We study the resistivity scaling in nanometer-sized metallic wires due to surface roughness and grain-boundaries, currently the main cause of electron scattering in nanoscaled interconnects. The resistivity has been obtained with the Boltzmann transport equation, adopting the relaxation time approximation (RTA) of the distribution function and the effective mass approximation for the conducting electrons. The relaxation times are calculated exactly, using Fermi's golden rule, resulting in a correct relaxation time for every sub-band state contributing to the transport. In general, the relaxati…
We report on the electrical characterisation of a series of thin chromium oxide films, grown by dc sputtering, to evaluate their suitability for use as on-chip resistors in nanoelectronics. By increasing the level of oxygen doping, the room-temperature sheet resistance of the chromium oxide films was varied from 28$Ω/ \square$ to 32.6k$Ω/ \square$. The variation in resistance with cooling to 4.2K in liquid helium was investigated; the sheet resistance at 4.2K varied with composition from 65$Ω/ \square$ to above 20G$Ω/ \square$. All of the films measured displayed ohmic behaviour at all measure…
We study the transport properties of nanoscale superconducting (S) devices in which two superconducting electrodes are bridged by two parallel ferromagnetic (F) wires, forming an SFFS junction with a separation between the two wires less than the superconducting coherence length. This allows crossed Andreev reflection to take place. We find that the resistance as a function of temperature exhibits behavior reminiscent of the re-entrant effect and, at low temperatures and excitation energies below the superconducting gap, the resistance corresponding to antiparallel alignment of the magnetizati…
We address an unexpectedly large rectification using a simple quantum wire with correlated site potentials. The external electric field, associated with voltage bias, leads to unequal charge currents for two different polarities of external bias and this effect is further enhanced by incorporating the asymmetry in wire-to-electrode coupling. Our calculations suggest that in some cases almost cent percent rectification is obtained for a wide bias window. This performance is valid against disorder configurations and thus we can expect an experimental verification of our theoretical analysis in n…
We study Coulomb drag in a pair of parallel one-dimensional electron systems within the framework of the Tomanaga-Luttinger model. We find that Coulomb coupling has a much stronger effect on one dimensional wires than on two-dimensional layers: At zero temperature the trans-resistivity {\em diverges}, due to the formation of locked charge density waves. At temperature well above a cross-over temperature $T^*$ the trans-resistivity follows a power law $ρ\propto T^x$, where the interaction-strength dependent exponent $x$ is determined by the Luttinger Liquid parameter $K_{c-}$ of the relative ch…
We show that electron--electron scattering gives a positive contribution to the resistivity of ballistic multimode wires whose width is much smaller than their length. This contribution is not exponentially small at low temperatures and therefore may be experimentally observable. It scales with temperature as $T^2$ for three-dimensional channels and as $T^{5/2}$ for two-dimensional ones.
We present an overview of current-induced effects in nanoscale conductors with emphasis on their description at the atomic level. In particular, we discuss steady-state current fluctuations, current-induced forces, inelastic scattering and local heating. All of these properties are calculated in terms of single-particle wavefunctions computed using a scattering approach within the static density-functional theory of many-electron systems. Examples of current-induced effects in atomic and molecular wires will be given and comparison with experimental results will be provided when available.
Coupled-wire descriptions of unconventional quantum states in twisted nanostructures
Institute of Physics, Academia Sinica（中央研究院物理研究所）；National Center for Theoretical Sciences（国家理论科学中心）；Department of Electronics and Electrical Engineering, National Yang Ming Chiao Tung University（国立阳明交通大学电子电气工程学系）
We predict that conduction electrons in a semiconductor film containing a centered square array of metal nanowires normal to its plane are bound in quantum states around the central wires, if a positive bias voltage is applied between the wires at the square vertices and these latter. We obtain and discuss the eigenenergies and eigenfunctions of two models with different dimensions. The results show that the eigenstates can be grouped into different shells. The energy differences between the shells is typically a few tens of meV, which corresponds to frequencies of emitted or absorbed photons …
We present an optical investigation of surface plasmon polaritons propagating along nanoscale Au-wires, lithographically defined on GaAs substrates. A two-axis confocal microscope was used to perform spatially and polarization resolved measurements in order to confirm the guiding of surface plasmon polaritons over lengths ranging from $5-20 μm$ along nanowires with a lateral dimension of only $\approx 100 nm$. Finite difference time domain simulations are used to corroborate our experimental observations and highlight the potential to couple proximal quantum dot emitters to propagating plasmon…
The resistivity due to a domain wall in ferromagnetic metallic wire is calculated based on the linear response theory. The interaction between conduction electrons and the wall is expressed in terms of a classical gauge field which is introduced by the local gauge transformation in the electron spin space. It is shown that the wall contributes to the decoherence of electrons and that this quantum correction can dominate over the Boltzmann resisitivity, leading to a decrease of resisitivity by nucleation of a wall. The conductance fluctuation due to the motion of the wall is also investigated. …
Graphene nanoribbon interconnects are fabricated, and the extracted resistivity is compared to that of Cu. It is found that the average resistivity at a given line-width (18nm<W<52nm) is about 3X that of a Cu wire, whereas the best GNR has a resistivity comparable to that of Cu. The conductivity is found to be limited by impurity scattering as well as LER scattering; as a result, the best reported GNR resistivity is 3X the limit imposed by substrate phonon scattering. This study reveals that even moderate-quality graphene nanowires have the potential to outperform Cu for use as on-chip interco…
Three-dimensional topological insulators host surface states with linear dispersion, which manifest as a Dirac cone. Nanoscale transport measurements provide direct access to the transport properties of the Dirac cone in real space and allow the detailed investigation of charge carrier scattering. Here, we use scanning tunnelling potentiometry to analyse the resistance of different kinds of defects at the surface of a (Bi0.53Sb0.47)2Te3 topological insulator thin film. The largest localized voltage drop we find to be located at domain boundaries in the topological insulator film, with a resist…
We study the way back-scattering electron--electron interaction generates Coulomb drag between quantum wires with different densities. At low temperature $T$ the system can undergo a commensurate-- incommensurate transition as the potential difference $|W|$ between the two wires passes a critical value $Δ$, and this transition is reflected in a marked change in the dependence of drag resistivity on $W$ and $T$. At high temperature a density difference between the wires suppresses Coulomb drag induced by back scattering, and we use the Tomonaga--Luttinger model to study this suppression in deta…
Interaction between electron and acoustic phonon in an in-plane magnetic field induced gapped quantum wire with Rashba spin-orbit interaction is studied. We calculate acoustic phonon limited resistivity ($ρ$) and phonon-drag thermopower ($S_g$) due to two well known mechanisms of electron-phonon interaction namely, deformation potential (DP) and piezoelectric (PE) scattering. In the so called Bloch-Gruneisen temperature limit both $ρ$ and $S_g$ depend on temperature ($T$) in a power law fashion i.e. $ρ$ or $S_g\sim T^{ν_T}$. For resistivity, $ν_T$ takes the value $5$ and $3$ due to DP and PE s…
We study superconductivity suppression due to thermal fluctuations in disordered wires using the replica nonlinear $σ$-model ($NLσM$). We show that in addition to the thermal phase slips there is another type of fluctuations that result in a finite resistivity. These fluctuations are described by saddle points in $NLσM$ and cannot be treated within the Ginzburg-Landau approach. The contribution of such fluctuations to the wire resistivity is evaluated with exponential accuracy. The magnetoresistance associated with this contribution is negative.
Micrometer width and nanometer thick wires with different shapes were produced $\approx 3~\upmu$m below the surface of a diamond crystal using a microbeam of He$^+$ ions with 1.8~MeV energy. Initial samples are amorphous and after annealing at $T\approx 1475$~K, the wires crystallized into a graphite-like structures, according to confocal Raman spectroscopy measurements. The electrical resistivity at room temperature is only one order of magnitude larger than the in-plane resistivity of highly oriented pyrolytic bulk graphite and shows a small resistivity ratio($ρ(2{\rm K})/ρ(315{\rm K}) \appr…
A brief review of the nanoscale free-electron model of metal nanowires is presented. This continuum description of metal nanostructures allows for a unified treatment of cohesive and conducting properties. Conductance channels act as delocalized chemical bonds whose breaking is responsible for jumps in the conductance and force oscillations. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of a nanowire, and much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing fac…
The low temperature negative domain wall (DW) contribution to the resistivity observed in expitaxial Fe microstructures has been investigated as a function of film thickness. The DW spin structure changes from Bloch to Neel-like with decreasing film thickness. Results suggest that an interplay between orbital effects in the internal magnetic fields near DWs and thin film surface scattering are at the origin of the observed negative wall contribution.
We report on the electrical and thermal transport properties of nickel nanoparticles with crystallite size from 23.1 to 1.3 nm. These nanoparticles show a systematic metal to insulator transition with the change in the conduction type from n to p type, colossal Seebeck coefficient, and ultralow thermal conductivity at 300 K as the crystallite size drops. The electrical resistivity analysis reveals a dramatic change in the electronic excitation spectrum indicating the opening of an energy gap, and cotunneling and Coulomb blockade of the charge carriers. Seebeck coefficient shows transport energ…
We have measured the resistances (and resistivities) of Ag and Cu nanowires of diameters ranging from 15nm to 200nm in the temperature range 4.2K-300K with the specific aim to assess the applicability of the Bloch-Grüneisen formula for electron phonon resistivity in these nanowires. The wires were grown within polymeric templates by electrodeposition. We find that in all the samples the resistance reaches a residual value at T=4.2K and the temperature dependence of resistance can be fitted to the Bloch-Grüneisen formula in the entire temperature range with a well defined transport Debye temper…
Electronically phase separated manganite wires are found to exhibit controllable metal-insulator transitions under local electric fields. The switching characteristics are shown to be fully reversible, polarity independent, and highly resistant to thermal breakdown caused by repeated cycling. It is further demonstrated that multiple discrete resistive states can be accessed in a single wire. The results conform to a phenomenological model in which the inherent nanoscale insulating and metallic domains are rearranged through electrophoretic-like processes to open and close percolation channels.
Single atom metallic wires of arbitrary length are of immense technological and scientific interest. We describe a novel silicon-only template enabling the self-organised growth of isolated micrometer long surface and subsurface single-atom chains. It consists of a one dimensional, defect-free reconstruction - the Haiku core, here revealed for the first time in details - self-assembled on hydrogenated Si(001) terraces, independent of any step edges. We discuss the potential of this Si-in-Si template as an appealing alternative to vicinal surfaces for nanoscale patterning.
We study the current through a quantum wire side coupled to a quantum dot, and compare it with the case of an embedded dot. The system is modeled by the Anderson Hamiltonian for a linear chain, with one atom either coupled to (side-dot) or substituted by (embedded dot) a magnetic impurity. For realistic (small) hopping of the dot to the rest of the system, an exact relationship between both conductivities holds. We calculate the temperature dependence for moderate values of the Coulomb repulsion U using an interpolative perturbative scheme. For sufficiently large U and temperature greater than…
Accelerated Discovery of Topological Conductors for Nanoscale Interconnects
NORDITA, KTH Royal Institute of Technology and Stockholm University（北欧理论粒子物理研究所，皇家理工学院和斯德哥尔摩大学）；University of Connecticut（康涅狄格大学）；Northwestern University（西北大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）；National Yang Ming Chiao Tung University（国立阳明交通大学）；Academia Sinica（中央研究院）
The increasing resistance of Cu interconnects for decreasing dimensions is a major challenge in continued downscaling of integrated circuits beyond the 7-nm technology node as it leads to unacceptable signal delays and power consumption in computing. The resistivity of Cu increases due to electron scattering at surfaces and grain boundaries of the interconnects at the nanoscale. Topological semimetals, owing to their topologically protected surface states and suppressed electron backscattering, are promising material candidates to potentially replace current Cu interconnects as low-resistance …
We theoretically study the Coulomb drag resistivity and plasmon modes behavior for a system composed of two parallel p-type doped GaS monolayers with Mexican-hat valence energy band using the Boltzmann transport theory formalism. We investigate the effect of temperature,$\ T$, carrier density,$\ p$, and layer separation,$\ d$, on the plasmon modes and drag resistivity within the energy-independent scattering time approximation. Our results show that the density dependence of plasmon modes can be approximated by$\ p^{0.5}$. Also, the calculations suggest a$\ d^{0.2}$ and a$\ d^{0.1}$ dependenci…
We report measurements of the four terminal temperature dependent resistance of narrow Au wires implanted with ~100 ppm Fe impurities in proximity to superconducting Al films. The wires show an initial decrease in resistance as the temperature is lowered through the superconducting transition of the Al films, but then show an increase in resistance as the temperature is lowered further. In contrast to the case of pure Au wires in contact with a superconducting film, the resistance at the lowest temperatures rises above the normal state resistance. Analysis of the data shows that, in addition t…
We investigate the influence of the chemical potential mismatch $Δ$ (different electron densities) on Coulomb drag between two parallel ballistic quantum wires. For pair collisions, the drag resistivity $ρ_{\rm D}(Δ)$ shows a peculiar anomaly at $Δ=0$ with $ρ_{\rm D}$ being finite at $Δ=0$ and vanishing at any nonzero $Δ$. The "bodyless" resonance in $ρ_{\rm D}(Δ)$ at zero $Δ$ is only broadened by processes of multi-particle scattering. We analyze Coulomb drag for finite $Δ$ in the presence of both two- and three-particle scattering within the kinetic equation framework, focusing on a Fokker-P…
Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron model, which predicts cylinders in certain intervals of radius to be linearly unstable. In this paper, I study how a small, localized perturbation of such an unstable wire grows exponentially and propagates along the wire with a well-defined front. The front is found to be pulled, and forms a coherent pattern behind it. It is well described by a linear marginal s…
