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 with the junction. We use our analysis to propose and study some microscopic models of a dissipative junction which employ the edge states of a quantum Hall liquid. These models realize some specific forms of the M-matrix whose entries depends on the tunneling amplitudes between the different edges.
We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear $I(V)$ curve. We also demonstrate that all quantities measured under a coherent time dependent bias can be reconstructed from their dc counterpart with a photo-assisted tunneling relation. We confirm these predictions by implementing the circuit and measuring…
Heat dissipation and its relation to thermopower in single-molecule junctions
受最近实验的启发[Lee et al.Nature 498，209（2013）]，我们在此提出了载流单分子结中焦耳加热的详细理论分析。通过结合量子输运的Landauer方法与从头计算，我们展示了如何加热的分子结的电极是由它的电子结构。特别是，我们表明，在一般情况下，热量是不相等的结的两个电极中耗散，它取决于偏置极性（或等效的电流方向）。这些加热不对称性与结的热电势密切相关，因为这两个量都由非常相似的原理控制。我们通过分析基于具有不同锚定基团的苯衍生物的单分子结来说明这些想法。热耗散和热功率之间的密切关系提供了探索基本现象的一般策略，如珀尔帖效应或量子干涉效应对分子传输结焦耳加热的影响。
An integral part of scattering theory calculations in continuum quantum systems involves identifying appropriate boundary conditions in addition to writing down the correct Hamiltonian. In the simplest problem of scattering in one dimensional lattice, scattering due to an on-site potential and scattering due to an unequal bond (in otherwise translationally invariant lattice) give different results for scattering amplitudes. While the scattering problems in the continuum and the lattice models can be mapped to one another for scattering due to on-site potential, the equivalent continuum model f…
We present a theoretical study of the heat dissipation in single-molecule junctions. In order to investigate the heat dissipation in the electrodes and the relationship between the transmission spectra and the electronic structures, we consider a toy model that in which electrodes linked by a two-level molecular bridge. By using of the Landauer approach, we show how heat dissipation in the electrodes of a molecular junction is related to its transmission characteristics. We show that in general heat is not equally dissipated in the left and right electrodes of the junction and it depends on th…
We study time resolved transport properties of a $Y$-junction composed of interacting one-dimensional quantum wires using a bosonization approach. In particular, we investigate the AC conductivity of the $Y$-junction formed from finite length Tomonaga-Luttinger liquid wires based on a plasmon scattering approach for injected charge pulses of arbitrary shapes. In addition, we calculate the tunneling current and quantum noise of the $Y$-junction arising from point-like tunneling impurities at the junction, including finite temperature effects. Our results will be useful for designing nano-electr…
We calculate the tunneling density of states (TDOS) in a three wire junction of interacting spin-1/2 electrons, and find an anomalous enhancement of the TDOS in the zero bias limit, even for repulsive interactions for several bosonic fixed points. This enhancement is physically related to the reflection of holes from the junction for incident electrons, and it occurs only in the vicinity of the junction ($x < v_{\rm min}/2ω$ where $v_{\rm min}$ is the minimum of the velocity of charge or spin excitations and $ω$ is the bias frequency), crossing over to the bulk value which is always suppressed…
We explore the thermoelectric properties of gold atomic chains bridging gold electrodes by means of \textit{ab initio} and semi-empirical calculations, and heuristic reasoning. We predict the thermoelectric voltage induced by a temperature difference across such junctions to oscillate, repeatedly changing sign, as a function of the number of atoms $N$ making up the atomic chain. We also predict the amplitude of the oscillations to be proportional to $N$ for long atomic chains. Further we predict the thermoelectric voltage to change sign, in some cases, if the junction is stretched without chan…
We analyze the charge and thermal transport at a junction of interacting quantum wires close to equilibrium. Within the framework of Tomonaga-Luttinger liquids, we compute the thermal conductance for a wide class of boundary conditions and detail the physical processes leading to the breakdown of the Wiedemann-Franz law at the junction. We show how connecting external reservoirs to the quantum wires affects the conductance tensors close to the various fixed points of the phase diagram of the junction. We therefore distinguish two types of violation of the Wiedemann-Franz law: a "trivial" one, …
We consider a wire network of ferromagnetic impurities on the surface of an $s$-wave superconductor with strong Rashba spin-orbit interaction. Within the topological phase, zero-energy Majorana fermions appear at wire end-points as well as at junctions between an odd number of wire segments, while no low-energy states are present at junctions between an even number of wire segments, providing strong experimentally accessible signatures for Majorana fermions. We also investigate the quasiparticle energy gap with respect to varying the Rashba spin-orbit coupling and magnetic impurity strength.
We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a sp…
A systematic stability analysis of the renormalisation group flow for the normal-superconductor-normal junction of Luttinger liquid wires
本文研究了两个Luttinger液丝超导结两端电导的重整化群流。我们使用SU（4）群的生成元来计算与围绕该系统的各个固定点的重整化群流相关联的幂律，以生成表示与给定固定点S-矩阵的小偏差的S-矩阵的适当参数化（先前在Phys. Rev. B 77，155418（2008）中获得），然后我们进行全面的稳定性分析。特别地，对于透射、反射、Andreev反射和交叉Andreev反射为中间值的非平凡不动点，我们证明了系统有11个独立的方向可以被扰动，这些方向是相关的或不相关的，还有5个方向是边缘的.我们得到的幂律与这些相关和不相关的扰动。与双线电荷守恒结的情况不同，这里我们证明了存在幂律，它们是V（0）和V（2 k_{F}）的非线性函数（其中V（k）表示动量k处电子间相互作用势的傅里叶变换）。我们还得到了在这个固定点附近线性响应电导对偏压或温度的幂律依赖关系。
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…
Josephson junctions and superconducting wires when probed with current pulses exhibit stochastic switching from superconducting to a stable non-zero voltage state. Electrical current dependence of the switching probability (so called S-curve) or switching current distribution is a fingerprint of the physics governing the escape process. This work addresses the criterion of independent switching event in a series of switching experiments. Treating Josephson junction as an electrical coin with current-tuned switching probability we investigate effect of correlation between switching events on th…
We formulate and apply a low-energy transport theory for hybrid quantum devices containing junctions of topological superconductor (TS) wires and conventional normal (N) or superconducting (S) leads. We model TS wires as spinless $p$-wave superconductors and derive their boundary Keldysh Green's function, capturing both the Majorana end state and continuum quasiparticle excitations in a unified manner. We also specify this Green's function for a finite-length TS wire. Junctions connecting different parts of the device are described by the standard tunneling Hamiltonian. Using this Hamiltonian …
The $4π$ Josephson Effect is a distinguishing feature of a topological Josephson junction. However, stringent conditions make it hard to observe in experiments. Here we numerically study the transient transport properties in a topological Josephson junction. We show that the $4π$ Josephson current can be sustained for a significant time (around several $μs$ with suitable conditions). Furthermore, we compare the behaviors of Josephson current in different conditions, identifying three main regimes: First, when both the superconducting wires of the Josephson junction lie in the topologically non…
We theoretically investigate Josephson junctions with a phase shift of $π$ in various proximity induced one-dimensional superconductor models. One of the salient experimental signatures of topological superconductors, namely the fractionalized $4 π$ periodic Josephson effect, is closely related to the occurrence of a characteristic zero energy bound state in such junctions. We make a detailed analysis of a more general type of $π$-junctions coined "phase winding" junctions where the phase of the order parameter rotates by an angle $π$ while its absolute value is kept finite. Such junctions hav…
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 study the spectrum of Andreev bound states and Josephson currents across a junction of $N$ superconducting wires which may have $s$- or $p$-wave pairing symmetries and develop a scattering matrix based formalism which allows us to address transport across such junctions. For $N \ge 3$, it is well known that Berry curvature terms contribute to the Josephson currents; we chart out situations where such terms can have relatively large effects. For a system of three $s$- or three $p$-wave superconductors, we provide analytic expressions for the Andreev bound state energies and study the Josephs…
We investigate the dynamics of hybrid junctions made of the topological superconductor (TS) and normal metal (N) wires. We consider an X-Y-Z configuration for the junctions where X, Y, Z = TS, N. We assume the wires X and Z being semi-infinite and in thermal equilibrium. We connect the wires X and Z through the short Y wire at some time, and numerically study time-evolution of the full device. For TS-N-TS device, we find a persistent, oscillating electrical current at both junctions even when there is no thermal or voltage bias, and the TS wires are identical. The amplitude and period of the o…
We study a general Majorana junction, where N helical nanowires are connected to a common s-wave superconductor proximity-inducing Majorana bound states in the wires. The normal part of each wire (j=1,...,N) acts as connected lead, where electrons can tunnel into the respective Majorana state γ_{A,j}. The Majorana states at the other end, γ_{B,j}, are coupled to each other by an arbitrary tunnel matrix. We examine the conditions for even-odd parity effects in the tunnel conductance for various junction topologies.
The anomalous $4π$-periodic ac Josephson effect, a hallmark of topological Josephson junctions, was experimentally observed in a quantum spin Hall insulator. This finding is unexpected due to time-reversal symmetry preventing the backscattering of the helical edge states and therefore suppressing the $4π$-periodic component of the Josephson current. Here we analyze the two-particle inelastic scattering as a possible explanation for this experimental finding. We show that a sufficiently strong inelastic scattering restores the $4π$-periodic component of the current beyond the short Josephson ju…
We study the Josephson effect in a trijunction formed by two topological superconductor (TS) wires and a conventional $s$-wave superconductor. Using a boundary Green's function formalism, analytical results for the current-phase relation are obtained in various limiting cases by modeling the TS wires via the low-energy limit of a Kitaev chain. We show that Josephson transport critically depends on the spin canting angle $θ$ between the boundary spin polarizations of the TS wires, which in turn suggests that the spin structure of Majorana states can be accessed through supercurrent measurements…
