Transport and optical response of molecular junctions UCSD July 20-21, 2009 Michael Galperin University of California at San Diego UCSD July 20-21, 2009 – p.1
Introduction UCSD July 20-21, 2009 – p.2
Introduction Timescale → BO Energy scale Weak el-ph coupling ∆ E 2 + (Γ / 2) 2 � M ≪ M L R Moderately strong E el-ph coupling ∆ E 2 + (Γ / 2) 2 � M ≥ = L + R UCSD July 20-21, 2009 – p.2
Introduction IETS RIETS e-e interaction Noise Non-linear conductance Heating Light-matter interaction J. Phys.: Condens. Matter 19 , 103201 (2007) Science 319 , 1056 (2008). UCSD July 20-21, 2009 – p.2
Introduction IETS RIETS |2> e-e interaction L R Noise |1> Non-linear conductance Heating Light-matter Phys. Rev. Lett. 95 , 206802 (2005) interaction J. Chem. Phys. 124 , 234709 (2006) Nano Lett. 9 , 758 (2009) UCSD July 20-21, 2009 – p.2
Experiments Metal enhanced fluorescence (Cy5 on Ag) J.Zhang et al. Nano Lett. 7 , 2101 (2007) UCSD July 20-21, 2009 – p.3
Experiments Intramolecular photon emission in STM S.W.Wu et al. Phys. Rev. B 77 , 205430 (2008) UCSD July 20-21, 2009 – p.3
Experiments SERS of molecules on nanoparticles S.Nie and S.R.Emory. Science 275 , 1102 (1997) UCSD July 20-21, 2009 – p.3
Experiments Simultaneous Raman and conduction D.R.Ward et al. Nano Lett. 8 , 919 (2008) UCSD July 20-21, 2009 – p.3
Experiments Heating detected by Raman Z.Ioffe et al. Nature Nanotechnology 3 , 727 (2008) UCSD July 20-21, 2009 – p.3
HOMO-LUMO model Absorption line shape of molecule in biased junction Light induced current in molecular junction Fluorescence from current carrying molecular bridge Current from electronic excitations in the leads Raman spectroscopy of biased junctions Phys. Rev. Lett. 95 , 206802 (2005); 96 , 166803 (2006) J. Chem. Phys. 124 , 234709 (2006); 128 , 124705 (2008) Nano Lett. 9 , 758 (2009); J. Chem. Phys. 130 , 144109 (2009) UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Fluxes considered electronic current through the molecule L energy flow between |2> the molecule and L R electron-hole |1> excitations in the R leads incident or emitted photon flux UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Fluxes considered electronic current through the molecule |2> energy flow between L e e the molecule and R electron-hole e |1> excitations in the leads incident or emitted photon flux UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Fluxes considered electronic current through the molecule e |2> energy flow between the molecule and E F electron-hole |1> excitations in the e leads incident or emitted photon flux UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Fluxes considered electronic current through the molecule e |2> |2> energy flow between the molecule and ph ph electron-hole |1> |1> excitations in the e leads incident or emitted photon flux UCSD July 20-21, 2009 – p.4
HOMO-LUMO model ˆ H 0 + ˆ ˆ H = V ˆ c † � � � c † a † H 0 = ε m ˆ m ˆ c m + ε k ˆ k ˆ c k + � ω α ˆ α ˆ a α m =1 , 2 α k ∈{ L,R } ˆ V M + ˆ ˆ V N + ˆ V = V P � � V ( MK ) ˆ � � c † c m + H.c. V M = ˆ k ˆ km K = L,R m =1 , 2; k ∈ K � � V ( NK ) ˆ � � c † c † c 1 + H.c. V N = ˆ k ˆ c k ′ ˆ 2 ˆ kk ′ K = L,R k � = k ′ ∈ K � � ˆ � c † c 1 + H.c. V ( P ) V P = a α ˆ ˆ 2 ˆ α α UCSD July 20-21, 2009 – p.4
HOMO-LUMO model SE due to electron tunneling V ( MK ) g k ( τ 1 , τ 2 ) V ( MK ) � Σ MK,mm ′ ( τ 1 , τ 2 ) = mk km ′ k ∈ K ’ 2 1 projections (WBL and no mixing) Σ r MK,mm ′ = − iδ mm ′ Γ MK,m / 2 Σ < MK,mm ′ ( E ) = iδ mm ′ f K ( E )Γ MK,m Σ > MK,mm ′ ( E ) = − iδ mm ′ [1 − f K ( E )]Γ MK,m UCSD July 20-21, 2009 – p.4
HOMO-LUMO model SE due to e-h excitations in the contacts 2 � � � V ( NK ) Σ NK ( τ 1 , τ 2 ) = � g k ( τ 2 , τ 1 ) g k ′ ( τ 1 , τ 2 ) � � k � = k ′ ∈ K kk ′ � � � G 22 ( τ 1 , τ 2 ) 0 × 0 G 11 ( τ 1 , τ 2 ) k 1 2 1 2 ’ 2 1 k 2 UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Projections � dω Σ < 2 π B NK ( ω, µ K ) G < NK,mm ( E ) = m ( E + ω ) m ¯ ¯ � dω Σ > 2 π B NK ( ω, µ K ) G > NK,mm ( E ) = m ( E − ω ) m ¯ ¯ with � 2 � � � V ( NK ) � B NK ( ω, µ K ) = 2 π dE � � kk ′ � k � = k ′ ∈ K × δ ( E − ε k ) δ ( E + ω − ε k ′ ) f K ( E )[1 − f K ( E + ω )] � 2 ρ e − h � � V ( NK ) � ≡ 2 π K ( ω ) UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Simplified version when ε 21 ≫ Γ 1 , 2 � � n 2 0 Σ < NK = iB NK 0 0 � � 0 0 Σ > NK = − iB NK 0 1 − n 1 where B NK = B NK ( ε 21 ) UCSD July 20-21, 2009 – p.4
HOMO-LUMO model SE due to coupling to photon field 2 � � � V ( P ) Σ P ( τ 1 , τ 2 ) = i � � � α α � � � F α ( τ 2 , τ 1 ) G 22 ( τ 1 , τ 2 ) 0 × 0 F α ( τ 1 , τ 2 ) G 11 ( τ 1 , τ 2 ) 2 1 2 ’ 2 1 UCSD July 20-21, 2009 – p.4
HOMO-LUMO model 2 � � � V ( P ) Σ < P ( E ) = � � � α α � � � (1 + N α ) G < 22 ( E + ω α ) 0 × N α G < 0 11 ( E − ω α ) 2 � � � V ( P ) Σ > P ( E ) = � � � α α � � � N α G > 22 ( E + ω α ) 0 × (1 + N α ) G > 0 11 ( E − ω α ) N 0 = 1 for pumping mode ( absorption flux ) N α = 0 for absorbing modes ( fluorescence ) UCSD July 20-21, 2009 – p.4
HOMO-LUMO model Simplified version for emission flux when ε 21 ≫ Γ 1 , 2 � � n 2 0 Σ < = iγ P ( ε 21 ) P 0 0 � � 0 0 Σ > = − iγ P ( ε 21 ) P 0 1 − n 1 2 � � � V ( P ) where γ P ( ω ) = 2 π � δ ( ω − ω α ) � � α α � UCSD July 20-21, 2009 – p.4
Flux expression � + ∞ dE 2 π � Tr [Σ B < ( E ) G > ( E ) − Σ B > ( E ) G < ( E )] I B = −∞ with B 0 = . . . P 0 , 22 or minus P 0 , 11 for absorption flux ML or minus MR for current through the junction P, 11 or minus P, 22 for fluorescence UCSD July 20-21, 2009 – p.5
Absorption line shape General expression � + ∞ dE Σ < P 0 , 22 ( E ) G > 22 ( E ) − Σ > P 0 , 22 ( E ) G < � � I abs ( ω 0 ) = 22 ( E ) 2 π � −∞ Simplified version (Lorentzian) ε 1 ≪ µ L,R ≪ ε 2 (low bias) coupling to the photon field is weak Γ 1 , 2 ≪ ε 21 , | ε 1 , 2 − E F | 2 � � � V ( P ) � � ( ε 2 − ω 0 − ε 1 ) 2 + (Γ / 2) 2 × Γ M, 1 Γ M, 2 Γ 0 � I abs ( ω 0 ) = Γ 1 Γ 2 � UCSD July 20-21, 2009 – p.6
Absorption line shape +9 ) ( 10 =0.5 V =1.0 V ε 21 = 2 eV =1.1 V 12 γ P = 10 − 6 eV =1.2 V =1.5 V I abs (photons/s) T = 300 K 8 B NL = B NR = 0 . 1 eV Γ ML/R, 1 = 0 . 01 eV 4 Γ ML/R, 2 = 0 . 2 eV 0 1 2 3 4 0 (eV) partial population of LUMO (HOMO) distortes the Lorentzian shape UCSD July 20-21, 2009 – p.6
Light induced current Radiation field in resonance with the molecular optical transition Molecules with strong charge-transfer transitions DMEANS (4-Dimethylamino-4’-nitrostilbene) 7 D (ground) → 31 D (first excited singlet) all-trans Retinal in Poly-methyl methacrylate films 6 . 6 D → 19 . 8 D ( 1 B u electronic state) 40 Å CdSe nanocrystals 0 D → 32 D (first excited state) If optical charge transfer is parallel to the wire axis optical pumping → charge flow between the two leads UCSD July 20-21, 2009 – p.7
Light induced current General expression � + ∞ dE 2 π � Tr [Σ < ML ( E ) G > ( E ) − Σ > ML ( E ) G < ( E )] I sd = −∞ Simplified version ( ω 0 ∼ ε 21 , Φ = 0 , Γ 1 , 2 ≪ ε 21 ) I sd = | V ( P ) | 2 Γ Γ ML, 1 Γ MR, 2 − Γ ML, 2 Γ MR, 1 0 ( ε 2 − ω 0 − ε 1 ) 2 + (Γ / 2) 2 Γ 1 Γ 2 � The yield of the effect � I sd � = Γ ML, 1 Γ MR, 2 − Γ ML, 2 Γ MR, 1 Y c = I abs Γ M, 1 Γ M, 2 Φ=0 UCSD July 20-21, 2009 – p.7
Light induced current -10 ) Φ = 0 ( 10 ε 21 = 2 eV γ P = 10 − 6 eV 5 T = 300 K I sd (A) B NL = B NR = 0 . 1 eV 3 Γ ML/R, 1 = 0 . 2 eV Γ ML, 2 = 0 . 02 eV Γ MR, 2 = 0 . 3 eV 1 = 10 − 3 eV V ( P ) 0 0 1 2 3 4 0 (eV) peak at the HOM0-LUMO gap frequency UCSD July 20-21, 2009 – p.7
Light induced current ( 10 -7 ) Φ = 0 0 =1.9 eV 0 =1.7 eV ε 21 = 2 eV 20 0 =1.5 eV γ P = 10 − 6 eV 15 T = 300 K I sd (A) B NL = B NR = 0 . 1 eV 10 Γ ML, 1 /MR, 2 = 0 . 2 eV Γ ML, 2 /MR, 1 = 0 . 02 eV 5 V ( P ) = 0 . 02 eV 0 0.0 0.5 1.0 (V) If the level position is pinned to the contact to which it is coupled stronger → NDR UCSD July 20-21, 2009 – p.7
Fluorescence Light emission from STM junctions e excites surface plasmon which later emits time-dependent potential of a tunneling e → electronic excitation of the molecule → fluorescence current carrying situation with excited state formed with a finite probability → photon emission. . . UCSD July 20-21, 2009 – p.8
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