Many-body theory of electric and thermal transport in single-molecule junctions INT Program “From Femtoscience to Nanoscience: Nuclei, Quantum Dots and.

Slides:



Advertisements
Similar presentations
From weak to strong correlation: A new renormalization group approach to strongly correlated Fermi liquids Alex Hewson, Khan Edwards, Daniel Crow, Imperial.
Advertisements

Control of transport through Fano resonances in molecular wires T. A. Papadopoulos, I. M. Grace and C. J. Lambert Department of Physics, Lancaster University,
A. Pecchia, A. Di Carlo Dip. Ingegneria Elettronica, Università Roma “Tor Vergata”, Italy A. Gagliardi, Th. Niehaus, Th. Frauenheim Dep. Of Theoretical.
Huckel I-V 3.0: A Self-consistent Model for Molecular Transport with Improved Electrostatics Ferdows Zahid School of Electrical and Computer Engineering.
Chemistry 2 Lecture 1 Quantum Mechanics in Chemistry.
QUANTUM TRANSPORT IN THE TUNNELING AND COTUNNELING REGIMENS Javier F. Nossa M.
Lecture 1: A New Beginning References, contacts, etc. Why Study Many Body Physics? Basis for new Devices Complex Emergent Phenomena Describe Experiments.
Non-equilibrium physics Non-equilibrium physics in one dimension Igor Gornyi Москва Сентябрь 2012 Karlsruhe Institute of Technology.
1 Molecular electronics: a new challenge for O(N) methods Roi Baer and Daniel Neuhauser (UCLA) Institute of Chemistry and Lise Meitner Center for Quantum.
Title Transport Through Single Molecules: Resonant Transmission, Rectification, Spin Filtering, and Tunneling Magnetoresistance Harold U. Baranger, Duke.
Transport Calculations with TranSIESTA
1 Nonequilibrium Green’s Function Approach to Thermal Transport in Nanostructures Jian-Sheng Wang National University of Singapore.
Superconducting transport  Superconducting model Hamiltonians:  Nambu formalism  Current through a N/S junction  Supercurrent in an atomic contact.
Chaos and interactions in nano-size metallic grains: the competition between superconductivity and ferromagnetism Yoram Alhassid (Yale) Introduction Universal.
Quantum charge fluctuation in a superconducting grain Manuel Houzet SPSMS, CEA Grenoble In collaboration with L. Glazman (University of Minnesota) D. Pesin.
Application to transport phenomena  Current through an atomic metallic contact  Shot noise in an atomic contact  Current through a resonant level 
14. April 2003 Quantum Mechanics on the Large Scale Banff, Alberta 1 Relaxation and Decoherence in Quantum Impurity Models: From Weak to Strong Tunneling.
Physics 452 Quantum mechanics II Winter 2011 Karine Chesnel.
“Quantum computation with quantum dots and terahertz cavity quantum electrodynamics” Sherwin, et al. Phys. Rev A. 60, 3508 (1999) Norm Moulton LPS.
Renormalised Perturbation Theory ● Motivation ● Illustration with the Anderson impurity model ● Ways of calculating the renormalised parameters ● Range.
Universality in ultra-cold fermionic atom gases. with S. Diehl, H.Gies, J.Pawlowski S. Diehl, H.Gies, J.Pawlowski.
Theory of vibrationally inelastic electron transport through molecular bridges Martin Čížek Charles University Prague Michael Thoss, Wolfgang Domcke Technical.
Crystal Lattice Vibrations: Phonons
Field theoretical methods in transport theory  F. Flores  A. Levy Yeyati  J.C. Cuevas.
Avraham Schiller / Seattle 09 equilibrium: Real-time dynamics Avraham Schiller Quantum impurity systems out of Racah Institute of Physics, The Hebrew University.
Kondo, Fano and Dicke effects in side quantum dots Pedro Orellana UCN-Antofagasta.
Slava Kashcheyevs Bernd Kästner (PTB, Braunschweig, Germany) Mark Buitelaar (University of Cambridge, UK) AAMP’2008, Ratnieki, Latvia Low-frequency excitation.
Magnetopolaronic effects in single-molecule transistor
Transport properties: conductance and thermopower
Radiation induced photocurrent and quantum interference in n-p junctions. M.V. Fistul, S.V. Syzranov, A.M. Kadigrobov, K.B. Efetov.
