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[资源] 有关非平衡态格林函数(NEGF)的一些文献

Anantram, M. P. and T. R. Govindan (1998). "Conductance of carbon nanotubes with disorder: A numerical study." Physical Review B (Condensed Matter) 58(8): 4882.
We study the conductance of carbon nanotube wires in the presence of disorder, in the limit of phase-coherent transport. For this purpose, we have developed a simple numerical procedure to compute transmission through carbon nanotubes and related structures. Two models of disorder are considered, weak uniform disorder and isolated strong scatterers. In the case of weak uniform disorder, our simulations show that the conductance is not significantly affected by disorder when the Fermi energy is close to the band center. Further, the transmission around the band center depends on the diameter of these zero band-gap wires. We also find that the calculated small bias conductance as a function of the Fermi energy exhibits a dip when the Fermi energy is close to the second subband minima. In the presence of strong isolated disorder, our calculations show a transmission gap at the band center, and the corresponding conductance is very small. (33 refs.)
  这篇主要讲NEGF的应用。



  Choi, H. J., J. Ihm, et al. (2000). "Defects, quasibound states, and quantum conductance in metallic carbon nanotubes." Physical Review Letters 84(13): 2917.
The effects of impurities and local structural defects on the conductance of metallic carbon nanotubes are calculated using an ab initio pseudopotential method within the Landauer formalism. Substitutionally doped boron or nitrogen produces quasibound impurity states of a definite parity and reduces the conductance by a quantum unit (2e{sup 2}/h) via resonant backscattering. These resonant states show strong similarity to acceptor or donor states in semiconductors. The Stone-Wales defect also produces quasibound states and exhibits quantized conductance reduction. In the case of a vacancy, the conductance shows a much more complex behavior than the prediction from the widely used {pi}-electron tight-binding model. CP 2000 The American Physical Society. (25 Refs.)


  DATTA, S. (1989). "Steady-state quantum kinetic equation." Physical Review B (Condensed Matter) 40(8): 5830-3.
Starting from the Dyson equation in the Keldysh formulation, the author derives a kinetic equation for steady-state quantum transport under the simplifying assumption that the inelastic scattering is caused by uncorrelated point scatterers, such as impurities with internal degrees of freedom. This assumption allows him to write a transport equation that involves only the electron density and not the spatial correlations of the wave function. Assuming local thermodynamic equilibrium he then simplifies the transport equation to a form which resembles the Landauer-Buttiker formula extended to include a continuous distribution of probes. (8 refs.)
  这篇文献推导了稳态下格林函数所遵循的方程。

  DATTA, S. (1990). "A simple kinetic equation for steady-state quantum transport." Journal of Physics: Condensed Matter 2(40): 8023-52.
An important problem in quantum transport is to understand the role of dissipative processes. In this paper the author assume a model in which phase-breaking and dissipation are caused by the interaction of electrons with a reservoir of oscillators through a delta potential. In this model the self-energy is a delta function in space, leading to a kinetic equation with a simple physical interpretation. A novel treatment of the contacts is used to introduce the external current into the kinetic equation. One specializing to linear response the author obtains an integral equation that looks like the Buttiker formula (1961) extended to a continuous distribution of probes. The author show that this equation can be reduced to the usual Buttiker formula which involves only the actual physical probes. Dissipation modifies the transmission coefficients, and the author presents explicit expressions derived from this model. Also, in a homogeneous medium the integral equation reduces to the diffusion equation, it the electrochemical potential is assumed to vary slowly. This paper serves to establish a bridge between the quantum kinetic approach which rigorously accounts for the exclusion principle and the one-particle approach which is intuitively appealing. (23 refs.)


  Galperin, M. and A. Nitzan (2003). "NEGF-HF method in molecular junction property calculations." Molecular Electronics Iii 1006: 48.
nonequilibrium Green's function formalism at the Hartree-Fock level (NEGF-HF)


  Ke, S. H., H. U. Baranger, et al. (2004). "Electron transport through molecules: Self-consistent and non-self-consistent approaches." Physical Review B 70(8): 085410.
A self-consistent method for calculating electron transport through a molecular device is developed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the framework of the nonequilibrium Green function approach. To avoid the substantial computational cost in finding the I-V characteristic of large systems, we also develop an approximate but much more efficient non-self-consistent method. Here the change in effective potential in the device region caused by a bias is approximated by the main features of the voltage drop. As applications, the I-V curves of a carbon chain and an aluminum chain sandwiched between two aluminum electrodes are calculated-two systems in which the voltage drops very differently. By comparing to the self-consistent results, we show that this non-self-consistent approach works well and can give quantitatively good results.


  Ke, S. H., H. U. Baranger, et al. (2005). "Contact atomic structure and electron transport through molecules." Journal of Chemical Physics 122(7): 074704.
Using benzene sandwiched between two Au leads as a model system, we investigate from first principles the change in molecular conductance caused by different atomic structures around the metal-molecule contact. Our motivation is the variable situations that may arise in break junction experiments; our approach is a combined density functional theory and Green function technique. We focus on effects caused by (1) the presence of an additional Au atom at the contact and (2) possible changes in the molecule-lead separation. The effects of contact atomic relaxation and two different lead orientations are fully considered. We find that the presence of an additional Au atom at each of the two contacts will increase the equilibrium conductance by up to two orders of magnitude regardless of either the lead orientation or different group-VI anchoring atoms. This is due to a resonance peak near the Fermi energy from the lowest energy unoccupied molecular orbital. In the nonequilibrium properties, the resonance peak manifests itself in a negative differential conductance. We find that the dependence of the equilibrium conductance on the molecule-lead separation can be quite subtle: either very weak or very strong depending on the separation regime. (C) 2005 American Institute of Physics.


  Khan, F. S., J. H. Davies, et al. (1987). "Quantum transport equations for high electric fields." Physical Review B (Condensed Matter) 36(5): 2578.
The authors have studied quantum-mechanical transport equations for nondegenerate electrons in semiconductors in high electric fields. Their calculations use Kadanoff and Baym's formalism (1962), based on Green functions, treat only fields that are constant in space and time, and are restricted to weak scattering. First, they derive an approximate solution to the equation of motion of the retarded Green function in an electric field, with a careful check of its validity. This is used in deducing the conditions under which the quantum-mechanical transport equation reduces to the Boltzmann equation. They find, in agreement with some previous studies, that the electric field causes a 'broadening' of the delta function in semiclassical transition rates, a result of the 'intracollisional field affect.' The Boltzmann equation fails when this broadening exceeds some characteristic energy scale (usually k{sub B}T), which occurs at fields of a few MV m{sup -1} in conventional semiconductors. These results are strongly dependent on the ansatz used to reduce the Green function to a distribution function. The scattering-out term is usually much less sensitive to the electric field than the scattering-in term. They exploit this to construct an integral transport equation, valid in high electric fields, which differs from the Boltzmann equation only in having a broadened function replacing the delta function in the scattering-in rates. It should be possible to solve this equation using standard numerical techniques and gain quantitative information on the intracollisional field effect. (36 refs.)



  Mahan, G. D. (1987). "Quantum transport equation for electric and magnetic fields." Physics Reports 145(5): 251.
A quantum Boltzmann equation is derived which is valid for electron transport in electric and magnetic fields including all many-body effects. A solution in both DC and AC electric fields is given for electrons in simple metals. The solution for transport in large magnetic fields is also given including a theory of the Shubnikov-deHaas oscillators which includes inelastic phonon scattering rigorously. (42 refs.)


  Paulsson, M. (2002). Non Equilibrium Green's Functions for Dummies: Introduction to the One Particle NEGF equations.


  Rammer, J. and H. Smith (1986). "Quantum field-theoretical methods in transport theory of metals." Reviews of Modern Physics 58(2): 323.
The authors review the Keldysh method of obtaining kinetic equations for normal and superconducting metals. The use of the method is illustrated by examples involving electron-impurity, electron-phonon, and electron-electron scattering, both within and beyond the quasiclassical approximation. (111 refs.)


  Ren, Z. (2001). NANOSCALE MOSFETS: PHYSICS, SIMULATION AND DESIGN, Purdue University.


  San-Huang, K., H. U. Baranger, et al. (2005). "Electron transport through molecules: Gate-induced polarization and potential shift." Physical Review B (Condensed Matter and Materials Physics) 71(11): 113401.
We analyze the effect of a gate on the conductance of molecules by separately evaluating the gate-induced polarization and the potential shift of the molecule relative to the leads. The calculations use ab initio density functional theory combined with a Green function method for electron transport. For a general view, we study several systems: (1) atomic chains of C or Al sandwiched between Al electrodes, (2) a benzene molecule between Au leads, and (3) (9,0) and (5,5) carbon nanotubes. We find that the polarization effect is small because of screening, while the effect of the potential shift is significant, providing a mechanism for single-molecule transistors. (20 refs.)


  Taylor, J., H. Guo, et al. (2001). "Ab initio modeling of quantum transport properties of molecular electronic devices." Physical Review B 63(24): 245407.



  Venugopal, R. (2003). MODELING QUANTUM TRANSPORT IN NANOSCALE TRANSISTORS, Purdue University.


  Xue, Y., S. Datta, et al. (2002). "First-principles based matrix Green's function approach to molecular electronic devices: general formalism." Chemical Physics 281(2/3): 151-70.
Transport in molecular electronic devices is different from that in semiconductor mesoscopic devices in two important aspects: (1) the effect of the electronic structure and (2) the effect of the interface to the external contact. A rigorous treatment of molecular electronic devices will require the inclusion of these effects in the context of an open system exchanging particle and energy with the external environment. This calls for combining the theory of quantum transport with the theory of electronic structure starting from the first-principles. We present a self-consistent yet tractable matrix Green's function (MGF) approach for studying transport in molecular electronic devices, based on the non-equilibrium Green's function formalism of quantum transport and the density functional theory (DFT) of electronic structure using local orbital basis sets. By separating the device rigorously (within an effective single-particle theory) into the molecular region and the contact region, we can take full advantage of the natural spatial locality associated with the metallic screening in the electrodes and focus on the physical processes in the finite molecular region. This not only opens up the possibility of using the existing well-established technique of molecular electronic structure theory in transport calculations with little change, but also allows us to use the language of qualitative molecular orbital theory to interpret and rationalize the results of the computation. We emphasize the importance of the self-consistent charge transfer and voltage drop on the transport characteristics and describe the self-consistent formulation for both device at equilibrium and device out of equilibrium. For the device at equilibrium, our method provides an alternative approach for solving the molecular chemisorption problem. For the device out of equilibrium, we show that the calculation of elastic current transport through molecules, both conceptually and computationally, is no more difficult than solving the chemisorption problem. (96 refs.)


  Xue, Y. and M. A. Ratner (2003). Application of a non-equilibrium Green's function method to electrical transport through single molecular-assembled metallic nanoparticles. Bioinspired Nanoscale Hybrid Systems. Symposium, 2-4 Dec. 2002, Boston, MA, USA, Warrendale, PA, USA: Mater. Res. Soc, 2003.


  Xue, Y. and M. A. Ratner (2004). "End group effect on electrical transport through individual molecules: a microscopic study." Physical Review B (Condensed Matter and Materials Physics) 69(8): 85403-1.

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