Fundamental aspects of transport innanostructures and atomic physicsCollaboratorsNeil Bushong (NC)Yuriy Pershin (USC)Chih-Chun (LANL)Mike Zwolak (OSU)Roberto DAgosta (Spain)Giovanni Vignale (U. Missouri)

Outline Introduction to the transport problem Many-body effects related to viscosity of the electron liquid (large for structures with smaller transmissions) Properties of steady states and predictions

Theory: Microcanonical picture of transport Experiments: Atomic gases in optical lattices

Outline Introduction to the transport problem Many-body effects related to viscosity of the electron liquid (large for structures with smaller transmissions) Properties of steady states and predictions

Theory: Microcanonical picture of transport Experiments: Atomic gases in optical lattices

Field: nanoscale electronics Atomic point contactsMolecular junctionsFast DNA sequencingTans et al. (1997)Scheer et al. (1998)from Nitzan et al. (2003)Lagerqvist et al. (2006)Nanotubes/wiresZ.Q. Li et al. (2006)Organic electronics

What do we want to describe ?RSolved ?Not quite, especially at the atomic level !

Major difference with macro/mesoscopic systemsLarge current densitiesincreased e-e, e-ph scatteringforces

Why is the problem difficult (and interesting) ? The system is out of equilibrium (non-equilibrium statistical mechanics is still an open subject; do we need to go beyond Hamiltonian dynamics?)

Interactions among electrons (Coulomb blockade, correlations, non-Fermi liquid behavior)

Interactions among electrons and ions (e.g., el-phonon scattering, current-induced forces)

Interaction with the environment (dissipation and dephasing)

Physical properties are quite sensitive to atomic details

From experiment to model system Closed systemOpen system: dynamical interaction with reservoirsApproximation 1: open quantum systems

From experiment to model system In general, no closed equation of motion for rsApproximation 1: open quantum systemsBattery dense spectrumNo initial correlationsSmall interaction

From experiment to model system Approximation 2: ideal steady stateAssume existence of at least one steady state solutionStill many-body open quantum system !

From experiment to model system Approximation 3: openness vs boundary conditionsLoss of information

From experiment to model system Approximation 4: mean-field approximationNon-interacting electronsNon-interacting electronsWith or w/o interactionIf leads are interacting NO closed equation of motion for the current !

From experiment to model system Approximation 5: independent channels and energy fillingNon-interacting electronsNon-interacting electronsWith or w/o interaction

The Landauer current Non-interacting electronsFrom scattering theoryThis formula has nothing to do with NEGF !!!

Interacting sample From NEGFNon-interacting electronsNon-interacting electronsWith interactionsMeir and Wingreen, 1992

Physical origin of many-body corrections:linear-response theory Current conservationGauge invariance

Physical origin of many-body corrections:linear-response theory +++ Proper current-current response functionFor a non-interacting system

Outline Introduction to the transport problem Many-body effects related to viscosity of the electron liquid (large for structures with smaller transmissions) Properties of steady states and predictions

Theory: Microcanonical picture of transport Experiments: Atomic gases in optical lattices

Interactions in the whole system:the microcanonical picture of transport M. Di Ventra, T.N. Todorov, (J. Phys. Cond. Matt. 2004)

Fast relaxation of momentumBushong, Sai and M. Di Ventra (Nano Letters 2005)1/nc tc /E m w2/p2 2 1 fswmomentum relaxation time

Comparison with Landauer formulaChen, Zwolak and Di Ventra , in preparation

Entanglement entropyChen, Zwolak and Di Ventra , in preparationKlich and Levitov, PRL 2009GaussianBinomialApproximateExactC(t) = correlation matrixPL = projection operatorLR

Electron flowSai, Bushong, Hatcher, and Di Ventra , PRB 2007Quasi-2D electron liquid,TDDFTV= 0.2V

Hydrodynamics of the electron liquidMartin and Schwinger, Phys. Rev. (1959)Exact!Information on all e-e interactions (generally unknown)n = densityv = j/nA hydrodynamic formulation is more natural in QM than in classical physicsAnticipates TDDFT by many years !

Fast relaxation of momentumBushong, Sai and M. Di Ventra (Nano Letters 2005)1/nc tc /E m w2/p2 2 1 fswmomentum relaxation time

Quantum Navier-Stokes equationsR. DAgosta and M. Di Ventra, JPCM (2006)1)2)3)

Conductance quantization from hydrodynamics1D, stationary, non-viscous fluidBernoulliQuantized conductance is the one of a 1D ideal, non-viscous charged fluidDAgosta and M. Di Ventra, JPCM (2006)

Electron Dynamics

Electron dynamics in nanostructures similar to a viscous liquidPredictionsturbulenceelectron heatingeffect on ion heating

Turbulence in nanoscale systemsDAgosta and M. Di Ventra, JPCM (2006)Actual atomic structureApprox. potentialadiabaticnon-adiabaticQPCsmolecules

Turbulence in nanoscale systemsDAgosta and M. Di Ventra, JPCM (2006)laminarturbulentAdiabatic constrictions (e.g., QPC), laminar flowNonadiabatic constrictions (e.g., molecules), turbulent flow

Time-Dependent Current DFTno memory, Markov approx. Vignale and Kohn PRL 1996; Vignale, Ullrich and Conti (1997)bulk viscosity

Electron turbulenceBushong, Gamble, and M. Di Ventra (Nano Lett. 2007); DAgosta and Di Ventra JPCM (2006)nanoscale, for fully developed turbulenceEddies sizeClosed system, quasi-2D electron liquid, TDCDFTTDCDFTNS

