Temperature Dependence

1. 8 8 4 4 40 20 0 -20 -40 B (T) B (T) 0 0 -4 -4 30 -8 -8 20 10 8 0 -10 4 sxy (e2/h) B(T) -20 0 -30 -4 -8 -40 -20 0 20 40 Vg(V) 2 μm Sxx B DT Vxx Syx B TEP DT Vyx Iheater Rnear Vg Rfar SiO2 T = 302K Si T = 301K Thermoelectric and Magnetothermoelectric Transport Measurements of Graphene Yuri M. Zuev1, Willy Chang2, Philip Kim2 1Department of Applied Physics 2Department of Physics, Columbia University, New York, USA Motivation Graphene Fabrication Magnetic Field Dependence 2) e-beam lithography followed by Ti/Au 3/30nm evaporation 3) Oxygen plasma etching to isolate graphene 1) Mechanical exfoliation deposition of graphene on degenerately doped 300nm SiO2/Si substrate • Thermopower (TEP) is sensitive to electron-hole asymmetry of a material system • Most transport experiments on graphene measure only conductance, G. We can verify the validity of the Boltzmann formulation of transport with the Mott relation by measuring TEP • Applying a magnetic field we investigate the Nernst effect in a 2D electronic system in the quantum Hall regime • The anomalous N = 0Landau level (LL) in graphene can be probed by TEP measurements single layer graphene 2 μm SEM image (13kx) of graphene TEP device Optical microscope image (100x) of graphene on SiO2 In-Situ Measurement of TEP Boltzmann Transport conductivity TEP Transport Coefficients: can be applied to mesoscopic systems Mott Relation: in disorder free limit: U. Sivan and Y. Imry, PRB 33 (1986) measure TEP and conductance as a function of temperature and carrier density Shubnikov-de Hass type oscillations in TEP Generalized Mott Relation: M. Jonson and S.M. Girvin PRB 29 (1984) Conclusions Semiclassical Mott Relation Temperature Dependence • Carrier diffusion generates TEP in graphene that scales linearly with temperature • For B = 0T, the Mott relation matches measured TEP well at low temperatures • At B = 9T, quantized Sxx is maximal at LL centers and shows anomalous peaks near the N = 0 Landau level quantum oscillations at low temperatures (T < 30K) quantum Hall effect B = 0T diffusive thermopower TEP T hole-like mobility = 3000cm2/Vs electron-like Mott relation agreement N = Landau level index N = 0 deviations near N = 0LL N = 1 N = 2 N = -3 N = -2 N = 3 N = -1 for more details see cond-mat:0812.1393v1 Support for this work was provided by the Nanoscale Science and Engineering Initiative of the NSF under Grants No. CHE-0117752 and CHE- 0641523 and by the New York State Office of Science, Technology, and Academic Research (NYSTAR). Sxx and Syx tend to zero between Landau levels (dotted lines above) negative TEP positve TEP