Nonequilibrium Transport Properties Research Articles

Revisiting the Green-Kubo relation for friction in nanofluidics.

A central aim of statistical mechanics is to establish connections between a system's microscopic fluctuations and its macroscopic response to a perturbation. For non-equilibrium transport properties, this amounts to establishing Green-Kubo (GK) relationships. In hydrodynamics, relating such GK expressions for liquid-solid friction to macroscopic slip boundary conditions has remained a long-standing problem due to two challenges: (i) The GK running integral of the force autocorrelation function decays to zero rather than reaching a well-defined plateau value, and (ii) debates persist on whether such a transport coefficient measures an intrinsic interfacial friction or an effective friction in the system. Inspired by ideas from the coarse-graining community, we derive a GK relation for liquid-solid friction where the force autocorrelation is sampled with a constraint of momentum conservation in the liquid. Our expression does not suffer from the "plateau problem" and unambiguously measures an effective friction coefficient, in an analogous manner to Stokes' law. We further establish a link between the derived friction coefficient and the hydrodynamic slip length, enabling a straightforward assessment of continuum hydrodynamics across length scales. We find that continuum hydrodynamics describes the simulation results quantitatively for confinement length scales all the way down to 1nm. Our approach amounts to a straightforward modification to the present standard method of quantifying interfacial friction from molecular simulations, making possible a sensible comparison between surfaces of vastly different slippage.

Coulomb Blockade in a Nonthermalized Quantum Dot.

We investigate nonequilibrium transport properties of a quantum dot in the Coulomb blockade regime under the condition of negligible inelastic scattering during the dwelling time of the electrons in the dot. Using the quantum kinetic equation we show that the absence of thermalization leads to a double step in the distribution function of electrons on the dot, provided that it is symmetrically coupled to the leads. This drastically changes nonlinear transport through the dot resulting in an additional (compared to the thermalized case) jump in the conductance at voltages close to the charging energy, which could serve as an experimental manifestation of the absence of thermalization.

Spin effects on transport and zero-bias anomaly in a hybrid Majorana wire-quantum dot system

We examine the impact of spin effects on the nonequilibrium transport properties of a nanowire hosting Majorana zero-energy modes at its ends, coupled to a quantum dot junction with ferromagnetic leads. Using the real-time diagrammatic technique, we determine the current, differential conductance and current cross-correlations in the nonlinear response regime. We also explore transport in different magnetic configurations of the system, which can be quantified by the tunnel magnetoresistance. We show that the presence of Majorana quasiparticles gives rise to unique features in all spin-resolved transport characteristics, in particular, to zero-bias anomaly, negative differential conductance, negative tunnel magnetoresistance, and it is also reflected in the current cross-correlations. Moreover, we study the dependence of the zero-bias anomaly on various system parameters and demonstrate its dependence on the magnetic configuration of the system as well as on the degree of spin polarization in the leads. A highly nontrivial behavior is also found for the tunnel magnetoresistance, which exhibits regions of enhanced or negative values—new features resulting from the coupling to Majorana wire.

The electronic transport properties of armchair carbon nanotubes with single and multiple horizontal boron-nitride lines: Unusual effects of high bias voltage on I-V characteristics

We investigate the electronic band structure properties for different arrangements of infinite horizontal boron nitride (BN) lines in the (6,6) armchair carbon nanotube. Depending on the arrangement of the boron and nitrogen atoms, the horizontal BN lines can be viewed as single or multiple BN segments along the contour of the host carbon nanotube. According to the geometrical orientation of the BN segment(s) in the circular direction, the band gap energy can be tuned providing semiconducting properties for the parallel geometries and metallic behaviors for the antiparallel geometries respectively. For the non-equilibrium transport properties, the current-voltage characteristics for such structures are also examined. Conventional fluctuations in the current are obtained for the high bias voltage as a sign of the resonant tunneling effects in the electronic transport process. However, unusual current-voltage characteristics are reported for particular BN segment configurations in the anti-parallel multiple geometry. The transmission functions and the local currents are respectively presented pointing out more details about such discrepancy in both the electronic transport process near the Fermi level and the nature of the corresponding wave functions. All calculations are performed by means of the density functional tight-binding approach as implemented in the DFTB+ software package.

Spin transport properties of highly lattice-matched all-Heusler-alloy magnetic tunnel junction

A highly lattice-matched all-Heusler-alloy magnetic tunnel junction (MTJ) is proposed by associating half metallic CoFeTiSi electrode and non-magnetic semiconductor Fe2TiSi barrier. Based on the non-equilibrium Green's function combined with first-principles calculations, spin transport mechanism is studied by analyzing the transmission coefficient, local density of states, and scattering states. The calculated equilibrium tunnel magnetoresistance (TMR) ratio in CoFeTiSi/Fe2TiSi/CoFeTiSi reaches up to about 3.30 × 108%, which is much higher than in CoFeTiSi/MgO/CoFeTiSi. The calculated scattering states reveal that CoFeTiSi/Fe2TiSi/CoFeTiSi MTJ possesses two transport channels, and the contribution of channel I to the total transport is about 80%, which plays a dominate role. The analyses on non-equilibrium spin transport properties reveal that CoFeTiSi/MgO/CoFeTiSi MTJ can output a high intensity transport current with complete spin polarization, and it can output a stable and highly efficient signal. The TMR ratio possesses an extremely large value of about 2.4 × 108% and even the bias voltage increases to 0.2 V, exhibiting a robust current-driven stability.

Non-Markovian transients in transport across chiral quantum wires using space–time non-equilibrium Green functions

We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied. We obtain the exact dynamical non-equilibrium Green function by solving Dyson’s equation analytically. Both the space–time dependent two and four-point functions are written down in a closed form in terms of simple functions of position and time. This allows us to obtain, among other things, the I–V characteristics for an arbitrary time-dependent bias. Our method is a superior alternative to competing approaches to non-equilibrium as we are able to account for transient phenomena as well as the steady state. We study the approach to steady state by computing the time evolution of the equal-time one-particle Green function. Our method can be easily applied to the problem of a double barrier contact whose internal properties can be adjusted to induce resonant tunneling leading to a conductance maximum. We then consider the case of a finite bandwidth in the point contact and calculate the non-equilibrium transport properties which exhibit non-Markovian behaviour. When a subsequently constant bias is suddenly switched on, the current shows a transient build up before approaching its steady state value in contrast to the infinite bandwidth case. This transient property is consistent with numerical simulations of lattice systems using time-dependent density matrix renormalization group suggesting thereby that this transient build up is merely due to the presence of a short distance cutoff in the problem description and not on the other details.

Temperature relaxation in strongly-coupled binary ionic mixtures

New facilities such as the National Ignition Facility and the Linac Coherent Light Source have pushed the frontiers of high energy-density matter. These facilities offer unprecedented opportunities for exploring extreme states of matter, ranging from cryogenic solid-state systems to hot, dense plasmas, with applications to inertial-confinement fusion and astrophysics. However, significant gaps in our understanding of material properties in these rapidly evolving systems still persist. In particular, non-equilibrium transport properties of strongly-coupled Coulomb systems remain an open question. Here, we study ion-ion temperature relaxation in a binary mixture, exploiting a recently-developed dual-species ultracold neutral plasma. We compare measured relaxation rates with atomistic simulations and a range of popular theories. Our work validates the assumptions and capabilities of the simulations and invalidates theoretical models in this regime. This work illustrates an approach for precision determinations of detailed material properties in Coulomb mixtures across a wide range of conditions.

Finite-temperature transport in one-dimensional quantum lattice models

The last decade has witnessed an impressive progress in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable, including the anisotropic spin-1/2 Heisenberg (also called spin-1/2 XXZ chain) and the Fermi-Hubbard model. Nevertheless, practical computations of, for instance, correlation functions and transport coefficients pose hard problems from both the conceptual and technical point of view. Only due to recent progress in the theory of integrable systems on the one hand and due to the development of numerical methods on the other hand has it become possible to compute their finite temperature and nonequilibrium transport properties quantitatively. Most importantly, due to the discovery of a novel class of quasilocal conserved quantities, there is now a qualitative understanding of the origin of ballistic finite-temperature transport, and even diffusive or super-diffusive subleading corrections, in integrable lattice models. We shall review the current understanding of transport in one-dimensional lattice models, in particular, in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, and we elaborate on state-of-the-art theoretical methods, including both analytical and computational approaches. Among other novel techniques, we discuss matrix-product-states based simulation methods, dynamical typicality, and, in particular, generalized hydrodynamics. We will discuss the close and fruitful connection between theoretical models and recent experiments, with examples from both the realm of quantum magnets and ultracold quantum gases in optical lattices.

Symmetrized decomposition of the Kubo-Bastin formula

The Smrcka-Streda version of Kubo's linear response formula is widely used in the literature to compute non-equilibrium transport properties of heterostructures. It is particularly useful for the evaluation of intrinsic transport properties associated with the Berry curvature of the Bloch states, such as anomalous and spin Hall currents as well as the damping-like component of the spin-orbit torque. Here, we demonstrate in a very general way that the widely used decomposition of the Kubo-Bastin formula introduced by Smrcka and Streda contains an overlap, which has lead to widespread confusion in the literature regarding the Fermi surface and Fermi sea contributions. To remedy this pathology, we propose a new decomposition of the Kubo-Bastin formula based on the permutation properties of the correlation function and derive a new set of formulas, without an overlap, that provides direct access to the transport effects of interest. We apply these new formulas to selected cases and demonstrate that the Fermi sea and Fermi surface contributions can be uniquely addressed with our symmetrized approach.

Magnetic field induced symmetry breaking in nonequilibrium quantum networks

We study the effect of an applied magnetic field on the nonequilibrium transport properties of a general cubic quantum network described by a tight-binding Hamiltonian with specially designed couplings to the leads that preserve open-system symmetries. We demonstrate that the symmetry of open systems can be manipulated by the direction of the magnetic field. Starting with all the symmetries preserved in absence of a field, the anisotropic and isotropic fields systematically break the symmetries, influencing all nonequilibrium properties. For simple cubic systems, we are able to identify the steady states that comprise of pure states, bath-dependent states (nonequilibrium steady states), and also nonphysical states. As an application, we show numerically for large cubic networks that the symmetry breaking can control nonequilibrium currents and that different environmental interactions can lead to novel features which can be engineered in artificial super-lattices and cold atoms.

Spin transport and dynamic properties of two-dimensional spin-momentum locked states

Materials with spin-momentum locked surface or interface states provide an interesting playground for studying physics and application of charge-spin current conversion. To characterize their non-equilibrium magnetic and transport properties in the presence of a time-dependent external magnetic field and a spin injection from a contact, we introduce three macroscopic variables: a vectorial helical magnetization, a scalar helical magnetization, and the conventional magnetization. We derive a set of closed dynamic equations for these variables by using the spinor Boltzmann approach with the collision terms consistent with the symmetry of spin-momentum locked states. By solving the dynamic equations, we predict several intriguing magnetic and transport phenomena which are experimentally accessible, including magnetic resonant response to an AC applied magnetic field, charge-spin conversion, and spin current induced by the dynamics of helical magnetization.

Nonadiabatic Molecular Dynamics at Metal Surfaces.

Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.

Thermochemical nonequilibrium modeling of oxygen in hypersonic air flows

The thermochemical nonequilibrium model for oxygen, O2, in collisions with atmospheric gas species, is modified in the present work. The vibrational relaxation time with high temperature corrections, dissociation reaction rates, equilibrium constants for the reverse reactions, the vibrational energy loss ratio due to chemical reaction, and the collision integrals for nonequilibrium transport properties are proposed to describe the thermochemical nonequilibrium of O2. The proposed set of thermochemical nonequilibrium parameters for O2 successfully reproduces existing shock-tube experimental data and the flight and ground experimental data of the ELECTRE vehicle, orbital reentry experiments (OREX) flight modules, and double-cone geometry in the LENS-XX facility. In post-shock and hypersonic flow calculations, it is found that the vibrational relaxation and coupled chemical reactions calculated using the present parameters occur more slowly than using the previous parameters. The delayed nonequilibrium chemical reactions contribute to the extension of the shock stand-off distance, and drastically change the reverse reaction near the wall of the hypersonic vehicle.

Electronic transport properties of silicon chains sandwiched between graphene electrodes: first-principles study

ABSTRACTThe effects of orientation and silicon chain length on the electronic transport properties for linear silicon chains sandwiched between two graphene electrodes are investigated by using non-equilibrium Green’s functions combined with density functional theory. Our results demonstrate that the conductance of single silicon chains can hardly be affected by its orientation, as there is negligible difference between the conductance of tilted and un-tilted chains, and the conductance is impacted greatly by the length of chains, i.e. the transmission coefficient is doubled for double chains. The equilibrium conductance of single silicon chains shows even-odd oscillating behavior, and its tendency decreases with the increase of the chain length. The non-equilibrium electronic transport properties for all types of chains are also calculated, and all current–voltage curves of silicon chains show a linear character. The frontier molecular orbitals, the total and projected density of states are used to analyse the electronic transport properties for all types of chains.

