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Chu W, Li X. A projection-based reduced-order method for electron transport problems with long-range interactions. J Chem Phys 2021; 155:114105. [PMID: 34551554 DOI: 10.1063/5.0059355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations since sufficiently large portions of the bath have to be included in the computation to accurately compute the Coulomb potential. This article presents a reduced-order approach by deriving an open quantum model for the reduced density matrix. To treat the transient dynamics, the problem is placed in a reduced-order framework. The dynamics described by the Liouville-von Neumann equation is projected to subspaces using a Petrov-Galerkin projection. In order to recover the global electron density profile as a vehicle to compute the Coulomb potential, we propose a domain decomposition approach, where the computational domain also includes segments of the bath that are selected using logarithmic grids. This approach leads to a multi-component self-energy that enters the effective Hamiltonian. We demonstrate the accuracy of the reduced model using a molecular junction built from lithium chains.
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Affiliation(s)
- Weiqi Chu
- Department of Mathematics, University of California, Los Angeles, California 90095, USA
| | - Xiantao Li
- Department of Mathematics, the Pennsylvania State University, University Park, Pennsylvania 16802, USA
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2
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Tuovinen R, van Leeuwen R, Perfetto E, Stefanucci G. Electronic transport in molecular junctions: The generalized Kadanoff-Baym ansatz with initial contact and correlations. J Chem Phys 2021; 154:094104. [PMID: 33685185 DOI: 10.1063/5.0040685] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The generalized Kadanoff-Baym ansatz (GKBA) offers a computationally inexpensive approach to simulate out-of-equilibrium quantum systems within the framework of nonequilibrium Green's functions. For finite systems, the limitation of neglecting initial correlations in the conventional GKBA approach has recently been overcome [Karlsson et al., Phys. Rev. B 98, 115148 (2018)]. However, in the context of quantum transport, the contacted nature of the initial state, i.e., a junction connected to bulk leads, requires a further extension of the GKBA approach. In this work, we lay down a GKBA scheme that includes initial correlations in a partition-free setting. In practice, this means that the equilibration of the initially correlated and contacted molecular junction can be separated from the real-time evolution. The information about the contacted initial state is included in the out-of-equilibrium calculation via explicit evaluation of the memory integral for the embedding self-energy, which can be performed without affecting the computational scaling with the simulation time and system size. We demonstrate the developed method in carbon-based molecular junctions, where we study the role of electron correlations in transient current signatures.
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Affiliation(s)
- Riku Tuovinen
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, 20014 Turku, Finland
| | - Robert van Leeuwen
- Department of Physics, Nanoscience Center, University of Jyväskylä, 40014 Jyväskylä, Finland
| | - Enrico Perfetto
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Gianluca Stefanucci
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
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3
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Chu W, Li X. Reduced-Order Modeling Approach for Electron Transport in Molecular Junctions. J Chem Theory Comput 2020; 16:3746-3756. [DOI: 10.1021/acs.jctc.9b01090] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Weiqi Chu
- Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, United States
- Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
| | - Xiantao Li
- Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
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4
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Tuovinen R, Sentef MA, Gomes da Rocha C, Ferreira MS. Time-resolved impurity-invisibility in graphene nanoribbons. NANOSCALE 2019; 11:12296-12304. [PMID: 31211315 DOI: 10.1039/c9nr02738f] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We investigate time-resolved charge transport through graphene nanoribbons supplemented with adsorbed impurity atoms. Depending on the location of the impurities with respect to the hexagonal carbon lattice, the transport properties of the system may become invisible to the impurity due to the symmetry properties of the binding mechanism. This motivates a chemical sensing device since dopants affecting the underlying sublattice symmetry of the pristine graphene nanoribbon introduce scattering. Using the time-dependent Landauer-Büttiker formalism, we extend the stationary current-voltage picture to the transient regime, where we observe how the impurity invisibility takes place at sub-picosecond time scales further motivating ultrafast sensor technology. We further characterize time-dependent local charge and current profiles within the nanoribbons, and we identify rearrangements of the current pathways through the nanoribbons due to the impurities. We finally study the behavior of the transients with ac driving which provides another way of identifying the lattice-symmetry breaking caused by the impurities.
