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High-field ground state of graphene at Dirac Point

American Physical Society March Meeting, Mar 16, 2009. High-field ground state of graphene at Dirac Point. J. G. Checkelsky, Lu Li and N.P.O. Princeton University. Ground state of Dirac point in high fields Thermopower at Dirac point. Checkelsky Li, NPO, PRL 08 Checkelsky, Li, NPO, PRB 09

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High-field ground state of graphene at Dirac Point

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  1. American Physical Society March Meeting, Mar 16, 2009 High-field ground state of graphene at Dirac Point J. G. Checkelsky, Lu Li and N.P.O. Princeton University • Ground state of Dirac point in high fields • Thermopower at Dirac point Checkelsky Li, NPO, PRL 08 Checkelsky, Li, NPO, PRB 09 Checkelsky, NPO, arXiv 08 National High Magnetic Field Lab., Tallahassee NSF-MRSEC DMR 084173

  2. Zero-energy mode, n=0 Landau Level For valley K , 2 valleys K, K’ For n=0 Landau Level 1) K-K’ valley index same as A-B sublattice index 2) Electrons on B sites only

  3. Broken Symmetry ground states Coulomb interaction energy in high-field state Nomura, MacDonald, PRL 06 Goerbig, Moessner, Doucot, PRB 06 Kun Yang, Das Sarma, MacDonald, PRB 06 Ezawa, JPSJ 06 Abanin, Lee, Levitov, PRL 06, 07 Fertig, Bray, PRL 06 Shimshoni, Fertig, Pai, 08 Alicea, Fisher, PRB 06 Gusynin, Miransky, Sharapov, Shovkovy, PRB 06 Khveshchenko, PRL 02

  4. Quantum Hall Ferromagnet and CPE modes Edge potentl zig-zag K Exchange K m 4-fold degen. K’ K’ Abanin, Lee, Levitov Fertig, Bray Bernevig, Zhang QHF state Counter-propg edge (CPE) modes At Dirac point, CPE modes protected Rxx ~ (h/e2) in intense fields (dissipative to very large H) Realization of quantized spin-Hall system

  5. Magnetic Catalysis (field induced gap) E(k) E(k) ky ky kx kx neutrino electron Applequist et al. 1986 Miransky et al. 1995, 2003, 2005, 2008 D. Khveshchenko 2002 Field H creates gap Mass term Chiral-symmetry breaking In (2+1) QED3 Field-enhancement of DOS at Dirac Point Exciton condensation of electron hole pairs Order parameter for H > Hc Equivalent to sublattice CDW

  6. The resistance Rxx and Hall conductivity in graphene Checkelsky, Li, Ong, PRL ‘08 Rxx diverges with H at Dirac Point s

  7. Divergent R0 and zero-Hall step Checkelsky, Li, Ong, PRL ‘08 R0 increases as T decreases At fixed H and T, n=0 peak dependent on V0 (offset voltage) sxy = 0 at n=0 At 14 T, n=0 LL split into 2 subbands Split resolved at 100 K

  8. Offset Gate voltage V0 -- an important parameter V0 Small offset V0 correlates with low disorder

  9. R0 saturates below 2 K Conductance saturates for T < 2 K Divergence in R0 steepest At 0.3 K Sample dependent

  10. Contour map of R0 at Dirac point in H-T plane R0 is exponentially sensitive to H but T-independent below 2 K

  11. Spurious features from self-heating Power dissipatnP > 10 pW  thermal runaway at Dirac point A major experimental obstacle

  12. Adopt ultralow dissipation measurement circuit Checkelsky, Li, NPO, PRB ‘09 Hold Vtot = 40 mV Phase detect I, Vxx and Vxy Power dissipated 10 aW to 3 fW

  13. Checkelsky, Li, NPO, PRB ‘09 At 0.3 K, R0 diverges to 40 MW Divergence in R0 seems singular

  14. Fits to Kosterlitz-Thouless correlation length over 3 decades 3-decade fit to KT correlation x

  15. Kosterlitz Thouless fit in Samples K52, J18 and J24 Checkelsky, Li, NPO, PRB ‘09 (29 T) (36 T) Slopes b are similar Hc sample dependt (32 T)

  16. Temperature dependences of R0 at fields H < Hc Checkelsky, Li, NPO, PRB ‘09 J18 Hc~ 32 T Thermally activated R0 = A exp(bD) D = 14 K At “low” H, R0 Saturates below 2 K

  17. Inference from ultralow dissip. measurements • At Dirac Point • Field drives a transition to insulating state at Hc • Divergence in R0 is exponential and singular. • CPE modes are not present (or destroyed in high fields) • Saturation of R0below 2 K for H < Hc • (Not caused by self-heating, we believe).

  18. Phase diagram in T-H plane at Dirac point H activated Hc saturates KT like T Constant-R0 contours Ordered insulator

  19. Thermopower in zero field E(k) m ky kx S is T-linear and large

  20. Thermoelectric response functions E y x Current response Measured E field Total charge current is zero (open boundaries) (thermopower) (Nernst effect)

  21. Thermopower at 5, 9 and 14 T • Features of thermopower • Charge antisymmetric • Peak at n=1 nearly indpt of H • Very weak T dependence below 50 K

  22. Nernst Signal (off-diagonal Syx) • Nernst signal in graphene • Charge symmetric • Nernst signal is anomalously large • at Dirac Point • 3. Peaks at n=0, but dispersive for • n=1,2,3… • At n=0, sign is positive • (similar to vortex-Nernst signal in • superconductors)

  23. Quantization of thermoelectric current S 1 2 3 m 2 3 1 axy m Girvin Jonson 1982 1) Current response to DT is off-diagonal Dirac axy is quantized indpt of n = 93 nA/K

  24. Convert to thermoelectric conductivities axx and axy 93 nA/K • Peaks well defined • axx is antisym. In e • axy is symmetric 93 nA/K axy peak very narrow at n=0 Within 20% of quantized value (need to estimate gradient more accurately)

  25. 1. Field induces transition to insulating state • at Hc that correlates with V0. • For H>Hc, R0 is thermally activated (D ~ 14 K), • H<Hc, R0saturates below 2 K. • 3. H<Hc, divergence fits KT form exp[2b/(h-1)1/2]. • 4. Large Nernst signal at Dirac point. • 5. axy consistent with quantization • ~ 90 nA/K indpt of T, H and n.

  26. END

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