Analysis of Nonequilibrium Transport Properties of Interacting Quantum Wire Models

We analyze nonequilibrium electronic transport properties of a typical interacting three-site quantum wire model within Hartree-Fock approximation making use of Keldysh formalism. Some rigorous formulas are provided for direct calculations when Coulomb repulsion is present. According to numerical calculations using above formulas, we investigate the conductance, transport currents, and on site electronic charges of the wire on some special occasions in the interacting case, and also compare them with the results in the noninteracting case.

Transport in perturbed classical integrable systems: The pinned Toda chain

Nonequilibrium and thermal transport properties of the Toda chain, a prototype of classically integrable system, subject to additional (nonintegrable) terms are considered. In particular, we study via equilibrium and nonequilibrium simulations, the Toda lattice with a power-law pinning potential, recently analyzed by Lebowitz and Scaramazza [ArXiv:1801.07153]. We show that, according to general expectations, even the case with quadratic pinning is genuinely non-integrable, as demonstrated by computing the Lyapunov exponents, and displays normal (diffusive) conductivity for very long chains. However, the model has unexpected dynamical features and displays strong finite-size effects and slow decay of correlations to be traced back to the propagation of soliton-like excitations, weakly affected by the harmonic pinning potential. Some novel results on current correlations for the standard integrable Toda model are also reported.

Effects of Spin–Orbit Coupling on Nonequilibrium Quantum Transport Properties of Hybrid Halide Perovskites

The ground-state properties of organic–inorganic hybrid halide perovskites (OHHP) are significantly affected by spin–orbit coupling (SOC). In this paper, we report on an investigation of the nonequilibrium quantum transport properties of MAPbI3 (MA = CH3NH3), considering the cases of noncollinear spin polarization including SOC, noncollinear spin polarization excluding SOC, and no spin polarization, using Keldysh nonequilibrium Green’s function formalism combined with density functional theory calculations. Our results indicate that the enhancement of nonequilibrium quantum transport properties is largely determined by SOC. The calculated current density for noncollinear spin polarization including SOC is about 1 order of magnitude higher than that for no spin polarization, resulting from the increase of nonequilibrium transmission coefficient in the bias window and the increase of electron density in the conduction band contributed by the p-state of Pb. The results demonstrate that SOC is essential for u...

A broadened classical master equation approach for treating electron-nuclear coupling in non-equilibrium transport.

We extend the broadened classical master equation (bCME) approach [W. Dou and J. E. Subotnik, J. Chem. Phys. 144, 024116 (2016)] to the case of two electrodes, such that we may now calculate non-equilibrium transport properties when molecules come near metal surfaces and there is both strong electron-nuclear and strong metal-molecule coupling. By comparing against a numerically exact solution, we show that the bCME usually works very well, provided that the temperature is high enough that a classical treatment of nuclear motion is valid. Finally, in the low temperature (quantum) regime, we suggest a means to incorporate broadening effects in the quantum master equation (QME). This bQME works well for fairly low temperatures.

Spin-polarized electric current in silicene nanoribbons induced by atomic adsorption

We investigate the nonequilibrium transport properties of a silicene armchair nanoribbon with a random distribution of adsorbed atoms in apex positions. A ferromagnetic insulator grown below the nanoribbon splits spin-up and spin-down electron bands and gives rise to a spin polarization of the conductance. The conductance vanishes when the Fermi energy matches the adatom levels due to the coupling of adatom localized states with the continuum spectra of the nanoribbon. This is the well-known Fano effect, resulting in a spin-dependent antiresonance in the conductance. The different antiresonance energies of spin-up and spin-down electrons give rise to a full spin polarization of the conductance in a broad energy window. This spin-dependent Fano effect opens the possibility to using it in spintronics as a tuneable source of polarized electrons.

Nonequilibrium transport through a disordered molecular nanowire

We investigate the non-equilibrium transport properties of a disordered molecular nanowire. The nanowire is regarded as a quasi-one-dimensional organic crystal composed of self-assembled molecules. One orbital and a single random energy are assigned to each molecule while the intermolecular coupling does not fluctuate. Consequently, electronic states are expected to be spatially localized. We consider the regime of strong localization, namely, the localization length is smaller than the length of the molecular wire. Electron-vibron interaction, taking place in each single molecule, is also taken into account. We investigate the interplay between disorder and electron-vibron interaction in response to either an applied electric bias or a temperature gradient. To this end, we calculate the electric and heat currents when the nanowire is connected to leads, using the Keldysh non-equilibrium Green's function formalism. At intermediate temperature, scattering by disorder dominates both charge and heat transport. We find that the electron-vibron interaction enhances the effect of the disorder on the transport properties due to the exponential suppression of tunneling.