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Affiliation(s)
- Riku Tuovinen
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany.
| | - Michael A Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany.
| | - Claudia Gomes da Rocha
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Mauro S Ferreira
- School of Physics, Trinity College Dublin, Dublin 2, Ireland and Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN) and Advanced Materials and Bioengineering Research (AMBER) Centre, Trinity College Dublin, Dublin 2, Ireland
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5
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Zwolak M. Communication: Gibbs phenomenon and the emergence of the steady-state in quantum transport. J Chem Phys 2018; 149:241102. [PMID: 30599719 PMCID: PMC6602063 DOI: 10.1063/1.5061759] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Simulations are increasingly employing explicit reservoirs-internal, finite regions-to drive electronic or particle transport. This naturally occurs in simulations of transport via ultracold atomic gases. Whether the simulation is numerical or physical, these approaches rely on the rapid development of the steady state. We demonstrate that steady state formation is a manifestation of the Gibbs phenomenon well-known in signal processing and in truncated discrete Fourier expansions. Each particle separately develops into an individual steady state due to the spreading of its wave packet in energy. The rise to the steady state for an individual particle depends on the particle energy-and thus can be slow-and ringing oscillations appear due to filtering of the response through the electronic bandwidth. However, the rise to the total steady state-the one from all particles-is rapid, with time scale π/W, where W is the bandwidth. Ringing oscillations are now also filtered through the bias window, and they decay with a higher power. The Gibbs constant-the overshoot of the first ring-can appear in the simulation error. These results shed light on the formation of the steady state and support the practical use of explicit reservoirs to simulate transport at the nanoscale or using ultracold atomic lattices.
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Affiliation(s)
- Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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6
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Senjean B, Nakatani N, Tsuchiizu M, Fromager E. Multiple impurities and combined local density approximations in site-occupation embedding theory. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2368-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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7
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Dittmann N, Splettstoesser J, Helbig N. Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory. PHYSICAL REVIEW LETTERS 2018; 120:157701. [PMID: 29756889 DOI: 10.1103/physrevlett.120.157701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Revised: 11/28/2017] [Indexed: 06/08/2023]
Abstract
We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.
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Affiliation(s)
- Niklas Dittmann
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41298 Göteborg, Sweden
- Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen, Germany
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Janine Splettstoesser
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-41298 Göteborg, Sweden
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany
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8
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Thoss M, Evers F. Perspective: Theory of quantum transport in molecular junctions. J Chem Phys 2018; 148:030901. [DOI: 10.1063/1.5003306] [Citation(s) in RCA: 105] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael Thoss
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - Ferdinand Evers
- Institute of Theoretical Physics, University of Regensburg, Universitätsstr. 31, D-93053 Regensburg, Germany
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9
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Li J, Duan Y, Li T, Li H. Extreme electron transport suppression in siloxane ring-based molecular devices. Phys Chem Chem Phys 2018; 20:23352-23362. [DOI: 10.1039/c8cp03616k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Siloxane ring-based molecular devices possess excessive transport suppression and size-dependent transport decay, based on an analysis of electronic coupling.
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Affiliation(s)
- Jie Li
- Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials
- Ministry of Education
- Shandong University
- Jinan 250061
- People's Republic of China
| | - Yunrui Duan
- Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials
- Ministry of Education
- Shandong University
- Jinan 250061
- People's Republic of China
| | - Tao Li
- Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials
- Ministry of Education
- Shandong University
- Jinan 250061
- People's Republic of China
| | - Hui Li
- Key Laboratory for Liquid–Solid Structural Evolution and Processing of Materials
- Ministry of Education
- Shandong University
- Jinan 250061
- People's Republic of China
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10
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Kurth S, Stefanucci G. Transport through correlated systems with density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:413002. [PMID: 28684662 DOI: 10.1088/1361-648x/aa7e36] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We present recent advances in density functional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer-Büttiker(LB) + DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB + DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.
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Affiliation(s)
- S Kurth
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Dpto. de Física de Materiales, Universidad del País Vasco UPV/EHU, Av. Tolosa 72, E-20018 San Sebastián, Spain. IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain. Author to whom any correspondence should be addressed
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11
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Yamada A, Feng Q, Hoskins A, Fenk KD, Dunietz BD. Achieving Predictive Description of Molecular Conductance by Using a Range-Separated Hybrid Functional. NANO LETTERS 2016; 16:6092-6098. [PMID: 27636328 DOI: 10.1021/acs.nanolett.6b02241] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The conductance of molecular bridges tends to be overestimated by computational studies in comparison to measured values. While this well-established trend may be related to difficulties for achieving robust bridges, the employed computational scheme can also contribute to this tendency. In particular, caveats of the traditional functionals employed in first-principles-based calculations can lead to discrepancies reflected in exaggerated conductance. Here, we show that by employing a range-separated hybrid functional the calculated values are within the same order as the measured conductance for all four considered cases. On the other hand, with B3LYP, which is a widely used functional, the calculated values greatly overestimate the conductance (by about 1-2 orders of magnitude). The improved description of the conductance with a RSH functional builds on achieving a physically meaningful treatment of the quasi particles associated with the frontier orbitals.