Caltech collaboration for DNA-organized Nanoelectronics The Caltech DNA- nanoelectronics team.
1 P. Huai, Feb. 18, 2005 Electron PhononPhoton Light-Electron Interaction Semiclassical: Dipole Interaction + Maxwell Equation Quantum: Electron-Photon.
Conductance of Single Molecular Junctions
Laboratoire Matériaux et Microélectronique de Provence UMR CNRS Marseille/Toulon (France) - M. Bescond, J-L. Autran, M. Lannoo 4 th.
TEMPLATE DESIGN © SIMULATION OF RESONANT TUNNELING DIODES FOR NANOELECTRONIC APPLICATIONS Palla Pavankumar, Perumalla.
Absorption Spectra of Nano-particles
Meir-WinGreen Formula
Confined Carriers DRAGICA VASILESKA PROFESSOR ARIZONA STATE UNIVERSITY.
T. K. T. Nguyen, M. N. Kiselev, and V. E. Kravtsov The Abdus Salam ICTP, Trieste, Italy Effect of magnetic field on thermoelectric coefficients of a single.
Figure Experimental setup of a mechanically controllable break- junction with (a) the flexible substrate, (b) the counter supports, (c) the notched.
Probing the conductance superposition law in single-molecule circuits with parallel paths H. Vazquez 1, R. Skouta 2, S. Schneebeli 2, M. Kamenetska 1,
Supercurrent through carbon-nanotube-based quantum dots Tomáš Novotný Department of Condensed Matter Physics, MFF UK In collaboration with: K. Flensberg,
Conduction and Transmittance in Molecular Devices A. Prociuk, Y. Chen, M. Shlomi, and B. D. Dunietz GF based Landauer Formalism 2,3 Computing lead GF 4,5.
Electronic States and Transport in Quantum dot Ryosuke Yoshii YITP Hayakawa Laboratory.
L4 ECE-ENGR 4243/ FJain 1 Derivation of current-voltage relation in 1-D wires/nanotubes (pp A) Ballistic, quasi-ballistic transport—elastic.
Single-molecule-mediated heat current between an electronic and a bosonic bath In Collaboration with: Avi Schiller, The Hebrew University Natan Andrei,
Two Level Systems and Kondo-like traps as possible sources of decoherence in superconducting qubits Lara Faoro and Lev Ioffe Rutgers University (USA)
Vanderbilt MURI meeting, June 14 th &15 th 2007 Band-To-Band Tunneling (BBT) Induced Leakage Current Enhancement in Irradiated Fully Depleted SOI Devices.
Quantum pumping and rectification effects in interacting quantum dots Francesco Romeo In collaboration with : Dr Roberta Citro Prof. Maria Marinaro University.
Quantum Two 1. 2 Evolution of Many Particle Systems 3.
1 MODELING MATTER AT NANOSCALES 4. Introduction to quantum treatments The variational method.
Physics “Advanced Electronic Structure” Lecture 1. Theoretical Background Contents: 1. Historical Overview. 2. Basic Equations for Interacting Electrons.
1 of xx Coulomb-Blockade Oscillations in Semiconductor Nanostructures (Part I & II) PHYS 503: Physics Seminar Fall 2008 Deepak Rajput Graduate Research.
Mesoscopic physics and nanotechnology
Charge pumping in mesoscopic systems coupled to a superconducting lead
Kondo effect in a quantum dot without spin Hyun-Woo Lee (Postech) & Sejoong Kim (Postech  MIT) References: H.-W. Lee & S. Kim, cond-mat/ P. Silvestrov.
Computational Physics (Lecture 22) PHY4061. In 1965, Mermin extended the Hohenberg-Kohn arguments to finite temperature canonical and grand canonical.
Comp. Mat. Science School Electrons in Materials Density Functional Theory Richard M. Martin Electron density in La 2 CuO 4 - difference from sum.
Flat Band Nanostructures Vito Scarola
Kondo Effect Ljubljana, Author: Lara Ulčakar
Tunable excitons in gated graphene systems
Vivek Sinha (09MS 066) Amit Kumar (09 MS 086)
Single-molecule transistors: many-body physics and possible applications Douglas Natelson, Rice University, DMR (a) Transistors are semiconductor.
Lecture 7 DFT Applications
Nonequilibrium Quantum Mechanics of a Single-Molecule Heterojunction
Coulomb Blockade and Single Electron Transistor
Full Current Statistics in Multiterminal Mesoscopic Conductors
Nonlinear response of gated graphene in a strong radiation field
Multiscale Modeling and Simulation of Nanoengineering:
Quantum One.
Presentation transcript:

Many-body theory of electric and thermal transport in single-molecule junctions INT Program “From Femtoscience to Nanoscience: Nuclei, Quantum Dots and Nanostructures,” July 31, 2009 Charles Stafford

1. Fundamental challenges of nanoelectronics (a physicist’s perspective) Fabrication: Lithography → self-assembly? For ultrasmall devices, even single-atom variations from device to device (or in device packaging) could lead to unacceptable variations in device characteristics → environmental sensitivity. Contacts/interconnects to ultrasmall devices. Switching mechanism: Raising/lowering energy barrier necessitates dissipation of minimum energy k B T per cycle → extreme power dissipation at ultrahigh device densities. Tunneling & barrier fluctuations in nanoscale devices.

Molecular electronics Fabrication: large numbers of identical “devices” can be readily synthesized with atomic precision. (Making the contacts is the hard part!) But does not (necessarilly) solve fundamental problem of switching mechanism.

Single-molecule junction ≈ ultrasmall quantum dot Similarities and differences: Typically, π-orbitals of the carbon atoms are the itinerant degrees of freedom. Charging energy of a single π-orbital: U ~ 9eV. Charging energy of a benzene molecule: ‹U› ~ 5eV. Nearest-neighbor π-π hopping integral: t ~ 2 – 3eV. Lead-molecule coupling: Γ ~ 0.5eV (small parameter?). Electronic structure unique for each molecule---not universal!

Alternative switching mechanism: Quantum interference David M. Cardamone, CAS & S. Mazumdar, Nano Letters 6, 2422 (2006); CAS, D. M. Cardamone & S. Mazumdar, Nanotechnology 18, (2007); U.S. Patent Application, Serial No. 60/784,503 (2007) (a)Phase difference of paths 1 and 2: k F 2d = π → destructive interference blocks flow of current from E to C. All possible Feynman paths cancel exactly in pairs. (b) Increasing coupling to third terminal introduces new paths that do not cancel, allowing current to flow from E to C.

Self-consistent Hartree-Fock calculation for a benzene heterojunction

Proposed structure for a QuIET: Tunable Fano anti-resonance due to vinyl linkage Real  (not decoherence) 3

I-V Characteristic of a QuIET based on sulfonated vinylbenzene Despite the unique quantum mechanical switching mechanism, the QuIET mimics the functionality of a macroscopic transistor on the scale of a single molecule! Increasing gate voltage causes electronic states of vinyl linkage to couple more strongly to benzene, introducing symmetry-breaking scattering.

General schematic of a QuIET Source, drain, and gate nodes of QuIET can be functionalized with “alligator clips” e.g., thiol groups, for self-assembly onto pre-patterned metal/semiconducting electrodes (cf. Aviram, US Patent No. 6,989,290).

Example of a class of QuIETs based on benzene Conducting polymers (e.g., polythiophene, polyaniline) connect to source and drain; semiconducting polymer (e.g., alkene chain) connects to gate electrode. Lengths of polymeric sidegroups can be tailored to facilitate fabrication and fine-tune electrical properties.

Example of a class of QuIETs based on [18]-annulene Interference due to aromatic ring; Polymeric sidegroups for interconnects/control element(s).

2. The nonequilibrium many-body problem Mean-field calculations based on density-functional theory are the dominant paradigm in quantum chemistry, including molecular junction transport. They are unable to account for charge quantization effects (Coulomb blockade) in single-molecule junctions! HOMO-LUMO gap not accurately described; no distinction of transport vs. optical gap. Many-body effects beyond the mean-field level must be included for a quantitative theory of transport in molecular heterojunctions. To date, only a few special solutions in certain limiting cases (e.g., Anderson model; Kondo effect) have been obtained to the nonequilibrium many-body problem. There is a need for a general approach that includes the electronic structure of the molecule.

