Dirac Cone Systems. Miguel Monteverde. LPS, Univ. Paris-Sud, CNRS, UMR 8502, F Orsay Cedex, France.

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1 Dirac Cone Systems Miguel Monteverde LPS, Univ. Paris-Sud, CNRS, UMR 8502, F Orsay Cedex, France.

2 Outline Introduction to graphene and applications Dirac Cones on graphene Dirac Cones on -(BEDT-TTF) 2 I 3

3 Introduction 2/3 What is graphene? Graphene

4 Introduction 2/3 What is graphene? Strong bond Graphene Weak bonds (Van der Waals) Graphite

5 Introduction 2/3 What is graphene? Strong bond Novoselov & Geim (2005) Graphene Weak bonds (Van der Waals) Graphite

with a graphite flake Put in a scotch tape Exfoliate many times Apply

6 How we make graphene? Exfoliation technique Geim & Kim (2008) Fabrication Process : Start with a graphite flake Put in a scotch tape Exfoliate many times Apply to clean wafer (SiO 2 ~ 300nm) Search for graphene with optical microscope / Raman spectra Few Layers Graphene 20um Graphene

7 Introduction 2/3 What makes graphene so interesting? Number of graphene publications* with graphene in their title Discovery Year

8 Introduction 2/3 Graphene applications potentiality Composites Supercapacitors 10 um Large size graphene production Bistables Memories Flexible and transparent electronics Fast electronics

9 Introduction 2/3 What makes graphene so interesting? Graphene properties : Strongest material Y~ 1 TPa U ~ 42 N/m Changgu Lee, et.al. (2008) Optically transparent (Absorption 2.3%) P.Blake, et.al. (2008) Best thermal conductor k ~ 5000 W/mK A.A.Balandin, et.al. (2008) Best electrical conductor at room Temperature j ~ma/ m ~10 5 cm 2 /Vs Very special electrical conductor : Dirac band structure Wallace (1947)

Composites Composite materials with 0.1% graphene : Si 3 N 4 + 1.

1% Graphene Tensile strength 0.1% Graphene Fracture Toughness Fracture Energy 0.

10 Composites Composite materials with 0.1% graphene : Si 3 N vol% graphene - large contact surface - Is strong and stiff - It avoids crack propagation +40% +53% +126% Epoxy 0.1% SWNT 0.1% MWNT 0.1% Graphene Tensile strength 0.1% Graphene Fracture Toughness Fracture Energy 0.1% Graphene Crack propagation rate is reduced by 1 to 2 order of magnitude Mohammad A. Rafiee, Javad Rafiee, Zhou Wang, Huaihe Song, Zhong-Zhen Yu, and Nikhil Koratkar ACS Nano 3 (2009), 3884 Luke S. Walker, Victoria R. Marotto, Mohammad A. Rafiee, Nikhil Koratkar, and Erica L. Corral ACS Nano 5 (2011), 3182

Bistable Memories Reduced Graphene Oxide R H /R L ~10 6 5 um 100 10 1 0.1 0.01 0.

Sinitskii and J.M. Tour Nature Materials 7 (2008), 966 K.

11 Bistable Memories Reduced Graphene Oxide R H /R L ~ um Pulse width (khz) Graphene memories based on Reduced Graphene Oxide and CVD graphene Y. Li, A. Sinitskii and J.M. Tour Nature Materials 7 (2008), 966 K.S.Vasu, S. Sampath and A.K. Sood Solid State Communications 151 (2011), 1084 X. Wang, W. Xie, J. Du, C. Wang, N. Zhao and J.B. Xu Advance Materials 24 (2012), High On/Off ratio - Mass production (repeatability) - Resilient: - Large retention time (+months) - Temperature (200 C) - Radiation (+20 8keV) - Average writing and deleting speed - High Resistance

12 Flexible & transparent electronics Touch screen PET y electrodes PET Graphene x electrodes Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros O zyilmaz, Jong-Hyun Ahn, Byung Hee Hong and Sumio Iijima Nature Nanotechnology 5 (2010), 574

13 Flexible & transparent electronics Graphene vs indium tin oxide (ITO): (for use as a transparent conductive coating) - ITO is brittle - Indium becomes rare and expensive while CVD graphene is low cost - ITO is less transparent and more resistive - ITO is not flexible - Graphene has long cycle-life (+1000 bends) Applications : flat-panel displays touch screens organic light-emitting diodes (OLEDs) solar cells Sukang Bae, Hyeongkeun Kim, Youngbin Lee, Xiangfan Xu, Jae-Sung Park, Yi Zheng, Jayakumar Balakrishnan, Tian Lei, Hye Ri Kim, Young Il Song, Young-Jin Kim, Kwang S. Kim, Barbaros O zyilmaz, Jong-Hyun Ahn, Byung Hee Hong and Sumio Iijima Nature Nanotechnology 5 (2010), 574

14 Industrial production of large size Graphene 2005 Exfoliated 2008 Epitaxial (on SiC) 2010 CVD 10 um 2 1 cm 2 1 m US$ / m

15 Outline Introduction to graphene and applications Dirac Cones on graphene Dirac Cones on -(BEDT-TTF) 2 I 3

16 Quantum transport in graphene Miguel Monteverde, C. Ojeda Aristizabal, R. Weil, M. Ferrier, S. Gueron, H. Bouchiat, J.N. Fuchs and D. Maslov LPS, Univ. Paris-Sud, CNRS, UMR 8502, F Orsay Cedex, France.

17 Introduction 2/3 What makes graphene so interesting? Graphene properties : Strongest material Y~ 1 TPa U ~ 42 N/m Changgu Lee, et.al. (2008) Optically transparent (Absorption 2.3%) P.Blake, et.al. (2008) Best thermal conductor k ~ 5000 W/mK A.A.Balandin, et.al. (2008) Best electrical conductor at room Temperature j ~ma/ m ~10 5 cm 2 /Vs Very special electrical conductor : Dirac band structure Wallace (1947)

18 Conventional 2DEG band structure Conventional 2DEG electrons holes massive fermions electron-hole asymmetry E e =ħ 2 k F2 / 2 m e * massive fermions physics

19 Graphene electronic band structure Conventional 2DEG electrons holes massive fermions electron-hole asymmetry E e =ħ 2 k F2 / 2 m e * Graphene k F =0 F = semiclasical physics not valid! m*~1/ (d 2 E/dk 2 ) Dirac cone band spectrum E=ħ v F k F (m*=0) v F ~10 6 m/s massless fermions massless fermions physics

F2 / 2 m e * Graphene Dirac cone band spectrum E=ħ v F k F (m*=0) v F ~10 6 m/s

20 Graphene electronic band structure Why few-layer graphene? Conventional 2DEG electrons holes massive fermions electron-hole asymmetry E e =ħ 2 k F2 / 2 m e * Graphene Dirac cone band spectrum E=ħ v F k F (m*=0) v F ~10 6 m/s massless fermions Bilayer Graphene E=ħ 2 k F2 / 2 m * m*=0.03 m e massive fermions (Low energy) massive vs. massless fermions

fermions Bilayer Graphene zero gap tunable carrier density and type

21 Graphene electronic band structure Why few-layer graphene? Conventional 2DEG electrons massive fermions holes Graphene massless fermions Bilayer Graphene zero gap tunable carrier density and type electron-hole symmetry massive fermions (Low energy) V G massive vs. massless fermions

22 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons holes

23 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons At Dirac point no charge is present (ballistic) holes perfect transmission across barriers via evanescent modes Conductivity quantization = 4e 2 / h

24 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons At Dirac point no charge is present (ballistic) holes perfect transmission across barriers via evanescent modes Conductivity quantization = 4e 2 / h Geim, et.al. (2007) The mystery of the missing pi ( ) Experiment min = 4e 2 /h Theory min = 4e 2 / h

25 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons At Dirac point no charge is present (ballistic) holes Measurement of the local electrostatic potential J.Martin, et.al. (2007) SET electrons holes V g n n When n ~ 0

26 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons At Dirac point no charge is present (ballistic) holes Measurement of the local electrostatic potential J.Martin, et.al. (2007) SET electrons holes V g n n When n ~ 0 Morpurgo (2008)

27 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons ~ V G Out of Dirac point Diffusive ~ 10 3 cm 2 /Vs what type of impurities? holes

28 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons holes ~ V G Out of Dirac point Diffusive ~ 10 3 cm 2 /Vs what type of impurities? Neutral-short range and weak impurities: Fermi golden rule & Drude tr -1 ~ D(E F ) ~ k F = 2 v F k F tr ~ const

29 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons holes ~ V G Out of Dirac point Diffusive ~ 10 3 cm 2 /Vs what type of impurities? Neutral-short range and weak impurities: Fermi golden rule & Drude tr -1 ~ D(E F ) ~ k F = 2 v F k F tr ~ const Charged (screened) impurities: Thomas-F. approximation, Fermi golden rule & Drude U ~ q -1 TF ~ k -1 F -1 tr ~ U 2 D(E F ) ~ k -1 F = 2 v F k F tr ~ k F2 ~ 2 V g

30 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons holes ~ V G Out of Dirac point Diffusive ~ 10 3 cm 2 /Vs what type of impurities? Neutral-short range and weak impurities: Fermi golden rule & Drude tr -1 ~ D(E F ) ~ k F = 2 v F k F tr ~ const Charged (screened) impurities: Thomas-F. approximation, Fermi golden rule & Drude U ~ q -1 TF ~ k -1 F -1 tr ~ U 2 D(E F ) ~ k -1 F = 2 v F k F tr ~ k F2 ~ 2 V g 55 (T) Ethanol 25 Ethanol (T) Measured Expected Geim (2009)

31 Is (V G ) in graphene understood? Novoselov, et.al. (2005) electrons holes ~ V G Out of Dirac point Diffusive ~ 10 3 cm 2 /Vs what type of impurities? Neutral-short range and weak impurities: Fermi golden rule & Drude tr -1 ~ D(E F ) ~ k F = 2 v F k F tr ~ const Charged (screened) impurities: Thomas-F. approximation, Fermi golden rule & Drude U ~ q -1 TF ~ k -1 F -1 tr ~ U 2 D(E F ) ~ k -1 F = 2 v F k F tr ~ k F2 ~ 2 V g M.Monteverde, et.al. (2010) Graphene Bilayer Neutral-short range (R) and strong impurities: measurements of transport scattering times for both graphene and bilayer tr ~ k F ln 2 (k F R) ~ V g ln 2 (RV 0.5 g ) = 2 v F k F tr Most probable ad-atoms (binding affinity is improved by corrugation caused by the substrate).

32 Massless and Massive Fermions differences Quantum Hall Effect Universal Conductance Fluctuations Induced Superconductivity 2/3 n Dirac = 4 (n+1/2) B/ 0 n Massive = 4 n B/ 0 B C Dirac V g -1/4 B C Massive V g -1/2 2 Specular Andreev Reflexions? M.Monteverde, et.al. (2010) C.Ojeda-Aristizabal, et.al. (2010) C.Ojeda-Aristizabal, et.al. (2009)

33 Outline Introduction to graphene and applications Dirac Cones on graphene Dirac Cones on -(BEDT-TTF) 2 I 3

34 Dirac Cones on (BEDT TTF) 2 I 3 Miguel Monteverde, M.O. Goerbig, P. Auban Senzier, F.Navarin, H.Henck, C.R. Pasquier, C.Mézière, and P.Batail LPS, Univ. Paris Sud, CNRS, UMR 8502, F Orsay Cedex, France.

35 Graphene Dirac Point E F T F E F Theoretical Dirac Point Experimental Dirac Point

36 Graphene Dirac Point E F T F E F Theoretical Dirac Point Experimental Dirac Point J.Martin, et.al. (2007) T F ~ 100K E F Graphene Dirac Point electrons holes

37 Dirac-cone systems Organic conductor a (ET) 2 I 3 stacking conducting ET layers and insulating Iodine layers bulk material with strong 2D conductance

38 Dirac-cone systems Organic conductor a (ET) 2 I 3 P.Alemany, et.al. (2012) Tilted Dirac cones under pressure. Fermi level will be at Dirac point.

39 Magneto-conductance of a-et 2 I 3 J.S.Kim, et.al. (1993) Magneto-conductance: xx (0) Only one type of carrier:

40 Magneto-conductance of a-et 2 I 3 J.S.Kim, et.al. (1993) Monteverde, et.al. (2012) Magneto-conductance: Only one type of carrier:

41 Magneto-conductance of a-et 2 I 3 J.S.Kim, et.al. (1993) Monteverde, et.al. (2012) Magneto-conductance: Only one type of carrier: Two types of carriers: a-et 2 I 3 is a multicarrier system

42 Magneto-conductance of a-et 2 I 3 J.S.Kim, et.al. (1993) Monteverde, et.al. (2012) Magneto-conductance: Only one type of carrier: Two types of carriers: measurements of the carrier density

43 Magneto-conductance of a-et 2 I 3 J.S.Kim, et.al. (1993) Monteverde, et.al. (2012) Magneto-conductance: Only one type of carrier: Two types of carriers: measurements of the carrier density

44 Magneto-conductance of a-et 2 I 3 T T 2 the carrier density depend on temperature

45 Dirac-cone band structure Conventional 2DEG electrons holes massive fermions electron-hole asymmetry E M =ħ 2 k F2 / 2 m * D M =g v g s m* / 2 ħ 2 = constant n M (T) = f D de T (T»T F )

46 Dirac-cone band structure Conventional 2DEG electrons holes massive fermions electron-hole asymmetry E M =ħ 2 k F2 / 2 m * D M =g v g s m* / 2 ħ 2 = constant n M (T) = f D de T (T»T F ) Dirac - Cone Band structure massless fermions m*~1/ (d 2 E/dk 2 ) (m*=0) E=ħ v F k F D Dirac =g v g s E / 2 (ħv F ) 2 E Dirac-Point : n Dirac (T) = f D de T 2 (T»T F ) the carrier density depend on temperature

47 Magneto-conductance of a-et 2 I 3 Massive fermions n M (T) T (T»T F ) T T 2 Dirac fermions n D (T) T 2 (T»T F ) Coexistence of Massive and Dirac fermions

48 Magneto-conductance of a-et 2 I 3 Massive fermions n M (T) T (T»T F ) T T 2 Dirac fermions n D (T) T 2 (T»T F ) Coexistence of Massive and Dirac fermions

49 Graphene vs a-et 2 I 3 under pressure Dirac Point TF ~ 1K E F T F ~ 100K E F a ET 2 I pressure Graphene

50 Graphene vs a-et 2 I 3 under pressure Electron Correlations v F ~ 10 5 m/s r s ~? a ET 2 I pressure r s Dirac ~ e2 εħ v F v F ~ 10 6 m/s r s ~ 0.5 Graphene

51 Graphene vs a-et 2 I 3 under pressure Electron Correlations ~ T -2 Dirac / Massive system: Calculating the scattering times using Fermi golden rule 10-3 T (T~T F ) (T>T F ) ~ T -1 a ET 2 I pressure

52 Conclusions Coexistence of Dirac and Massive carriers T F Dirac ~1 K (2 order of magnitude lower than graphene) v F Dirac ~10 5 m/s (1 order of magnitude lower than graphene) Electronic correlations may be relevant! Electronic correlations are not only relevant but needs of both types of carriers to explain the physics. Mobility ratio Temperature dependence of the Mobility ratio Dirac Point Physics can be studied in others systems than graphene that can have an homogenous Fermi level.

53 Merry Christmas and Happy New Year Thanks for your attention

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