main sources: transport through andreev bound states in a graphene quantum dot travis dirks, taylor...

Main sources:Transport through Andreev Bound States in a Graphene Quantum DotTravis Dirks, Taylor L. Hughes, Siddhartha Lal, Bruno Uchoa, Yung-Fu Chen, Cesar Chialvo, Paul M. Goldbart, Nadya MasonDepartment of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USANature 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. GueronLaboratoire 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 ElectrodesPeter Rickhaus, Markus Weiss,* Laurent Marot, and Christian SchonenbergerDepartment of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, SwitzerlandNano Lett., 2012, 12 (4), pp 1942–1945, DOI: 10.1021/nl204415s

Endre Tóvári, 2012. dec. 13.

Superconducting proximity effect in graphene, Andreev reflection next to Quantum Hall edge states

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)

http://www.physics.wayne.edu/~nadgorny/research3.html http://arxiv.org/pdf/1005.0443.pdf

Travis Dirks, Taylor L. Hughes, Siddhartha Lal, Bruno Uchoa, Yung-Fu Chen, Cesar Chialvo, Paul M. Goldbart, Nadya MasonDepartment of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USANature Physics 7, 386–390 (2011) doi:10.1038/nphys1911


The shift shows bulk p-doping by the backgate and contacts.Asymmetry shows doping by contacts:

1 layer

10 layers

Work function mismatch at end contacts charge transferLow graphene DOS metal dominance p-doping under end leads

http://arxiv.org/pdf/0802.2267v3.pdf http://arxiv.org/pdf/0804.2040v1.pdf

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.

Rtunnel~10x-100xR2p


Pb:2Δ=2.6 meV

0,26 K0,45 K0,67 K0,86 K1,25 K1,54 K

Subgap peak amplitude, T↑:Decreasing until 0,8 K, constant after

Quantum regime: Classical dot regime:2

BE k T e C 2Bk T E e C

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

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.


Tunneling differential conductance map (logarithmic scale):

Subgap peaks from ABS

A phenomenological model that considers the effect of the SC proximity coupling on a singlepair of spin-split QD states:

. .

shift g

shift g

eff c c

H E V c c

h

U E V c c

c

221

4 2 22

ABSg eff shift gE V U E V U

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-).

Superposition of particle and hole states


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.

solid(dashed) lines represent states which have dominant particle(hole) character (ABS: hybridized e+h states)

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

Normal (single-particle) QD states do not contribute to subgap features.

2 subgap peaks (E-) from ABS: originated from 2 QD states (in this range)

http://arxiv.org/pdf/1005.0443.pdf

Revealing the electronic structure of a carbon nanotube carrying asupercurrentNature Physics 6, 965 (2010)

Superconducting proximity effect through graphene from zero field to the Quantum Hall regime.

Critical current vs gate voltage in zero magnetic field

Proximity effect in the Integer Quantum Hall regime

Superconductor-graphene-superconductor:SGS junction

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

Superconducting proximity effect:

Katsuyoshi Komatsu, Chuan Li, S. Autier-Laurent, H. Bouchiat and S. GueronLaboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France.Phys. Rev. B 86, 115412 (2012)



Critical current sensitive to:•Phase coherence length (must be longer than sample)•Interface quality•Ic suppressed by temperature

Nb, 200mK

ReW, 55mK

Ic suppressed around CNP (Dirac point)

CNP=charge neutrality point, n(Vg)≈0




200 mK55 mK

There is not a constant factor between ETh/eRN and Ic.

max 20 , c Th N ThI T E eR E D L

All pairs (e+h) contribute to the supercurrent with their phase.Specular reflection: not time-reversed trajectories, suppressed current.




C. W. J. Beenakker: Colloquium: Andreev reflection and Klein tunneling in graphene, REVIEWS OF MODERN PHYSICS, VOL 80, OCT.–DEC. 2008http://www.gdr-meso.phys.ens.fr/uploads/Aussois_2011/komatsu_GDR_forPDF.pdf


Doped graphene Near Dirac point

retroreflection specular reflection

Ky and ε are conserved, but the reflected hole is in the other band!

Deshpande et al., Phys. Rev. B 83, 155409 (2011)

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


70 mK; 0-7,5 T (<Bc for ReW)Quantum Hall effect in a wide sample

en Bh filling factor

2eG

h

due to inhomogeneities and scattering in the wide sample (imagine 3 parallel sheets)


ReW, 70 mK, Vg=-7..4V,B=7,5 T, no offset!

Vg

ReW, 55 mK, Vg=0,offset by 100 Ω

B

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 statessometimes the total round-trip dephasing doesn’t average to zero (tuning of interference), unlike at B=0 (puddles, crit. current suppressed)


Zero field: reduced supercurrent near charge neutrality point, due to dephasing originating from specular reflection at charge puddles.

High field – Quantum Hall regime:

(ReW: high Hc superrconductor)

Aharonov-Bohm type effect in the edge state

• 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

Quantum Hall Effect in Graphene with Superconducting ElectrodesPeter Rickhaus, Markus Weiss,* Laurent Marot, and Christian SchonenbergerDepartment of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, SwitzerlandNano Lett., 2012, 12 (4), pp 1942–1945, DOI: 10.1021/nl204415s

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

Nb: upper critical field ~4 T at 4K

widequadratic

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

quadratic

2-terminal conductance on quadratic samples:•clear plateaus, despite the mixing•corrected for contact resistance by mathing QH plateau at B>Bc2


cuts at constant filling factor

Nb: upper critical field ~4 T at 4K

3.2T 4T


3.2T 4T

• 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)


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

EPL, 91 (2010) 17005, doi: 10.1209/0295-5075/91/17005

2e2/h

Weak disorder at S-2DEG interface, with 1 spin-degenerate edge state


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:

(If the superconductor covers a single edge, ϴ= 0 and no current can enter the superconductor (without intervalley scattering, for ν = 2). )

Weak disorder at S-G interface, with 1 spin-degenerate edge state

Phys. Rev. Lett. 2007, 98, 157003

Andreev reflection can be used to detect the valley polarization of edge states

probably strong intervalley scattering

Deviations are due to intervalley scattering

N=0 Landau level’s edge states are valley-polarized: ideally cosϴ=-1, doubling of conductancemeasurement: 1.1x increase in SC statestrong intervalley scattering

N=1, 2 Landau levels’ edge states are valley degenerate (unlike N=0):less sensitive to disorder+further from edgesstronger conductance enhancement

For clean edges, conductance doubling would be expected for all LLs

Thank you for your attention!

main sources: transport through andreev bound states in a graphene quantum dot travis dirks, taylor...

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