Nonequilibrium Green’s functions

Real-time Green’s functions

Dyson-Keldysh equations

Molecular Junction Hamiltonian Coulomb interaction (localized orthonormal basis): Leads modeled as noninteracting Fermi gases: Lead-molecule coupling (electrostatic coupling included in H mol (1) ):

Molecular Junction Green’s Functions All (steady-state) physical observables of the molecular junction can be expressed in terms of G and G <. Dyson equation: Coulomb self-energy must be calculated approximately. G obeys the equation of motion: Once G is known, G < can be determined by analytic continuation on the Keldysh contour. Tunneling self-energy:

Electric and Thermal Currents Tunneling width matrix:

Elastic and inelastic contributions to the current

Elastic transport: linear response

3. Application to specific molecules: Effective π-electron molecular Hamiltonian For the purpose of this talk we consider conjugated organic molecules. Transport due primarily to itinerant  electrons. Sigma band is filled and doesn’t contribute appreciably to transport. Effective charge operator, including polarization charges induced by lead voltages: Parameters from fitting electronic spectra of benzene, biphenyl, and trans- stilbene up to 8-10eV: Accurate to ~1% U=8.9eV,t=2.64eV, ε=1.28 Castleton C.W.M., Barford W., J. Chem. Phys. Vol 17 No. 8 (2002)

Enhanced thermoelectric effects near transmission nodes

Effect of a finite minimum transmission

Formal solution of the equations of motion → tunneling self-energy → Coulomb self-energy Eliminating lead-molecule GF Eliminating 2-body GF

4. The Coulomb self-energy

Sequential-tunneling limit: Σ C (0) Nonequilibrium steady-state probabilities determined by detailed balance: Tunneling width matrix:

Correction to the Coulomb self-energy

Self-consistent Hartree-Fock correction to the Coulomb self-energy of a diatomic molecule Narrowing of transmission resonances; No shift of transmission peak or node positions; No qualitative effect on transmission phase; Correction small in (experimentally relevant) cotunneling regime.

Coulomb blockade in a diatomic molecule

Higher-order corrections to the Coulomb self-energy: RPA

5. Results for 1,4-benzenedithiol-Au junctions

Determining the lead-molecule coupling: thermopower Experimentally the BDT junction’s Seebeck coefficient is found to be 7.0 .2  V/K Baheti et al, Nano Letters Vol 8 No 2 (2008) Find that  Au -  0 =-3.22 ±.04eV, about 1.5eV above the HOMO level (hole dominated) Experimentally the linear-conductance of BDT is reported to be 0.011G 0 (2e 2 /h) Xiaoyin Xiao, Bingqian Xu, and N.J Tao. Nano-letters Vol 4, No. 2 (2004) Comparison with calculated linear-response gives  =.63 ±.02eV We can express the thermopower in terms of the transmission probability

Differential conductance spectrum of a benzene(1,4)dithiol-Au junction Junction charge quantized within ‘molecular diamonds.’ Transmission nodes due to quantum interference. Resonant tunneling through molecular excited states at finite bias. Justin P. Bergfield & CAS, Physical Review B 79, (2009)

Resonant tunneling through molecular excitons Justin P. Bergfield & CAS, Physical Review B 79, (2009)

Conclusions Electron transport in single-molecule junctions is a key example of a nanosystem far from equilibrium, and poses a challenging nonequilibrium quantum many-body problem. Transport through single molecules can be controlled by exploiting quantum interference due to molecular symmetry. Large enhancement of thermoelectric effects predicted at transmission nodes arising due to destructive quantum interference. Open questions: Corrections to Coulomb self-energy beyond RPA Fabrication, fabrication, fabrication…

Self-consistent Hartree-Fock correction to the Coulomb self-energy of ‘isolated’ molecule Narrowing of transmission resonances; No shift of transmission peak or node positions; No qualitative effect on transmission phase; Correction small in (experimentally relevant) cotunneling regime.

Molecular ‘Coulomb Diamond’ Intra-molecular correlation effects Excited state transport Fano-like lineshapes Energy N N+1 N+2 Energy  lead

Alternative switching mechanism: Quantum interference (a)Phase difference of paths 1 and 2: k F 2d = π → destructive interference blocks flow of current from E to C. All possible Feynman paths cancel exactly in pairs. (b) Increasing coupling to third terminal introduces new paths that do not cancel, allowing current to flow from E to C.

Elastic and inelastic contributions to the current

Molecular Junction Green’s Functions All (steady-state) physical observables of the molecular junction can be expressed in terms of G and G <. Example: elastic transmission function G obeys the equation of motion: Once G is known, G < can be determined by analytic continuation on the Keldysh contour. Tunneling width matrix: