Niels Bohr Summer Institute 2005 Transport in mesoscopic and single-molecule systems 15-26 August 2005 - Workshop and summer school Inelastic Electronic Transport in the Smallest Fullerene C 20 Bridge Au Au C 20 Takahiro YAMAMOTO Tokyo University of Science
Introduction Electronic Transport in the Fullerene Bridge Large Internal Current Shuttle Motion between electrodes H. Park, et al., Nature 407, 57 (2000); K. Leo, Nature 407, 35 (2000). L.Y. Gorelik et al., Phys. Rev. Lett. 80, 4526 (1998). S. Nakanishi and M. Tsukada, Phys. Rev. Lett., 87, 126801 (2001) The electron-vibration interaction affects remarkably to transport properties of the fullerene C 60 bridge.
Strength of the Electron-Vibration Coupling Electron-Vibration coupling (mev) C 20 C 28 C 60 A. Devos and M. Lannoo, Phys. Rev. B, 58, 8236 (1998). The strength decreases with increasing a number of carbon atoms. The smallest fullerene C 20 has a largest electron-vibration coupling among the fullerenes. The fullerene C 20 was synthesized by Prinzbach et al. [Nature 407, 60 (2000)].
This Study Inelastic Electronic Transport through the C 20 20 Bridge Methods 1) Tight-binding molecular-dynamics (TBMD) method C. H. Xu, et al., J. Phys. Condens. Matter 4, 6047 (1992). T.Yamamoto et al., PRL 95, 065501 (2005) Au Au 2)Keldysh nonequilibrium Green s function (NEGF) formalism C 20 Steady-state Keldysh equation: Dyson equation: * can be exactly calculated for one-dimensional leads. * is perturbativelly calculated within the self-consistent Born approximation. Hartree Fock
Stable Structure of the C 20 Bridge Optimization Simulated Annealing using the TBMD Method with Nosé-Hoover thermostat: [Before] Jahn-Teller Distortion [After] I h symmetry D 3d symmetry b a c c c Fig.1. Stable structure of C 20 TABLE 1. Bond length of the optimized C 20 TBMD LDA GGA 1.519 Å 1.510 Å 1.510 Å 1.469 Å 1.450 Å 1.450 Å 1.464 Å 1.443 Å 1.443 Å 1.435 Å 1.409 Å 1.407 Å TBMD results are difference by less than 1% from LDA and GGA results [G. Galli et al., Phys. Rev. B 57, 1860 (1998)].
Vibrational Energies of C 20 Bridge Method Diagonalization of the force-constant matrix derived from TBMD TABLE: Vibrational energy (mev) of the C 20 bridge. A 1g 62.6 100.8 106.6 135.3 141.4 161.6 A 2g 66.8 88.9 140.2 A 1u 69.2 74.0 131.5 151.3 A 2u 11.1 72.0 91.4 112.4 127.7 149.2 E g 29.9 56.2 76.8 94.6 119.9 132.6 135.9 146.6 155.7 E u 68.9 72.1 73.4 92.4 113.3 132.4 135.9 146.6 155.7 * The energies are classified by irreducible representation of D 3d symmetry group.
I-V Characteristics of the C 20 Bridge 0.6 Current [µa] 0.4 0.2 0 Total Current Elastic Current Bias voltage [mv] The total current deviates slightly upward from the elastic current. Inelastic electron-vibration scattering plays the role of accelerator for electrons.
Differential Conductance of C 20 Bridge 0.19 Differential conductance [G 0 ] 0.18 0.17 0.16 0.15 Total Elastic Bias voltage [mv] The differential conductance shows large discontinuous steps at particular bias voltage.
Selection Rule Coupling Strength i j 0.19 Coupling Strength [arb. unit] Conductance [G 0 ] 0.18 0.17 0.16 0.15 Vibrational energy [mev] Bias voltage [mv]
Controlling the Shuttle Motion of C 20 Coupling strength for the shuttle motion [arb. unit] Au Au Au Au 2.0 1.0 0 1.0 2.0 Fermi level [ev] V G Coupling Strength [arb. unit] Shuttle motion Incident electron energy [mev] Source Gate Drain The The shuttle shuttle motion motion can can be be induced induced by by tuning tuning the the gate gate voltage voltage!!
Power Dissipation into Molecular Vibrations 15 3.0 P vib [nw] 10 5 P vib /P tot [%] 2.0 1.0 0 0 Bias voltage [mv] Bias voltage [mv] The dissipation power P vib into molecular vibrations is relatively small (< 3% up to V bias =100mV) compared to the total power P tot.
Conclusions Inelastic Electronic Transport through the C 20 Bridge We investigate effects of molecular vibrations on electronic transport in the C 20 bridge by using the NEGF formalism combined with the TBMD method. Results in This Work The differential conductance curve exhibits large discontinuous steps when the applied bias-voltage matches particular vibration energies. The physical origin of the stepwise conductance is clarified by analyzing electronic structures. The shuttle motion of fullerenes between electrodes can be controlled by tuning the gate voltage opportunely. The local heating caused by the molecular vibrations of the C 20 bridge is not a serious bottleneck for functions of fullerene-based molecular devices.