0.02 V (Laminar)Bushong, Gamble and M. Di Ventra (Nano Lett. 2007)

3 V (Turbulent)Bushong, Gamble and M. Di Ventra (Nano Lett. 2007)

Possible exp. verificationBushong, Pershin and M. Di Ventra (Phys. Rev. Lett. 2007)Laminar

Possible exp. verificationTurbulentBushong, Pershin and M. Di Ventra (Phys. Rev. Lett. 2007)

Possible exp. verificationBushong, Pershin and M. Di Ventra (Phys. Rev. Lett. 2007)

Electron Dynamics

Electron dynamics in nanostructures similar to a viscous liquidPredictionsturbulenceelectron heatingeffect on ion heating

DAgosta, Sai and M. Di Ventra, Nano Lett. (2006)Power in the junction:Heat dissipated in the electrodes:Electron heating: elementary considerations

viscosityElectron heating from hydrodynamics Heat equation (no turbulence)Thermal conductivityDAgosta, Sai and M. Di Ventra, Nano Lett. (2006)e.g. Au QPC

Electron Dynamics

Electron dynamics in nanostructures similar to a viscous liquidPredictionsturbulenceelectron heatingeffect on ion heating

Ionic Heating: elementary considerations Y-C Chen, M. Zwolak, M. Di VentraNano Letters (2003)

T.N. Todorov Phil. Mag, (1998)Power in the junction:Heat dissipated in the electrodes:

Effect of heating on shot noise and currentChen, Di Ventra, PRB (2003); Phys. Rev. Lett. (2005)Agrait et al., Phys. Rev. Lett. (2002)?

Effect of el. and ion heating on inelastic scatteringExp.Th.DAgosta and M. Di Ventra, J. Phys. Cond. Matt. (2008)Djukic et al PRB (2005)

Effect on the ionic temperature: theoryDAgosta, Sai and M. Di Ventra, Nano Lett. (2006)

Figure 3Effect on the ionic temperature: exp.Huang et al. Nano Lett. (2006); Huang et al. (Nature Natotech., 2007)

Outline Introduction to the transport problem Many-body effects related to viscosity of the electron liquid (large for structures with smaller transmissions) Properties of steady states and predictions

Theory: Microcanonical picture of transport Experiments: Atomic gases in optical lattices

Interactions in the whole system:the microcanonical picture of transport M. Di Ventra, T.N. Todorov, (J. Phys. Cond. Matt. 2004)

Formation of steady statesBushong, Sai and M. Di Ventra (Nano Letters 2005)1/nc tc /E m w2/p2 2 1 fsw~ G0momentum relaxation timeThe formation of a steady state has nothing to do with the infinite nature of the electrodes

Cold atoms are ideal systems for studying transport phenomenaYou can choose:1.fermions or bosons2.harmonic trap, optical lattice, or both (Box-potential is coming soon!)3.single or multi components or species4.dimensions (3D, 2D, 1D, or mixed)You can tune:1.interactions among atoms (via Feshbach resonance)2.trap depth or lattice constant3.temperature4.density / filling factor

Observation of Fermi surfacesSuperfluid-Mott insulator transitionHambury-Brown-TwissexperimentI.Bloch, Nat. Phys. 1, 23 (2005)Quantum ratchetScience 326, 1241 (2009)Experimental tests: cold atoms

Density-induced transportLoading non-interacting single-species atoms into the ground state.Remove particles on the right half using photons.T=0, N particles:fermions:bosons:

Bosonic vs fermionic currentsbosons (quasi-condensate)fermions (Fermi sea)

More on the currentFermionic QSSC: Robust against trap and T

Bosonic current: Never reaches a finite QSSC even in the thermodynamic limit at T=0

Interaction-induced transport1. Loading non-interacting two-component fermions into the ground state.2. Turning on interactions on half of the lattice.Optically controlled collisions: Optical Feshbach resonance (coupling to auxiliary channels by photons. Realized in Yb and Sr, proposed for Li.): PRL 105, 050405; PRA 79, 021601; PRL 107,073202; PRL 108, 010401.

Equations of motionUsing Wicks decompositions at 2-particle level or 3-particle level show similar results.

QSSC and conducting-nonconducting transitionSimilar to the negative differential resistance in semiconductor devices.(Phys. Today 23, 35 (1970), IBM J. Res. Develop. 14, 61 (1970).)

Mismatch of energy spectra 1. The switch-on of U changes the energy dispersion of the left-half lattice.2. Moving a high-energy particle to a low-energy state or vice versa is forbidden by the underlying quantum dynamics.3. The blockade is dynamical. (unlike Mott insulator in equilibrium which is due to energy minimization.)

Conclusions Microcanonical picture of transport Many-body effects related to viscosity of the electron liquid (large for structures with smaller transmissions) Predictions (some verifiable in atomic lattices): Turbulence of the electron liquid Quasi-steady state formation also in finite systems Fermi distributions not necessary for the existence of a QSS Conducting-nonconducting transition due to interactions

Future direction:transport in a liquid environment

Idea: Transverse Transport

Idea: Transverse TransportM. Zwolak and M. Di Ventra, Nano Lett. 5, 421 (2005)

MD + Quantum TransportHamiltonian

Transverse Transport (dynamics)J. Lagerqvist, M. Zwolak, and M. Di Ventra, Nano Letters 2006

Current DistributionsJ. Lagerqvist, M. Zwolak, and M. Di Ventra, Nano Letters 2006Accuracy 99.9 %106 measurements/ sGenome seq. time < 3 daysNo parallelization

Idea: Transverse TransportM. Ramsey, UNCBranton et al., Harvardhttp://www.mcb.harvard.edu/branton/S.Y. ChouS. LindsayT. KawaiU. Penn, IBM, Samsung..