Time-dependent quantum transport and power-law decay of the transient current in a nano-relay and nano-oscillator

Time-dependent nonequilibrium Green's functions are used to study electron transport properties in a device consisting of two linear chain leads and a time-dependent interleads coupling that is switched on non-adiabatically. We derive a numerically exact expression for the particle current and examine its characteristics as it evolves in time from the transient regime to the long-time steady-state regime. We find that just after switch-on the current initially overshoots the expected long-time steady-state value, oscillates and decays as a power law, and eventually settles to a steady-state value consistent with the value calculated using the Landauer formula. The power-law parameters depend on the values of the applied bias voltage, the strength of the couplings, and the speed of the switch-on. In particular, the oscillating transient current decays away longer for lower bias voltages. Furthermore, the power-law decay nature of the current suggests an equivalent series resistor-inductor-capacitor circuit wherein all of the components have time-dependent properties. Such dynamical resistive, inductive, and capacitive influences are generic in nano-circuites where dynamical switches are incorporated. We also examine the characteristics of the dynamical current in a nano-oscillator modeled by introducing a sinusoidally modulated interleads coupling between the two leads. We find that the current does not strictly follow the sinusoidal form of the coupling. In particular, the maximum current does not occur during times when the leads are exactly aligned. Instead, the times when the maximum current occurs depend on the values of the bias potential, nearest-neighbor coupling, and the interleads coupling.Comment: version accepted for publication in JA

Tunable heat pump by modulating the coupling to the leads

We follow the nonequilibrium Green's function formalism to study time-dependent thermal transport in a linear chain system consisting of two semi-infinite leads connected together by a coupling that is harmonically modulated in time. The modulation is driven by an external agent that can absorb and emit energy. We determine the energy current flowing out of the leads exactly by solving numerically the Dyson equation for the contour-ordered Green's function. The amplitude of the modulated coupling is of the same order as the interparticle coupling within each lead. When the leads have the same temperature, our numerical results show that modulating the coupling between the leads may direct energy to either flow into the leads simultaneously or flow out of the leads simultaneously, depending on the values of the driving frequency and temperature. A special combination of values of the driving frequency and temperature exists wherein no net energy flows into or out of the leads, even for long times. When one of the leads is warmer than the other, net energy flows out of the warmer lead. For the cooler lead, however, the direction of the energy current flow depends on the values of the driving frequency and temperature. In addition, we find transient effects to become more pronounced for higher values of the driving frequency.Comment: 10 pages; version 2 accepted for publication in PR

Dynamics of electron currents in nanojunctions with time-varying components and interactions

We study the dynamics of the electron current in nanodevices where there are time-varying components and interactions. These devices are a nanojunction attached to heat baths and with dynamical electron-phonon interactions and a nanojunction with photon beams incident and reflected at the channel. We use the two-time nonequilibrium Green's functions technique to calculate the time-dependent electron current flowing across the devices. We find that whenever a sudden change occurs in the device, the current takes time to react to the abrupt change, overshoots, oscillates, and eventually settles down to a steady value. With dynamical electron-phonon interactions, the interaction gives rise to a net resistance that reduces the flow of current across the device when a source-drain bias potential is attached. In the presence of dynamical electron-photon interactions, the photons drive the electrons to flow. The direction of flow, however, depends on the frequencies of the incident photons. Furthermore, the direction of electron flow in one lead is exactly opposite to the direction of flow in the other lead thereby resulting in no net change in current flowing across the device.Comment: 7 page

Role of the on-site pinning potential in establishing quasi-steady-state conditions of heat transport in finite quantum systems

We study the transport of energy in a finite linear harmonic chain by solving the Heisenberg equation of motion, as well as by using nonequilibrium Green's functions to verify our results. The initial state of the system consists of two separate and finite linear chains that are in their respective equilibriums at different temperatures. The chains are then abruptly attached to form a composite chain. The time evolution of the current from just after switch-on to the transient regime and then to later times is determined numerically. We expect the current to approach a steady-state value at later times. Surprisingly, this is possible only if a nonzero quadratic on-site pinning potential is applied to each particle in the chain. If there is no on-site potential a recurrent phenomenon appears when the time scale is longer than the traveling time of sound to make a round trip from the midpoint to a chain edge and then back. Analytic expressions for the transient and steady-state currents are derived to further elucidate the role of the on-site potential.Comment: version accepted for publication in PR

On the melting of the nanocrystalline vortex matter in high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced low concentration of columnar defects satisfying $B_\phi\le B$. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.Comment: 4 figure

Classical and quantum transport on square lattices and disordered clusters in two dimensions

The transport of a particle through disordered clusters can be treated either classically or quantum mechanically, depending on the size of the systems involved. In this thesis we employ both treatments. In the classical part we extend ordinary site percolation on a square lattice to fully coordinated (FC) percolation and to iterated fully coordinated (IFC) percolation models. FC percolation comes about by adding a full coordination requirement to ordinary site percolation. In IFC percolation we iterate this requirement one more time. We find all three models to belong to the same universality class. We also find a developing Euclidean signature as we iterate the models from ordinary to FC and then to IFC percolation. In the quantum part we study the transmittance of a particle traversing through square lattices and through disordered clusters. The square lattices and disordered clusters are attached to two semi-infinite chains serving as the input and output leads. The leads and the clusters are coupled together through either point to point contacts or busbar connections. In transport through square lattices we find resonant transmission and reflection whenever the energy of the incident particle is close to a doubly-degenerate eigenvalue of the uncoupled lattice. We also find the transmission to be sensitive to the type of coupling chosen. In transport through disordered clusters we find the transmission to decrease as the clusters become larger. This hints that states are localized. Furthermore, we find the transmission to be independent of the coupling chosen in the presence of strong disorder. This independence is lost in weakly disordered clusters. We also find hints of localized-to-localized transitions as we vary the degree of disorder. However, the clusters we have been studying are still too small to make definite conclusions. We thus find it necessary to extend our analyses to larger-sized clusters