Sub-gap conductance fluctuations in superconductor-graphene hybrid nanostructures

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1 Sub-gap conductance fluctuations in superconductor-graphene hybrid nanostructures G.Albert, B.Kaviraj, F.Gustavo, F.Lefloch, L.Jansen Laboratoire de Transport Electronique Quantique et Supraconductivité INAC, CEA Grenoble Prénom Nom - Guillaume Direction des Albert Sciences GDR de Méso la Matière 2010

Jansen Laboratoire de Transport Electronique Quantique et Supraconductivité

2 Outline Superconductor-Graphene hybrid nanostructures Conductance fluctuations in the normal state Superconductivity-enhanced fluctuations Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 2

Superconductivity-enhanced fluctuations Prénom Guillaume

3 Graphene A new nanomaterial : Monolayer of carbon atoms High mobility Field-effect devices A unique band structure : Linear dispersion relation 10µm Anomalous Quantum Hall Effect T = 4 K Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009) Dirac cones Novoselov et al.(2007) Nature 438, 197. Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 3

Castro Neto et al., Rev. Mod. Phys. 81, 109 (2009) Dirac cones Novoselov et al.

4 Graphene and superconductivity Specular Andreev reflection : C.W.J. Beenakker.(2007) Rev.Mod.Phys. 80, 1337 Some realizations : H.B.Heersche et al., Nature 446, (2007). X. Du et al., Phys. Rev. B 77, (2008). B.M Kessler et al., PRL 104, (2010). Observation of tunable Josephson effect Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 4

B 77, 184507 (2008). B.M Kessler et al., PRL 104, 047001 (2010).

lithography 1 Sample : 3 S-G-S junctions W = 3 µm, L = 300 nm Prénom

5 Sample design BIAS MEASURE I DC V DC I AC 10 µm V AC 10 µm Mechanical exfoliation on SiO 2 /Si wafer Deposition of Aluminum contacts by e-beam lithography 1 Sample : 3 S-G-S junctions W = 3 µm, L = 300 nm Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 5

6 Outline Superconductor-Graphene hybrid nanostructures Conductance fluctuations in the normal state Superconductivity-enhanced fluctuations Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 6

7 Field effect in the normal state Appearance of conductance fluctuations at low temperatures σ = n e µ Evaluation of the mobility : µ = V.cm²/s 10 µm Mean free path l = 10 nm Diffusion constant D = m²/s Thouless energy Eth = 40 µev = 0.5K The sample is small enough to see Universal Conductance Fluctuations Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 7

cm²/s 10 µm Mean free path l = 10 nm Diffusion constant D = 5.

Bouchiat et al., PRL 104, 186802 (2010) Study of correlations versus gate voltage Increase of UCF amplitude at Dirac point D. W.

8 Specific studies : UCF in graphene N.E. Stanley et al., PRB 77, (2008) Magnetic field signatures of UCF Decrease of UCF amplitude at Dirac point C. Ojeda-Aristizabal, H. Bouchiat et al., PRL 104, (2010) Study of correlations versus gate voltage Increase of UCF amplitude at Dirac point D. W. Horsell et al., Arxiv 0902:0904 (2009) Study of UCF correlations and weak localization amplitude No change UCF amplitude at Dirac point Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 8

9 Around the Dirac point Two sources of fluctuations : σ = n(ef) e µ(ef) Inhomogeneous sample : e h puddles at Dirac Point Martin et al., Nature Physics 4, (2008) Interferences : Universal conductance fluctuations L φ > L sample k f l > 1 Valid at the Dirac point? Percolating effects? Situation is not clear Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/2010 9

, Nature Physics 4,144-148 (2008) Interferences : Universal conductance fluctuations L φ > L sample k

10 Outline Superconductor-Graphene hybrid nanostructures Conductance fluctuations in graphene Superconductivity-enhanced fluctuations Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

11 Field effect and superconductivity Drop in the resistance of the S-G-S junction at T = 0.52 K Reproducible fluctuations get sharper Vgate = 0 V 10 µm Resistance nearly drops to zero at high gate voltage Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

52 K Reproducible fluctuations get sharper Vgate = 0 V 10 µm Resistance

12 Josephson effect in graphene Measurements of differential resistance at high gate voltage : Versus Temperature V gate = 30 V 2 = 100 µv Multiple Andreev reflections minima at 2 /2 and 2 /3 Central dip : Josephson effect ħic E J = = 10 µv 2e ~ k B T at 100mK Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

minima at 2 /2 and 2 /3 Central dip : Josephson effect ħic E J = = 10 µv 2e ~ k B T at

13 Josephson effect in graphene Measurements of differential resistance at high gate voltage : Versus Magnetic field V gate = 30 V T = 50 mk Critical field of the junction : H c = 140 Gauss B Fraunhofer-like pattern : Φ 0 = B x S Sample surface : S = 1 µm² Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

: H c = 140 Gauss B Fraunhofer-like pattern : Φ 0 = B x S Sample surface : S = 1 µm²

14 Josephson effect in graphene Measurements of differential resistance versus gate voltage : T = 50 mk Multiple Andreev reflections are still present Suppression of Josephson effect The amplitude of the peak varies strongly with small changes of the gate voltage Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

effect The amplitude of the peak varies strongly with small changes of the gate voltage

15 Enhanced conductance fluctuations Measurements of differential resistance at low gate voltage : T = 50 mk Strong fluctuations at zero bias Small fluctuations out of the gap Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

zero bias Small fluctuations out of the gap Prénom Guillaume Nom

Enhanced conductance fluctuations Study versus temperature : Tc = 520 mk Correlations between normal state and superconducting state Increase

16 Enhanced conductance fluctuations Study versus temperature : Tc = 520 mk Correlations between normal state and superconducting state Increase of fluctuations amplitude by a factor 4 below T c Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

of fluctuations amplitude by a factor 4 below T c Prénom Guillaume Nom

17 Enhanced conductance fluctuations Study versus Magnetic field : T = 50 mk Hc = 140 Gauss Suppression of the fluctuations below critical magnetic field Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

below critical magnetic field Prénom Guillaume Nom Albert -

18 Connection with other works Another observation of the phenomenon : J.Trbovic, N.Minder, F.Freitag, C.Schönenberger, Nanotechnology 21, (2010) dip Sub-gap enhanced Fluctuations A peak below the gap : peak C. Ojeda-Aristizabal, M.Ferrier, S. Guéron, H.Bouchiat, PRB 79, (2009). Suppression of the peak by cleaning the sample Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 9/20/

peak C. Ojeda-Aristizabal, M.Ferrier, S. Guéron, H.Bouchiat, PRB 79, 165436 (2009).

19 Pioneer works Theory : F. Zhou, B. Spivak, JETP 65, iss.4, Phase-sensitive transport through SNS junctions C.W.J. Beenakker, arxiv v2 (2005). Calculations for quasi-1d wires Experiments : K. Hecker, H. Hegger, A. Atland, K. Fiegle, PRL 79, (1997) Study of UCF in a N-S junction Factor 2x 2 observed in amplitude between N and S state V.T. Petrashov, V.N. Antonov, P. Delsing, R.Claeson, PRL 70, (1993) Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 20/09/

Fiegle, PRL 79, 1548-1550 (1997) Study of UCF in a N-S junction Factor 2x 2 observed in amplitude between N and S state V.T.

20 Conclusion Suppression of Josephson effect near the Dirac point Enhancement of conductance fluctuations by superconductivity Perspectives : Quantitative study of UCF and weak localization Need for a model of transport near the Dirac point Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 9/20/

UCF and weak localization Need for a model of transport near the Dirac point

21 The end Thank you for attention Prénom Guillaume Nom Albert - Direction GDR des Méso Sciences 2010 de la Matière 9/20/

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator Chang et al., Science 340, 167 (2013). Joseph Hlevyack, Hu Jin, Mazin Khader, Edward Kim Outline: Introduction: