Superconducting proximity effect in graphene, Andreev reflection next to Quantum Hall edge states Endre Tóvári, 2012. dec. 13. Main sources: Transport through Andreev Bound States in a Graphene Quantum Dot Travis Dirks, Taylor L. Hughes, Siddhartha Lal, Bruno Uchoa, Yung-Fu Chen, Cesar Chialvo, Paul M. Goldbart, Nadya Mason Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Nature Physics 7, 386–390 (2011) doi:10.1038/nphys1911 Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Katsuyoshi Komatsu, Chuan Li, S. Autier-Laurent, H. Bouchiat and S. Gueron Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France. Phys. Rev. B 86, 115412 (2012) Quantum Hall Effect in Graphene with Superconducting Electrodes Peter Rickhaus, Markus Weiss,* Laurent Marot, and Christian Schönenberger Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland Nano Lett., 2012, 12 (4), pp 1942–1945, DOI: 10.1021/nl204415s

Transport through Andreev Bound States in a Graphene Quantum Dot Andreev reflection—where an electron in a normal metal backscatters off a superconductor into a hole—forms the basis of low energy transport through superconducting junctions. Andreev reflection in confined regions gives rise to discrete Andreev bound states (ABS) Travis Dirks, Taylor L. Hughes, Siddhartha Lal, Bruno Uchoa, Yung-Fu Chen, Cesar Chialvo, Paul M. Goldbart, Nadya Mason Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Nature Physics 7, 386–390 (2011) doi:10.1038/nphys1911 http://www.physics.wayne.edu/~nadgorny/research3.html http://arxiv.org/pdf/1005.0443.pdf

Transport through Andreev Bound States in a Graphene Quantum Dot 1 layer 10 layers The shift shows bulk p-doping by the backgate and contacts. Asymmetry shows doping by contacts: Work function mismatch at end contacts  charge transfer Low graphene DOS  metal dominance  p-doping under end leads http://arxiv.org/pdf/0802.2267v3.pdf http://arxiv.org/pdf/0804.2040v1.pdf

Transport through Andreev Bound States in a Graphene Quantum Dot Rtunnel~10x-100xR2p Work-function mismatch under SC probe: charge density pinned below the contact  local n-doping  confinement The ABS form when the discrete QD levels are proximity coupled to the superconducting contact (Andreev refl. + Coulomb charging effects) For Dirac particles, it is not the height but the slope of the barrier that results in the scattering and possible confinement of charge carriers. Klein tunneling through smooth barriers CAN lead to confinement.

Transport through Andreev Bound States in a Graphene Quantum Dot If U<<Δeff, the spin-up and spin-down states of the QD are nearly degenerate. Near the EF of the SC, they are occupied by paired electrons/holes, and the QD effectively becomes incorporated as part of the SC interface. The conductance is then BTK-like and thus suppressed inside the gap, as in SC-normal interfaces having large tunnel barriers. 0,26 K 0,45 K 0,67 K 0,86 K 1,25 K 1,54 K Pb: 2Δ=2.6 meV If U>>Δeff: ↑ and ↓ are widely split in energy, promoting pair-braking, QD is like a normal metal. ABS are formed from the discrete QD states due to Andreev reflections on the SC-QD interface Subgap peak amplitude, T↑: Decreasing until 0,8 K, constant after Quantum regime: Classical dot regime:

Transport through Andreev Bound States in a Graphene Quantum Dot Tunneling differential conductance map (logarithmic scale): A phenomenological model that considers the effect of the SC proximity coupling on a single pair of spin-split QD states: Subgap peaks from ABS Superposition of particle and hole states If U=0: E-ABS > |Δeff| for every Vg.  U>Uc needed for subgap conductance. From 1 pair of spin-split QD states just one ABS will be inside the gap (E-).

Transport through Andreev Bound States in a Graphene Quantum Dot 2 subgap peaks (E-) from ABS: originated from 2 QD states (in this range) Essential parts: QD confined via a pn-junction in graphene (+U Coulomb charging energy is large enough) the low density of states in graphene the large tunneling barrier solid(dashed) lines represent states which have dominant particle(hole) character (ABS: hybridized e+h states) Normal (single-particle) QD states do not contribute to subgap features. A fit of the conductance data from the detailed transport calculations for a quantum dot with two levels, a finite charging energy, and with couplings to normal metal and superconducting leads.

Revealing the electronic structure of a carbon nanotube carrying a supercurrent Nature Physics 6, 965 (2010) http://arxiv.org/pdf/1005.0443.pdf

Superconductor-graphene-superconductor: Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Superconducting proximity effect: Superconductor-graphene-superconductor: SGS junction Critical current vs gate voltage in zero magnetic field Proximity effect in the Integer Quantum Hall regime Katsuyoshi Komatsu, Chuan Li, S. Autier-Laurent, H. Bouchiat and S. Gueron Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France. Phys. Rev. B 86, 115412 (2012) http://www.gdr-meso.phys.ens.fr/uploads/Aussois_2011/komatsu_GDR_forPDF.pdf

Ic suppressed around CNP (Dirac point) Nb, 200mK Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Superconducting proximity effect: Critical current sensitive to: Phase coherence length (must be longer than sample) Interface quality Ic suppressed by temperature Ic suppressed around CNP (Dirac point) Nb, 200mK ReW, 55mK CNP=charge neutrality point, n(Vg)≈0

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Critical current sensitive to: Phase coherence length (must be longer than sample) Interface quality Ic suppressed by temperature 200 mK 55 mK There is not a constant factor between ETh/eRN and Ic.

