Andreev transport in 2D topological insulators

Transcription

1 Andreev transport in 2D topological insulators Jérôme Cayssol Bordeaux University Visiting researcher UC Berkeley ( ) Villard de Lans Workshop 09/07/2011 1

2 General idea - Topological insulators (TIs) are time reversal invariant phases with insulating bulk + conducting edge/surface states. - The edge/surface states are very special metals with unique spin-momentum locking properties. - Proximity induced superconductivity can be used to probe both the edge/surface and bulk carriers of TIs. - Andreev reflection (AR) is the fundamental scattering process underlying the proximity effect. 2

3 Outline Introduction: topological insulators (2D) - Andreev scattering of 1D edge carriers - Andreev reflection of 2D bulk carriers Conclusion 3

4 Quantum Spin Hall state (2D topological insulator) Reviews: M.Z. Hasan and C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010) Xiao-Liang Qi, Shou-Cheng Zhang, arxiv: and Phys. Today 63 1, 33. 4

5 Quantum Spin Hall insulator 2D band insulator with an helical metal on the edge E Bulk states Gapped bulk Fermi level (Bulk states q - Absence of backscattering by non-magnetic impurities - No Anderson localisation 5

6 Systems hosting helical edge carriers Theory - Graphene with intrinsic spin-orbit coupling (Kane-Mele, PRL 2005) - HgTe/HgCd wells (Bernevig, Hughes, and Zhang, Science 2006) - InAs/GaSb wells (Liu, Hughes, Qi, Wang, and Zhang, PRL 2008) Experiments - HgTe/CdTe wells (Molenkamp s group, Science 2007 and 2009) - InAs/GaSb (Rice group) See Rui-Rui Du s talk (Friday morning) Ivan Knez, Rui-Rui Du,Gerard Sullivan, arxiv: , arxiv:

7 HgTeCd quantum wells: 2D states E Even under inversion symmetry CdTe HgTe CdTe d d (A) Odd under inversion symmetry From B.A. Bernevig, T.L. Hughes, and S.C. Zhang, Science 314, 1757 (2006) 7

8 Effective model near band inversion Four-band model (2 spin degenerated bands) Relativistic Dirac in 2D with a mass term vanishing at d=dc Band inversion driven by the HgTe layer width d: M(dc)=0 d<dc trivial state (no edge states) M/B<0 d>dc quantum spin Hall state (edge states) M/B>0 8

9 Experiments (Molenkamp group, Wurzburg) L= 20 microns L= 1 micron W=1 micron W=0.5 micron Doped Regime (p) Insulating regime Doped Regime (n) 9

10 Andreev reflection (1964) Incident electron (E < gap) Reflected electron N S N Reflected hole Two scattering mechanism: ordinary reflection or Andreev reflection R - Straight interface: Andreev reflection is a retroreflection. - Usually normal reflection prevails upon AR (potential barriers, Fermi velocities, ) 10

11 Andreev reflection of helical carriers P. Adroguer, C. Grenier, D. Carpentier, JC, P. Degiovanni, and E. Orignac, Phys. Rev. B 82, (2010). Collaboration with Ecole Normale Superieure Lyon 11

12 NS and NSN geometries l l N S N S N Gapped bulk Gapped bulk - Superconducting correlations are induced within the boundary states (below S) by proximity effect. - At the mean field level, this can be described by a pairing potential having a finite value below the superconductors. - Then the scattering problem in solved within the helical edge Liang Fu and C.L. Kane, Phys. Rev. Lett. 100, (2008) 12

13 Gap openings around the Fermi points E E 0 to 30 mev 0.1 mev q 13

14 NS geometry Incident electron E<Delta Reflected hole S Total Andreev reflection: No transmission below superconducting gap with Helical property of the normal edge 14

15 Kinematics E S q Numerical evidence in presence of disorder: Qing-Feng Sun, Yu-Xian Li, Wen Long, and Jian Wang, Phys. Rev. B 83, (2011) More general scattering theory: C. W. J. Beenakker, J. P. Dahlhaus, M. Wimmer, and A. R. Akhmerov Phys. Rev. B 83, (2011) + Beri PRB

16 Experimental confirmation Rui-Rui Du s talk (Friday morning) Good contacts (transparency=0.7) Total Andreev Reflection in spite of the potential barrier/finite transparency 16

17 Tunneling processes in NSN geometry For a standard metal, both electrons and holes can be transmitted through the gapped S Incident electron Reflected hole S Elastic cotunneling Andreev transmission Experiments CNT L.G. Herrmann et al, PRL 104, (2010) See Andrea Baumgartner s talk 17

18 No Andreev transmission in NSN geometry For the helical metal, the hole cannot be transmitted because the holes carrying the proper spin moves the towards the NS interface. Incident electron Reflected hole S 18

19 Kinematics E S q The incident electron carries up spin The transmitted hole state carries the wrong spin Scattering by a superconducting barrier = 2 outcomes instead of 4 outcomes 19

20 Electronic transmission Total Andreev reflection 20

21 Noise properties Noise power Is(t)Is(0) Maximal noise 2 outcomes = Andreev reflection + elastic cotunneling Vanishing noise 1 outcome=andreev reflection Vanishing noise 1 outcome=electron tunneling 21

22 Related work Koji Sato, Daniel Loss, and Yaroslav Tserkovnyak, Phys. Rev. Lett. 105, (2010) Interedge processes Interaction effects 22

23 Andreev reflection of 2D bulk carriers In HgTe/CdTe quantum wells Marine Guigou and JC, Phys. Rev. B 82, (2010) M. Guigou, P. Recher, JC and B. Trauzettel, arxiv: Postdoc in Bordeaux (2010) and now Wurzburg 23

24 General idea - Interplay of the relativistic dynamics of 2D massive Dirac fermions and superconductivity. - Similar to graphene, see colloquium: C. W. J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008) - Differences: - Massive Dirac fermions (crossover ultra/non-relativistic). - Angular asymmetry in the Andreev reflection probability and related spin Hall effect. 24

25 Graphene case Bogoliubov-de Gennes equation NS diffferential conductance From C. W. J. Beenakker, PRL 2006 and Rev. Mod. Phys. 80, 1337 (2008) 25

26 Hamiltonian and NS geometry effective Hamiltonian (Bernevig, Hughes and Zhang) Bogoliubov-de Gennes equation Our approximation: Delta (r) abrupt step and diagonal in (E,H) space. More recent and detailled analysis: M. Khaymovich, N. M. Chtchelkatchev, and V. M. Vinokur, Phys. Rev. B 84, (2011) D. Futterer, M. Governale, U. Zuelicke, J. König, arxiv:

27 E BdG band structure: electrons and holes Hole spectrum from the valence band conduction band (electronic states) Fermi level E=0 Hole spectrum from the conduction band Valence band (electronic states) 27 kx

28 Normal side 2D propagative and evanescent modes Electron: E(ks)=0 yields 4 modes: 2 propagative (k^2 > 0) and 2 evanescent (k^2<0) Hole: same as for electron Superconducting side 4=2+2 Bogoliubons: all evanescent 2 Bogoliubons whose decay length is set by the superconducting gap 2 Bogoliobons by the normal decay length Boundary conditions at NS interface (x=0) Graphene: only propagative No coexistence between evanescent and propagative 28

29 E Low energy Andreev reflection is an intraband process Usual retro Andreev reflection Electrons belong to the same band Situation for high doping levels kx (perpendicular to interface) 29

30 E Intermediate energy No Andreev reflection Hole in the gap (this regime does not exist for graphene in the absence of spin-orbit) Possible conversion to edge modes (M<0) 30 qx

31 E High energy Andreev reflection is an interband process Specular Andreev reflection Electrons belong to the opposite bands Requires LOW doping Observability HgTeCd vs graphene 31 qx

32 AR probability Low energy NS Differential conductance M<0 Positive M Negative M 32

33 Crossover from ultra- to non-relativistic AR probability NS Differential conductance graphene Non relativistic case The Andreev reflection is more suppressed by a Fermi wavevector mismatch in the nonrelativistic limit than in the graphene case. 33

34 Angular dependence of AR probability - We find that AR probability is asymmetric: The HgTe/CdTe model has inversion symmetry The inversion symmetry is broken by the interface - We still have time reversal symmetry: This leads to spin current along the interface 34

35 Relation to evanescent modes Andreev reflection probability Evanescent mode - More pronounced asymmetry located around M<0 (critical region) - The highest asymmetry is also observed when the evanescent modes are strongly developed 35

36 Device using this effect 36

37 Conclusion: Proximity induced (mesoscopic) superconductivity is useful tool to probe: - Helical edge carriers of the Quantum Spin Hall state - Relativistic dynamics of 2D carriers in HgTe/CdTe metallic wells Many thanks to collaborators: Marine Guigou (Bordeaux, now in Würzburg), Alexander Buzdin (Bordeaux) Pierre Adroguer, David Carpentier, Edmond Orignac (ENS Lyon) Bjoern Trauzettel, Patrik Recher (Würzburg) Ken-Ichiro Imura (Sendai, Hiroshima) Funding: ANR ISOTOP ENS Lyon-LOMA Bordeaux 37

38 Thanks for your attention! 38