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Affiliation(s)
- Atsushi Yamada
- Department of Chemistry and Biochemistry, Kent State University , Kent, Ohio 44242, United States
| | - Qingguo Feng
- Department of Chemistry and Biochemistry, Kent State University , Kent, Ohio 44242, United States
| | - Austin Hoskins
- Department of Chemistry and Biochemistry, Kent State University , Kent, Ohio 44242, United States
| | - Kevin D Fenk
- Department of Chemistry and Biochemistry, Kent State University , Kent, Ohio 44242, United States
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University , Kent, Ohio 44242, United States
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12
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Maitra NT. Perspective: Fundamental aspects of time-dependent density functional theory. J Chem Phys 2016; 144:220901. [DOI: 10.1063/1.4953039] [Citation(s) in RCA: 228] [Impact Index Per Article: 28.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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13
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Stefanucci G, Kurth S. Steady-State Density Functional Theory for Finite Bias Conductances. NANO LETTERS 2015; 15:8020-8025. [PMID: 26571349 DOI: 10.1021/acs.nanolett.5b03294] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.
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Affiliation(s)
- G Stefanucci
- Dipartimento di Fisica and European Theoretical Spectroscopy Facility (ETSF), Università di Roma Tor Vergata , Via della Ricerca Scientifica 1, 00133 Rome, Italy
- INFN, Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044 Frascati, Italy
| | - S Kurth
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Dpto. de Física de Materiales, Universidad del País Vasco UPV/EHU , Av. Tolosa 72, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, E-48013 Bilbao, Spain
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14
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Carrascal DJ, Ferrer J, Smith JC, Burke K. The Hubbard dimer: a density functional case study of a many-body problem. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:393001. [PMID: 26380948 DOI: 10.1088/0953-8984/27/39/393001] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.
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Affiliation(s)
- D J Carrascal
- Department of Physics, Universidad de Oviedo, 33007 Oviedo, Spain. Nanomaterials and Nanotechnology Research Center, Oviedo, Spain
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15
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Ness H. Nonequilibrium density matrix in quantum open systems: generalization for simultaneous heat and charge steady-state transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062119. [PMID: 25615056 DOI: 10.1103/physreve.90.062119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2014] [Indexed: 06/04/2023]
Abstract
We suggest a generalization of the expression of the nonequilibrium (NE) density matrix obtained by Hershfield's method for the cases where both heat and charge steady-state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalized Gibbs-like ensemble and is in full agreement with the general results of the McLennan-Zubarev nonequilibrium ensembles. The extra nonequilibrium terms are related to the entropy production in the system and characterize the fluxes of heat and particle. An explicit example, for the lowest-order expansion, is provide for a model system of noninteracting fermions.
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Affiliation(s)
- H Ness
- Department of Physics, Faculty of Natural and Mathematical Sciences, King's College London, Strand, London WC2R 2LS, United Kingdom
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16
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Optical Response of Extended Systems Using Time-Dependent Density Functional Theory. Top Curr Chem (Cham) 2014; 347:235-57. [DOI: 10.1007/128_2014_529] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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17
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Yu Z, Chen J, Zhang L, Wang J. First-principles investigation of quantum transport through an endohedral N@C60 in the Coulomb blockade regime. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:495302. [PMID: 24214776 DOI: 10.1088/0953-8984/25/49/495302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report an investigation of Coulomb blockade transport through an endohedral N@C60 weakly coupled with aluminum leads, employing the first-principles method combined with the Keldysh non-equilibrium Green's function derived from the equation of motion beyond the Hartree-Fock approximation. The differential conductance characteristics of the molecular device are calculated within the Coulomb blockade regime, which shows the Coulomb diamond as observed experimentally. When the gate voltage is less than that of the degeneracy point, there are two peaks in the differential conductance with an excited state induced by the change of the exchange interaction between the spin of C60 and the encapsulated nitrogen atom due to the transition from N@C(1-)(60) to N@C(2-)(60), while for a gate voltage larger than that of the degeneracy point, no excited state is available due to the quenching of exchange energy. As a result, there is only one Coulomb blockade peak in the differential conductance from the electron tunneling through the highest energy level below the Fermi level. Our first-principles results are in good agreement with experimental data obtained by an endohedral N@C60 molecular device.
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Affiliation(s)
- Zhizhou Yu
- Department of Physics and the Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China
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18
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Mirtschink A, Seidl M, Gori-Giorgi P. Derivative discontinuity in the strong-interaction limit of density-functional theory. PHYSICAL REVIEW LETTERS 2013; 111:126402. [PMID: 24093282 DOI: 10.1103/physrevlett.111.126402] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2013] [Indexed: 06/02/2023]
Abstract
We generalize the exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory to open systems with fluctuating particle numbers. When used in the self-consistent Kohn-Sham procedure on strongly interacting systems, this functional yields exact features crucial for important applications such as quantum transport. In particular, the steplike structure of the highest-occupied Kohn-Sham eigenvalue is very well captured, with accurate quantitative agreement with exact many-body chemical potentials. While it can be shown that a sharp derivative discontinuity is present only in the infinitely strongly correlated limit, at finite correlation regimes we observe a slightly smoothened discontinuity, with qualitative and quantitative features that improve with increasing correlation. From the fundamental point of view, our results obtain the derivative discontinuity without making the assumptions used in its standard derivation, offering independent support for its existence.
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Affiliation(s)
- André Mirtschink
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, Netherlands
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19
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Zheng X, Yan Y, Di Ventra M. Kondo memory in driven strongly correlated quantum dots. PHYSICAL REVIEW LETTERS 2013; 111:086601. [PMID: 24010458 DOI: 10.1103/physrevlett.111.086601] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2013] [Indexed: 06/02/2023]
Abstract
We investigate the real-time current response of strongly correlated quantum dot systems under sinusoidal driving voltages. By means of an accurate hierarchical equations of motion approach, we demonstrate the presence of prominent memory effects induced by the Kondo resonance on the real-time current response. These memory effects appear as distinctive hysteresis line shapes and self-crossing features in the dynamic current-voltage characteristics, with concomitant excitation of odd-number overtones. They emerge as a cooperative effect of quantum coherence-due to inductive behavior-and electron correlations-due to the Kondo resonance. We also show the suppression of memory effects and the transition to classical behavior as a function of temperature. All these phenomena can be observed in experiments and may lead to novel quantum memory applications.
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Affiliation(s)
- Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
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20
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Kurth S, Stefanucci G. Dynamical correction to linear Kohn-Sham conductances from static density functional theory. PHYSICAL REVIEW LETTERS 2013; 111:030601. [PMID: 23909303 DOI: 10.1103/physrevlett.111.030601] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2013] [Revised: 05/30/2013] [Indexed: 06/02/2023]
Abstract
For molecules weakly coupled to leads the exact linear Kohn-Sham (KS) conductance can be orders of magnitude larger than the true linear conductance due to the lack of dynamical exchange-correlation (xc) corrections. In this work we show how to incorporate dynamical effects in KS transport calculations. The only quantity needed is the static xc potential in the molecular junction. Our scheme provides a comprehensive description of Coulomb blockade without breaking the spin symmetry. This is explicitly demonstrated in single-wall nanotubes where the corrected conductance is in good agreement with experimental data whereas the KS conductance fails dramatically.
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Affiliation(s)
- S Kurth
- Nano-Bio Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco UPV/EHU, Centro Física de Materiales CSIC-UPV/EHU, Avenida Tolosa 72, E-20018 San Sebastián, Spain
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21
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Exact exchange-correlation potential of an ionic Hubbard model with a free surface. Sci Rep 2013; 3:2172. [PMID: 23838813 PMCID: PMC3707039 DOI: 10.1038/srep02172] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Accepted: 06/19/2013] [Indexed: 11/13/2022] Open
Abstract
In Kohn-Sham density functional theory (DFT) the interacting electron problem is mapped into a noninteracting problem in an effective potential vKS. It is known that the charge gap of the interacting system is different from the gap of the effective problem due to a jump Δxc in vKS when an electron is added but its magnitude and its role in the ubiquitous discrepancy between the experimental gaps and approximate DFT computations is poorly understood. Here we compute the exact vKS of a strongly interacting one-dimensional lattice model which can be driven from an ionic to a Mott insulating state. Presence of a “vacuum” region allows to determine the absolute value of vKS. We show that in the ionic regime Δxc is determined by nearest-neighbor interaction, while in the Mott regime Δxc is determined by on-site Hubbard interaction.