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Critical current sensitive to: Phase coherence length (must be longer than sample) Interface quality Ic suppressed by temperature All pairs (e+h) contribute to the supercurrent with their phase. Specular reflection: not time-reversed trajectories, suppressed current.

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Doped graphene Near Dirac point Deshpande et al., Phys. Rev. B 83, 155409 (2011) Ky and ε are conserved, but the reflected hole is in the other band! retroreflection specular reflection http://www.gdr-meso.phys.ens.fr/uploads/Aussois_2011/komatsu_GDR_forPDF.pdf C. W. J. Beenakker: Colloquium: Andreev reflection and Klein tunneling in graphene, REVIEWS OF MODERN PHYSICS, VOL 80, OCT.–DEC. 2008

http://www. gdr-meso. phys. ens http://www.gdr-meso.phys.ens.fr/uploads/Aussois_2011/komatsu_GDR_forPDF.pdf

http://www. gdr-meso. phys. ens http://www.gdr-meso.phys.ens.fr/uploads/Aussois_2011/komatsu_GDR_forPDF.pdf

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Quantum Hall effect in a wide sample 70 mK; 0-7,5 T (<Bc for ReW) due to inhomogeneities and scattering in the wide sample (imagine 3 parallel sheets) filling factor

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. B Vg ReW, 55 mK, Vg=0, offset by 100 Ω ReW, 70 mK, Vg=-7..4V, B=7,5 T, no offset! Sometimes a dip in dV/dI at zero bias, depending on gate and field. Dips (peaks) mean alternating constructive (destructive) interference of Andreev pairs - signature of proximity effect. conduction via a few edge statessometimes the total round-trip dephasing doesn’t average to zero (tuning of interference), unlike at B=0 (puddles, crit. current suppressed)

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime. Zero field: reduced supercurrent near charge neutrality point, due to dephasing originating from specular reflection at charge puddles. High field – Quantum Hall regime: ballistic-like conduction via a few channels (edge states) for some puddle configs (Vg) and fields the total dephasing doesn’t average to zero tuning of interference, and thus of the proximity effect Aharonov-Bohm type effect in the edge state (ReW: high Hc superrconductor)

Quantum Hall Effect in Graphene with Superconducting Electrodes Peter Rickhaus, Markus Weiss,* Laurent Marot, and Christian Schönenberger Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland Nano Lett., 2012, 12 (4), pp 1942–1945, DOI: 10.1021/nl204415s Nb: upper critical field ~4 T at 4K quadratic wide Quantum Hall regime: electron hitting the superconductor-graphene S-G interface : Andreev retroreflection (if in the same band) Andreev edge state (e and h orbits) propagates along the interface, perfect interface: doubling of conductance

Quantum Hall Effect in Graphene with Superconducting Electrodes 2-terminal: G is a mixture of σxx and σxy wide sample: W/L~70, σxx dominates no flat plateaus visible but G minima are (LL steps) enhanced G due to superconductivity below Bc, plus QHE

Quantum Hall Effect in Graphene with Superconducting Electrodes 2-terminal conductance on quadratic samples: clear plateaus, despite the mixing corrected for contact resistance by mathing QH plateau at B>Bc2 quadratic Nb: upper critical field ~4 T at 4K cuts at constant filling factor 3.2T 4T

Quantum Hall Effect in Graphene with Superconducting Electrodes 1.1, 1.4 and 1.8 factor decrease between 3.2 T and 4 T for ν=2, 6, 10 (narrow field range: no LL overlap) the conductance increase is more pronounced when more QH edge states are involved (ν=6, 10 ) upper limit: factor of 2 (ideal, fully transparent S-N interface) 3.2T 4T

Quantum Hall Effect in Graphene with Superconducting Electrodes Weak disorder at S-2DEG interface, with 1 spin-degenerate edge state ideal, fully transparent S-N interface: 2G0 incoming electron edge state scatters into 2 Andreev edge-states (hybridized electron-hole states, with τ1, 1-τ1 probability) after propagating along the S-N interface, the Andreev edge states scatter to an electron or a hole edge state at the opposite edge (τ2, 1-τ2) quasi-classical picture Landauer-Büttiker picture 2e2/h EPL, 91 (2010) 17005, doi: 10.1209/0295-5075/91/17005

Quantum Hall Effect in Graphene with Superconducting Electrodes Weak disorder at S-G interface, with 1 spin-degenerate edge state Andreev reflection can be used to detect the valley polarization of edge states N=0 Landau level’s edge states are valley-polarized: ideally cosϴ=-1, doubling of conductance measurement: 1.1x increase in SC statestrong intervalley scattering N=1, 2 Landau levels’ edge states are valley degenerate (unlike N=0): less sensitive to disorder+further from edgesstronger conductance enhancement With only the E=0 Landau level populated (ν = 2): conductance of the S-G interface only depends on the angle θ between the valley polarizations of incoming and outgoing edge-state Identical opposite edges, ν = 2: Deviations are due to intervalley scattering (If the superconductor covers a single edge, ϴ= 0 and no current can enter the superconductor (without intervalley scattering, for ν = 2). ) For clean edges, conductance doubling would be expected for all LLs probably strong intervalley scattering Phys. Rev. Lett. 2007, 98, 157003

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