BDT between Au leads

Víctor García Suárez

Outline

1) Experiment

2) Previous calculations

3) Electronic and transport properties

4) Other experiments and simulations

1) Experiment

Experiment

First transport measurement across a molecular junction

Mechanicaly controllable break junction with gold molecules adsorbed on the gold wire surface

Reed et al., Science 278, 252 (1997)

I-V characteristics

Conductance ~ 10-4 G0 (up to 0.1 G0, Tsutsui et al. Appl. Phys. Lett. 89, 163111 (2006))

2) Previous calculations

First theoretical calculation

BDT molecule connected to ideal electrodes

Qualitative agreement between theory and experiment

Current and conductaceDi Ventra et al., Phys. Rev. Lett. 84, 979 (2000)

Full ab-initio calculation

BDT molecule between Au(111) electrodes

Zero bias and out of equlibrium

Xue and Ratner , Phys. Rev. B 68, 115406 (2003)

LUMO

HOMO

Transmission

Other calculations

Other coupling configurations

Results did not agree with experiments

Stokbro et al., Computational Materials Science 27, 151 (2003)

Delaney and Greer, Phys. Rev. Lett. 93, 36805 (2004)

Transmission

Correlated electron transport

Quantitative agreement for the conductance but not for the I-V

3) Electronic and transport properties

First approximation to the transport properties

- Two-level system

Each level represents a sulphur level; both levels interact across the central part of the molecule

S S

Transmission obtained by changing the level coupling

Match to the Ab-initio HOMO

Smeagol results

BDT between Au(001) leads

SZ basis set; 9 atoms per lead; 93 atoms in total; slightlty stretched

Transmission and density of statesPhys. Rev. B 80, 085426 (2009)

Effect of stretching and I-V

BDT between Au(001) under stretching and bias voltage

Under strain the junction becomes asymmetric; qualitative I-V agreement

Phys. Stat. Sol. 7, 2443 (2007)

Effect of stretching

Effect of bias

Example of calculation

BDT between Au(001) leads with 9 atoms per slice

ABAB stacking; coupling on the hollow position (square); distance of 1.9 Å from the surface; periodic boundary conditions along the perpendicular directions; 93 atoms in total

Leads calculation

SystemName AuSystemLabel AuNumberOfAtoms 18NumberOfSpecies 1%block ChemicalSpeciesLabel 1 79 Au%endblock ChemicalSpeciesLabel%block PAO.BasisAu 1 n=6 0 1 5.0%endblock PAO.Basis%block Ps.lmax Au 1%endblock Ps.lmaxLatticeConstant 1.00 Ang%block LatticeVectors 6.120 6.120 0.000 6.120 -6.120 0.000 0.000 0.000 4.080%endblock LatticeVectorsAtomicCoordinatesFormat Ang%block AtomicCoordinatesAndAtomicSpecies 0.00 0.00 0.00 1 Au 1

... 0.00 6.12 2.04 1 Au 18%endblock AtomicCoordinatesAndAtomicSpecies

%block kgrid_Monkhorst_Pack 1 0 0 0.0 0 1 0 0.0 0 0 100 0.0%endblock kgrid_Monkhorst_Packxc.functional GGAxc.authors PBEMeshCutoff 200. RyMaxSCFIterations 10000DM.MixingWeight 0.1DM.NumberPulay 8DM.MixSCF1 TDM.Tolerance 1.d-4SolutionMethod diagonElectronicTemperature 150 KSaveElectrostaticPotential TBuildSuperCell TInitTransport TBulkTransport TBulkLead LRDM.UseSaveDM T

Extended molecule calculationSystemName Au.emSystemLabel Au.emNumberOfAtoms 93NumberOfSpecies 4%block ChemicalSpeciesLabel 1 1 H 2 6 C 3 16 S 4 79 Au%endblock ChemicalSpeciesLabelPAO.EnergyShift 0.02 Ry%block PAO.BasisSizes H SZ C SZ S SZ%endblock PAO.BasisSizes%block PAO.BasisAu 1 n=6 0 1 5.0%endblock PAO.Basis%block Ps.lmax Au 1%endblock Ps.lmaxLatticeConstant 1.00 Ang%block LatticeVectors 6.120 6.120 0.000 6.120 -6.120 0.000 0.000 0.000 27.042%endblock LatticeVectors

...EMTransport TBuildSuperCell TInitTransport TNEnergReal 500NEnergImCircle 50NEnergImLine 30NPoles 10VInitial 0.d0 eVVFinal 0.d0 eVNIVPoints 0Delta 2.d-4EnergLowestBound -8.d0 RyNSlices 1AtomLeftVCte 18AtomRightVCte 76TrCoefficients TNTransmPoints 800InitTransmRange -10.5d0 eVFinalTransmRange -0.5d0 eVPeriodicTransp TUseLeadsGF FHartreeLeadsLeft -6.44d0 AngHartreeLeadsRight 16.52d0 AngHartreeLeadsBottom -16.36013222 eVDM.UseSaveDM T

Dependence on the lateral size of the electrodes

Size of the electrodes a a function of the number of atoms per layer:

From 4 to 25 atoms per layer (Au 001)

Dependence on the basis set

Type of basis set on the electrodes and molecule:

From SZ in the molecule or leads to DZP in all atoms

Dependence on the number of lateral k-points

Number of k-points along the perpendicular directions

From the point to 24 k-points

5) Other experiments and simulations

2D conductance histograms of OPE molecules

Number of measurements as a function of length and conductance

An elliptical zone that moves down as a function of length and another circular zone for very stretched configurations

Wandlosky et al. Unpublished (yet)

Simulation of BDT with corrected levels (SAINT)

BDT coupled with different atomic configurations and tilt angles

Results that agree qualitatively and quantitatively with experiments

BDT between Au(111) surfaces

Rigid shift of levels

Conductance as a function of angle and coupling atom I

Hollow and top configurations

Hollow-hollow (not very probable) Hollow-top

Conductance as a function of angle and coupling atom II

Top-top

Conductance values

Top configuration

Fin