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Pertsova A, Stamenova M, Sanvito S. Time-dependent electron transport through a strongly correlated quantum dot: multiple-probe open-boundary conditions approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:105501. [PMID: 23380702 DOI: 10.1088/0953-8984/25/10/105501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We present a time-dependent study of electron transport through a strongly correlated quantum dot, which combines adiabatic lattice density functional theory in the Bethe ansatz local-density approximation (BALDA) to the Hubbard model, with the multiple-probe battery method for open-boundary simulations in the time domain. In agreement with the recently proposed dynamical picture of Coulomb blockade, a characteristic driven regime, defined by regular current oscillations, is demonstrated for a certain range of bias voltages. We further investigate the effects of systematically improving the approximation for the electron-electron interaction at the dot site (going from non-interacting, through Hartree-only to adiabatic BALDA) on the transmission spectrum and the I-V characteristics. In particular, a negative differential conductance is obtained at large bias voltages and large Coulomb interaction strengths. This is attributed to the combined effect of the electron-electron interaction at the dot and the finite bandwidth of the electrodes.
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Affiliation(s)
- A Pertsova
- School of Physics and CRANN, Trinity College Dublin, Dublin 2, Ireland.
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23
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Li Z, Tong N, Zheng X, Hou D, Wei J, Hu J, Yan Y. Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems. PHYSICAL REVIEW LETTERS 2012; 109:266403. [PMID: 23368590 DOI: 10.1103/physrevlett.109.266403] [Citation(s) in RCA: 69] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2012] [Revised: 10/07/2012] [Indexed: 06/01/2023]
Abstract
A hierarchical equations of motion based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing quantitatively Kondo resonance and Fermi-liquid characteristics, achieving the accuracy of the latest high-level numerical renormalization group approach, as demonstrated on single-impurity Anderson model systems. Its application to a two-impurity Anderson model results in differential conductance versus external bias, which correctly reproduces the continuous transition from Kondo states of individual impurity to singlet spin states formed between two impurities. The outstanding performance on characterizing both equilibrium and nonequilibrium properties of quantum impurity systems makes the hierarchical equations of motion approach potentially useful for addressing strongly correlated lattice systems in the framework of dynamical mean-field theory.
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Affiliation(s)
- ZhenHua Li
- Department of Physics, Renmin University of China, Beijing 100872, China
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24
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Elliott P, Fuks JI, Rubio A, Maitra NT. Universal dynamical steps in the exact time-dependent exchange-correlation potential. PHYSICAL REVIEW LETTERS 2012; 109:266404. [PMID: 23368591 DOI: 10.1103/physrevlett.109.266404] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2012] [Indexed: 06/01/2023]
Abstract
We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially nonlocal and time nonlocal dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of nonequilibrium dynamical situations relevant for modeling of photochemical or physical processes: field-free evolution of a nonstationary state, resonant local excitation, resonant complete charge transfer, and evolution under an arbitrary field. A lack of these steps in the usual approximations yields inaccurate dynamics, for example, predicting faster dynamics and incomplete charge transfer.
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Affiliation(s)
- P Elliott
- Department of Physics and Astronomy, Hunter College and the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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25
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Malet F, Gori-Giorgi P. Strong correlation in Kohn-Sham density functional theory. PHYSICAL REVIEW LETTERS 2012; 109:246402. [PMID: 23368350 DOI: 10.1103/physrevlett.109.246402] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2012] [Indexed: 06/01/2023]
Abstract
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe.
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Affiliation(s)
- Francesc Malet
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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26
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Akande A, Sanvito S. Persistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:055602. [PMID: 22248571 DOI: 10.1088/0953-8984/24/5/055602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The Bethe ansatz local density approximation (LDA) to lattice density functional theory (LDFT) for the one-dimensional repulsive Hubbard model is extended to current-LDFT (CLDFT). The transport properties of mesoscopic Hubbard rings threaded by a magnetic flux are then systematically investigated by this scheme. In particular we present calculations of ground state energies, persistent currents and Drude weights for both a repulsive homogeneous and a single impurity Hubbard model. Our results for the ground state energies in the metallic phase compare favorably well with those obtained with numerically accurate many-body techniques. Also the dependence of the persistent currents on the Coulomb and the impurity interaction strength, and on the ring size are all well captured by LDA-CLDFT. Our study demonstrates the value of CLDFT in describing the transport properties of one-dimensional correlated electron systems. As its computational overheads are rather modest, we propose this method as a tool for studying problems where both disorder and interaction are present.
