Where, and how, does energy dissipation of electrical energy take place in a ballistic wire? Fully two decades after the advent of the transmissive phenomenology of electrical conductance, this deceptively simple query remains unanswered. We revisit the quantum kinetic basis of dissipation and show its power to give a definitive answer to our query. Dissipation leaves a clear, quantitative trace in the non-equilibrium current noise of a quantum point contact; this signature has already been observed in the laboratory. We then highlight the current state of accepted understandings in the light of well-known yet seemingly contradictory measurements. The physics of mesoscopic transport rests not in coherent carrier transmission through a perfect and dissipationless metallic channel, but explicitly in their dissipative inelastic scattering at the wire's interfaces and adjacent macroscopic leads.
We investigate quantum fluctuations in thin superconducting wires. We demonstrate that quantum phase slips dominate the system behavior at low temperatures and are well in the measurable range for sufficiently thin wires. We discuss the effect of dissipation, predict a new quantum superconductor-to-metal (insulator) phase transitions for wires with thicknesses in the 10-nm range, evaluate the resistance R(T) of such wires and compare our results with recent experimental findings.
We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi liquid leads) or non-interacting electrons. We show that for a given matrix M, the eigenvalues of M^T M characterize the dissipation, and the eigenvectors identify the combinations of bias voltages which need to be applied to the different wires in order to maximize the dissipation associated …
Photo-induced charge separation in nanowires or molecular wires had been studied in previous experiments and simulations. Most researches deal with the carrier diffusions with the classical phenomenological models, or the static energy levels by quantum mechanics calculations. Here we give a dynamic quantum investigation on the charge separation and dissipation in molecule wires. The method is based on the time-dependent non-equilibrium Green's function theory. Polyacetylene chain and poly-phenylene are used as model systems with a tight-binding Hamiltonian and the wide band limit approximatio…
We report on the reinforcement of superconductivity in a system consisting of a narrow superconducting wire weakly coupled to a diffusive metallic film. We analyze the effective phase-only action of the system by a perturbative renormalization-group and a self-consistent variational approach to obtain the critical points and phases at T=0. We predict a quantum phase transition towards a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. We discuss implications for the DC resistivity of the wire.
We propose a general design of a metallic double-nanowire structure which may support an equilibrium dissipationless electric current in the presence of magnetic field. The structure consists of a compact wire element of a specific shape, which is periodically extended in one spatial dimension. Topologically, each wire element is equivalent to a ring, which supports a dissipationless current in the presence of magnetic flux similarly to the persistent electric current in a normal metal nanoring. Geometrically, each wire element breaks spatial inversion symmetry so that the equilibrium electric…
In many situations, the dual-purpose heater/thermometer wires used in the three-omega method, one of the most precise and sensitive techniques for measuring the thermal conductivity of thin films and interfaces, must include bends and curves to avoid obstructions on the surface of a sample. Although the three-omega analysis assumes that the heating wire is infinitely long and straight, recent experimental work has demonstrated that in some cases curved-wire geometries can be used without introducing detectable systematic error. We describe a general numerical method that can be used to calcula…
We investigate the effects of Majorana bound states on the ac response of a quantum resistor-capacitor circuit which is composed of a topological superconducting wire whose two ends are tunnel-coupled to a lead and a spinless quantum dot, respectively. The Majorana states formed at the two ends of the wire are found to suppress completely or enhance greatly the dissipation, depending on the strength of the overlap between two Majorana modes and/or the dot level. We compare the relaxation resistance and the quantum capacitance of the system with those of non-Majorana counterparts to find that t…
We investigate the role of local heating and forces on ions in the stability of current-carrying aluminum wires. We find that heating increases with wire length due to a red shift of the frequency spectrum. Nevertheless, the local temperature of the wire is relatively low for a wide range of biases provided good thermal contact exists between the wire and the bulk electrodes. On the contrary, current-induced forces increase substantially as a function of bias and reach bond-breaking values at about 1 V. These results suggest that local heating promotes low-bias instabilities if dissipation int…
The switching dynamics of a multiferroic nanomagnetic NAND gate with fan-in/fan-out is simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation while neglecting thermal fluctuation effects. The gate and logic wires are implemented with dipole-coupled 2-phase (magnetostrictive/piezoelectric) multiferroic elements that are clocked with electrostatic potentials of ~50 mV applied to the piezoelectric layer generating 10 MPa stress in the magnetostrictive layers for switching. We show that a pipeline bit throughput rate of ~ 0.5 GHz is achievable with proper magnet layout and sinusoidal four…
We analyze the operation of the wireless single-electron logic family based on single-electron-parametron cells. Parameter margins, energy dissipation, and the error probability are calculated using the orthodox theory of single-electron tunneling. Circuits of this family enable quasi-reversible computation with energy dissipation per bit much lower than the thermal energy, and hence may circumvent one of the main obstacles faced by ultradense three-dimensional integrated digital circuits.
In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire have been explained by coherent and dissipationless transmission of individual electrons across a one-dimensional barrier. This leaves untouched the central issue of conduction: a quantum wire, albeit ballistic, has finite resistance and so must dissipate energy. Exactly HOW does the quantum wire shed its excess electrical energy? We show that the answer is provided, uniquely, by many-body quantum kinetics. Not only does this inevitably lead to universal quantization of the conductance, in spite of dissipation;…
We first present a summary of recent results concerning the phononic energy transport properties of mesoscopic, suspended dielectric wires. We then discuss some related open problems concerning the fundamental lower limits on the vibrational damping rates of submicron-sized cantilever structures and also the possibility to create and detect quantum superpositions of spatially separated states for such structures.
