Dvira Segal

Thermal conductance through molecular wires

We consider phononic heat transport through molecular chains connecting two thermal reservoirs. For relatively short molecules at normal temperatures we find, using classical stochastic simulations, that heat conduction is dominated by the harmonic part of the molecular force-field. We develop a general theory for the heat conduction through harmonic chains in three-dimensions. Our approach uses the standard formalism that leads to the generalized ~quantum! Langevin equation for a system coupled to a harmonic heat bath, however the driving and relaxation terms are considered separately in a way that leads directly to the steady-state response and the heat current under nonequilibrium driving. A Landauer-type expression for the heat conduction is obtained, in agreement with other recent studies. We used this general formalism to study the heat conduction properties of alkane. We find that for relatively short ~1‐30 carbon molecules! the length and temperature dependence of the molecular heat conduction results from the balance of three factors: ~i! The molecular frequency spectrum in relation to the frequency cutoff of the thermal reservoirs, ~ii! the degree of localization of the molecular normal modes and ~iii! the molecule‐heat reservoirs coupling. The fact that molecular modes at different frequency regimes have different localization properties gives rise to intricate dependence of the heat conduction on molecular length at different temperature. For example, the heat conduction increases with molecular length for short molecular chains at low temperatures. Isotopically substituted disordered chains are also studied and their behavior can be traced to the above factors together with the increased mode localization in disordered chain and the increase in the density of low frequency modes associated with heavier mass substitution. Finally, we compare the heat conduction obtained from this microscopic calculation to that estimated by considering the molecule as a cylinder characterized by a macroscopic heat conduction typical to organic solids. We find that this classical model overestimates the heat conduction of single alkane molecules by about an order of magnitude at room temperature. Implications of the present study to the problem of heating in electrically conducting molecular junctions are pointed out.

Spin-boson thermal rectifier.

Rectification of heat transfer in nanodevices can be realized by combining the system inherent anharmonicity with structural asymmetry. We analyze this phenomenon within the simplest anharmonic system-a spin-boson nanojunction model. We consider two variants of the model that yield, for the first time, analytical solutions: a linear separable model in which the heat reservoirs contribute additively, and a nonseparable model suitable for a stronger system-bath interaction. Both models show asymmetric (rectifying) heat conduction when the couplings to the heat reservoirs are different.

Single mode heat rectifier: controlling energy flow between electronic conductors.

We study heat transfer between conductors, mediated by the excitation of a monomodal harmonic oscillator. Using a simple model, we show that the onset of rectification in the system is directly related to the nonlinearity of the electron gas dispersion relation. When the metals have a strictly linear dispersion relation, a Landauer-type expression for the thermal current holds, symmetric with respect to the temperature difference. Rectification becomes prominent when deviations from linear dispersion exist, and the fermionic model cannot be mapped into a harmonic bosonized representation. The effects described here are relevant for understanding radiative heat transfer and vibrational energy flow in electrically insulating molecular junctions.

Heating in current carrying molecular junctions

A framework for estimating heating and expected temperature rise in current carrying molecular junctions is described. Our approach is based on applying the Redfield approximation to a tight binding model for the molecular bridge supplemented by coupling to a phonon bath. This model, used previously to study thermal relaxation effects on electron transfer and conduction in molecular junctions, is extended and used to evaluate the fraction of available energy, i.e., of the potential drop, that is released as heat on the molecular bridge. Classical heat conduction theory is then applied to estimate the expected temperature rise. For a reasonable choice of molecular parameters and for junctions carrying currents in the nA range, we find the temperature rise to be a modest few degrees. It is argued, however, that using classical theory to describe heat transport away from the junction may underestimate the heating effect.

Heat rectification in molecular junctions

Heat conduction through molecular chains connecting two reservoirs at different temperatures can be asymmetric for forward and reversed temperature biases. Based on analytically solvable models and on numerical simulations we show that molecules rectify heat when two conditions are satisfied simultaneously: the interactions governing the heat conduction are nonlinear, and the junction has some structural asymmetry. We consider several simplified models where a two-level system (TLS) simulates a highly anharmonic vibrational mode, and asymmetry is introduced either through different coupling of the molecule to the contacts, or by considering internal molecular asymmetry. In the first case, we present analytical results for the asymmetric heat current flowing through a single anharmonic mode using different forms for the TLS-reservoirs coupling. We also demonstrate numerically, studying a realistic molecular model, that a uniform anharmonic molecular chain connecting asymmetrically two thermal reservoirs rectifies heat. This effect is stronger for longer chains, where nonlinear interactions dominate the transfer process. When asymmetry is related to the internal level structure of the molecule, numerical simulations reveal a nontrivial rectification behavior. We could still explain this behavior in terms of an effective system-bath coupling. Our study suggests that heat rectification is a fundamental characteristic of asymmetric nonlinear thermal conductors. This phenomenon is important for heat control in nanodevices and for understanding of energy flow in biomolecules.