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Affiliation(s)
- A Akande
- School of Physics and CRANN, Trinity College, Dublin 2, Ireland.
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27
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Stefanucci G, Kurth S. Towards a description of the Kondo effect using time-dependent density-functional theory. PHYSICAL REVIEW LETTERS 2011; 107:216401. [PMID: 22181899 DOI: 10.1103/physrevlett.107.216401] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2011] [Indexed: 05/31/2023]
Abstract
We demonstrate that the zero-temperature conductance of the Anderson model can be calculated within the Landauer formalism combined with static density-functional theory. The proposed approximate functional is based on finite-temperature density-functional theory and yields the exact Kohn-Sham potential at the particle-hole symmetric point. Furthermore, in the limit of zero temperature it correctly exhibits a derivative discontinuity which is shown to be essential to reproduce the conductance plateau. On the other hand, at the Kondo temperature the exact Kohn-Sham conductance overestimates the real one by an order of magnitude. To understand the failure of density-functional theory, we resort to its time-dependent version and conclude that the suppression of the Kondo resonance must be attributed to dynamical exchange-correlation corrections.
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Affiliation(s)
- G Stefanucci
- Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy
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28
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Dzhioev AA, Kosov DS. Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations. J Chem Phys 2011; 135:174111. [PMID: 22070296 DOI: 10.1063/1.3658736] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary, nonlinear kinetic equation for single-particle density matrix. We obtain the stability matrix by linearizing the kinetic equation around the fixed points and analyze the real part of its spectrum to assess the asymptotic time behavior of the fixed points. We derive expressions for the stability matrices within Hartree-Fock and linear response adiabatic time-dependent density functional theory. The stability analysis of multiple fixed points is performed within the nonequilibrium Hartree-Fock approximation for the electron transport through a molecule with a spin-degenerate single level with local Coulomb interaction.
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Affiliation(s)
- Alan A Dzhioev
- Department of Physics, Université Libre de Bruxelles, Campus Plaine, Brussels, Belgium
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29
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Kurth S, Stefanucci G. Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.01.016] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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30
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31
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Narumi T, Suzuki M, Hidaka Y, Asai T, Kai S. Active Brownian motion in threshold distribution of a Coulomb blockade model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051137. [PMID: 22181398 DOI: 10.1103/physreve.84.051137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2011] [Revised: 11/11/2011] [Indexed: 05/31/2023]
Abstract
Randomly distributed offset charges affect the nonlinear current-voltage property via the fluctuation of the threshold voltage above which the current flows in an array of a Coulomb blockade (CB). We analytically derive the distribution of the threshold voltage for a model of one-dimensional locally coupled CB arrays and propose a general relationship between conductance and distribution. In addition, we show that the distribution for a long array is equivalent to the distribution of the number of upward steps for aligned objects of different heights. The distribution satisfies a novel Fokker-Planck equation corresponding to active Brownian motion. The feature of the distribution is clarified by comparing it with the Wigner and Ornstein-Uhlenbeck processes. It is not restricted to the CB model but is instructive in statistical physics generally.
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Affiliation(s)
- Takayuki Narumi
- Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Fukuoka, Japan.
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32
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Verdozzi C, Karlsson D, Puig von Friesen M, Almbladh CO, von Barth U. Some open questions in TDDFT: Clues from lattice models and Kadanoff–Baym dynamics. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.04.035] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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33
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Song P, Nordlander P, Gao S. Quantum mechanical study of the coupling of plasmon excitations to atomic-scale electron transport. J Chem Phys 2011; 134:074701. [DOI: 10.1063/1.3554420] [Citation(s) in RCA: 87] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Evers F, Schmitteckert P. Broadening of the derivative discontinuity in density functional theory. Phys Chem Chem Phys 2011; 13:14417-20. [DOI: 10.1039/c1cp21247h] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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35
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Gál T, Geerlings P. Energy surface, chemical potentials, Kohn–Sham energies in spin-polarized density functional theory. J Chem Phys 2010; 133:144105. [DOI: 10.1063/1.3467898] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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