The dissipation induced by a metallic gate on the low-energy properties of interacting 1D electron liquids is studied. As function of the distance to the gate, or the electron density in the wire, the system undergoes a quantum phase transition from the Tomonaga-Luttinger liquid state to two kinds of dissipative phases, one of them with a finite spatial correlation length. We also define a dual model, which describes an attractive one dimensional metal with a Josephson coupling to a dirty metallic lead.
Electrical transport measurements were made on single-crystal Sn nanowires to understand the intrinsic dissipation mechanisms of a one-dimensional superconductor. While the resistance of wires of diameter larger than 70 nm drops precipitately to zero at Tc near 3.7 K, a residual resistive tail extending down to low temperature is found for wires with diameters of 20 and 40 nm. As a function of temperature, the logarithm of the residual resistance appears as two linear sections, one within a few tenths of a degree below Tc and the other extending down to at least 0.47 K, the minimum temperature…
One of the best known causes of dissipation in ac driven quantum systems stems from photon absorption. Dissipation can also be caused by the retarded response to the time-dependent excitation, and in general gives insight into the system's relaxation times and mechanisms. We address the dissipation in a mesoscopic normal wire with superconducting contacts, that sustains a supercurrent at zero frequency and that may be expected to remain dissipationless at frequency lower than the superconducting gap. We probe the high frequency linear response of a Normal/Superconductor ring to a time-dependen…
We develop a quantum theory of the nonlinear interaction between intense surface acoustic waves and electrons of a quantum well in the regime of moving quantum wires and dots. The quantum nonlinear interaction qualitatively differs from the classical one. In a system of electron wires driven by an acoustic wave the sound attenuation strongly decreases with increasing the sound intensity. However, even in the quantum limit the sound attenuation in the electron system remains nonzero due to residual scattering by impurities in the lowest subband. In the case of electron dots formed by two waves …
Mechanical resonators made with monolithic piezoelectric quartz crystals are promising for studying new physical phenomena. High mechanical quality factors ($Q$) exhibited by the mm-sized quartz resonators make them ideal for studying weak couplings or long timescales in the quantum regime. However, energy losses through mechanical supports pose a serious limiting factor for obtaining high quality factors. Here we investigate how the $Q$ of quartz resonators at deep cryogenic temperatures can be limited by several types of losses related to anchoring. We first introduce means to reduce the mec…
A prominent signature of Majorana bound states is the exotic Josephson effects they produce, the classic example being a fractional Josephson current with 4πperiodicity in the phase difference across the junction. Recent work established that topological insulator edges support a novel `magneto-Josephson effect', whereby a dissipationless current exhibits 4π-periodic dependence also on the relative orientation of the Zeeman fields in the two banks of the junction. Here, we explore the magneto-Josephson effect in junctions based on spin-orbit coupled quantum wires. In contrast to the topologica…
Table of contents 1. Introduction 2. Non-Fermi-liquid features of Fermi liquids: 1D physics in higher dimensions 3. Dzyaloshinskii-Larkin solution of the Tomonaga-Luttinger model 4. Renormalization group for interacting fermions 5. Single impurity in a 1D system: scattering theory for interacting electrons 6. Bosonization solution 7. Transport in quantum wires 7.1 Conductivity and conductance 7.2 Dissipation in a contactless measurement 7.3 Conductance of a wire attached to reservoirs 7.4 Spin component of the conductance 7.5 Thermal conductance: Fabry-Perrot resonances of plasmons 8. Appendic…
The paper discusses mechanisms for decay of supercurrents in ultrathin superconducting wires driven by quantum fluctuations. We argue that momentum conservation strongly suppresses probability of such decay and estimate the rates for two decay channels: potential scattering of condensate due to the disorder and attenuation of the plasmon mode due to the presence of normal component, i.e., Ohmic losses. We find that while both mechanisms yield non-zero decay rates, their values are too small to provide any substantial contribution to the resistivity of the wires. The rate associated with the la…
The ability to carry electric current with zero dissipation is the hallmark of superconductivity. It is this very property which is used in applications from MRI machines to LHC magnets. But, is it indeed the case that superconducting order is incompatible with dissipation? One notable exception, known as vortex flow, takes place in high magnetic fields. Here we report observation of dissipative superconductivity in far more basic configurations: superconducting nanowires with superconducting leads. We provide evidence that in such systems, normal current may flow in the presence of supercondu…
We examine the local density of states of an impurity level or a quantum dot coupled to a fractional quantum Hall edge, or to the end of a single one-dimensional Luttinger-liquid lead. Effects of an Ohmic dissipative bath are also taken into account. Using both analytical and numerical techniques we show that, in general, the density of states exhibits power-law frequency dependence near the Fermi energy. In a substantial region of the parameter space it simply reflects the behavior of the tunneling density of states at the end of a Luttinger-liquid, and is insensitive either to the value of t…
The quantum transport of electrons in a wire of localized dots by hopping, interaction and dissipation is calculated and a representation by an equivalent RCL circuit is found. The exact solution for the electric-field induced currents allows to discuss the role of virtual currents to decay initial correlations and Bloch oscillations. The dynamical response function in random phase approximation (RPA) is calculated analytically with the help of which the static structure function and pair correlation function are determined. The pair correlation function contains a form factor from the Brillou…
We present the first study of superconducting nanowires shunted with an external resistor, geared towards understanding and controlling coherence and dissipation in nanowires. The dynamics is probed by measuring the evolution of the V-I characteristics and the distributions of switching and retrapping currents upon varying the shunt resistor and temperature. Theoretical analysis of the experiments indicates that as the value of the shunt resistance is decreased, the dynamics turns more coherent presumably due to stabilization of phase-slip centers in the wire and furthermore the switching curr…
