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Register a new userTransport in nanoscale systems: the microcanonical versus grand-canonical picture
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Added by
Massimiliano Di Ventra
Publication date
2004
fields
Physics
and research's language is
English
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We analyse a picture of transport in which two large but finite charged electrodes discharge across a nanoscale junction. We identify a functional whose minimisation, within the space of all bound many-body wavefunctions, defines an instantaneous steady state. We also discuss factors that favour the onset of steady-state conduction in such systems, make a connection with the notion of entropy, and suggest a novel source of steady-state noise. Finally, we prove that the true many-body total current in this closed system is given exactly by the one-electron total current, obtained from time-dependent density-functional theory.
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The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the S-bend pattern in the caloric curve, which gives rise to negative microcanonical specific heats, and the bimodality of the energy distribution function at the transition temperatures. Models for a good folder are shown to be quite robust against perturbations in the interaction potential parameters.
Starting from a Su-Schrieffer-Heeger-like model inferred from first-principles simulations, we show that the metal-insulator transition in In/Si(111) is a first-order grand canonical Peierls transition in which the substrate acts as an electron reservoir for the wires. This model explains naturally the existence of a metastable metallic phase over a wide temperature range below the critical temperature and the sensitivity of the transition to doping. Raman scattering experiments corroborate the softening of the two Peierls deformation modes close to the transition.
We present a generic grand-canonical theory for the Peierls transition in atomic wires deposited on semiconducting substrates such as In/Si(111) using a mean-field solution of the one-dimensional Su-Schrieffer-Heeger model. We show that this simple low-energy effective model for atomic wires can explain naturally the occurrence of a first-order Peierls transition between a uniform metallic phase at high-temperature and a dimerized insulating phase at low temperature as well as the existence of a metastable uniform state below the critical temperature.
The phase of Aharonov-Bohm oscillations in mesoscopic metal rings in the presence of a magnetic field can be modulated by application of a DC-bias current I_DC. We address the question of how a variation of I_DC and hence of the microscopic phases of the electronic wave functions results in the macroscopic phase of the conductance oscillations. Whereas the first one can be varied continuously the latter has to be quantized for a ring in two-wire configuration by virtue of the Onsager symmetry relations. We observe a correlation between a phase flip by +/- pi and the amplitude of the oscillations.
Thermoelectric transport in nanoscale conductors is analyzed in terms of the response of the system to a thermo-mechanical field, first introduced by Luttinger, which couples to the electronic energy density. While in this approach the temperature remains spatially uniform, we show that a spatially varying thermo-mechanical field effectively simulates a temperature gradient across the system and allows us to calculate the electric and thermal currents that flow due to the thermo-mechanical field. In particular, we show that, in the long-time limit, the currents thus calculated reduce to those that one obtains from the Landauer-Buttiker formula, suitably generalized to allow for different temperatures in the reservoirs, if the thermo-mechanical field is applied to prepare the system, and subsequently turned off at ${t=0}$. Alternatively, we can drive the system out of equilibrium by switching the thermo-mechanical field after the initial preparation. We compare these two scenarios, employing a model noninteracting Hamiltonian, in the linear regime, in which they coincide, and in the nonlinear regime in which they show marked differences. We also show how an operationally defined local effective temperature can be computed within this formalism.
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