Heat flow in nonlinear molecular junctions : Master equation analysis

We investigate the heat conduction properties of molecular junctions comprising nonlinear interactions. We find that these interactions can lead to phenomena such as negative differential thermal conductance and heat rectification. Based on analytically solvable models we derive an expression for the heat current that clearly reflects the interplay between internal molecular anharmonic interactions, the strength of molecular coupling to the thermal reservoirs, and junction asymmetry. This expression indicates that negative differential thermal conductance shows up when the molecule is strongly coupled to the thermal baths, even in the absence of internal molecular nonlinearities. In contrast, diodelike behavior is expected for a highly anharmonic molecule with an inherent structural asymmetry.

Steady-state quantum mechanics of thermally relaxing systems

Abstract A theoretical description of quantum mechanical steady states is developed. Applications for simple quantum mechanical systems described in terms of coupled level structures yield a formulation equivalent to time independent scattering theory. Applications to steady states of thermally relaxing systems leads to time independent scattering theory in Liouville space that is equivalent to the tetradic Green’s function formalism. It provides however a direct route to derive particular forms of the Liouville equation applicable in steady-state situations. The theory is applied to study the conduction properties in the super-exchange model of a metal–molecule–metal contact weakly coupled to the thermal environment. The energy resolved temperature dependent transmission probability, as well as its coherent (tunneling) and incoherent (activated) parts, are calculated using the Redfield approximation. These components depend differently on the energy gap (or barrier), on the temperature and on the bridge length. The coherent component is most important at low temperatures, large energy gaps and small chain lengths. The incoherent component dominates in the opposite limits. The integrated transmission provides a generalization of the Landauer conduction formula for small junctions in the presence of thermal relaxation.

Conduction in molecular junctions: inelastic effects

Abstract The effect of a thermal environment on electron (or hole) transfer through molecular bridges and on the electron conduction properties of such bridges is studied. Our steady state formalism based on an extension of the Redfield theory [J. Phys. Chem. B 104 (2000) 3817; Chem. Phys. 268 (2001) 315] is extended in two ways: First, a better description of the weak-coupling limit, which accounts for the asymmetry of the energy dependence of the quasi-elastic component of the transmission is employed. Secondly, for strong coupling to the thermal bath the small polaron transformation is employed prior to the Redfield expansion. It is shown that the thermal coupling is mainly characterized by two physical parameters: the reorganization energy that measures the coupling strength and the correlation time (or its inverse – the spectral width) of the thermal bath. Implications for the observed dependence of the bridge-length dependence of the transmissions are discussed. It is argued that in the intermediate regime between tunneling behavior and site-to-site thermally induced hopping, the transport properties may depend on the interplay between the local relaxation rate and the transmission dynamics.

Numerically exact path-integral simulation of nonequilibrium quantum transport and dissipation

We develop an iterative, numerically exact approach for the treatment of nonequilibrium quantum transport and dissipation problems that avoids the real-time sign problem associated with standard Monte Carlo techniques. The method requires a well-defined decorrelation time of the nonlocal influence functional for proper convergence to the exact limit. Since finite decorrelation times may arise either from temperature or from a voltage drop at zero temperature, the approach is well suited for the description of the real-time dynamics of single-molecule devices and quantum dots driven to a steady state via interaction with two or more electron leads. We numerically investigate two nontrivial models: the evolution of the nonequilibrium population of a two-level system coupled to two electronic reservoirs, and quantum transport in the nonequilibrium Anderson model. For the latter case, two distinct formulations are described. Results are compared to those obtained by other techniques.

Molecular heat pump

We propose a molecular device that pumps heat against a thermal gradient. The system consists of a molecular element connecting two thermal reservoirs that are characterized by different spectral properties. The pumping action is achieved by applying an external force that periodically modulates molecular levels. This modulation affects periodic oscillations of the internal temperature of the molecule and the strength of its coupling to each reservoir resulting in a net heat flow in the desired direction. The heat flow is examined in the slow and fast modulation limits and for different modulation wave forms, thus making it possible to optimize the device performance.