Transcript Quantum Hall Effect in Graphene with Superconducting

Superconducting proximity effect in graphene,
Andreev reflection next to Quantum Hall edge states
Main sources:
Endre Tóvári, 2012. dec. 13.
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 UrbanaChampaign, 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
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.
The ABS form when the discrete QD levels are proximity coupled to the
superconducting contact (Andreev refl. + Coulomb charging effects)
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 SCnormal interfaces having large tunnel
barriers.
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
0,26 K
0,45 K
Pb: 0,67 K
0,86
K
2Δ=2.6
meV
1,25 K
1,54 K
Subgap peak amplitude, T↑:
Decreasing until 0,8 K, constant after
Quantum regime:
kBT
E
e2 C
Classical dot regime:
E
kBT
e2 C
Transport through Andreev Bound States in a Graphene Quantum Dot
Tunneling differential conductance map (logarithmic scale):
Subgap peaks from ABS
A phenomenological model that
considers the effect of the SC
proximity coupling on a single
pair of spin-split QD states:


H     Eshift Vg  c c 


    U  Eshift Vg  c c 
   eff c c  h.c.
ABS

E
1
2
V


U

4

 g 2
eff  2   2 Eshift Vg   U


Superposition of particle and hole states
If U=0: E-ABS > |Δeff| for every Vg.


2



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)
characterQD
(ABS:
Normal
(single-particle)
states do not
hybridized
states)
contribute
to e+h
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
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
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
Nb, 200mK
Ic suppressed around CNP (Dirac point)
ReW, 55mK
CNP=charge neutrality point, n(Vg)≈0
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
200 mK
55 mK
Icmax T  0 ETh eRN , ETh  D L2
There is not a constant factor between ETh/eRN and Ic.
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
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.fr/uploads/Aussois_2011/komatsu_GDR_forPDF.pdf
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)
G
  en Bh
filling factor
e2

h
due to inhomogeneities and
scattering in the wide sample
(imagine 3 parallel sheets)
Superconducting proximity effect through graphene from zero field to
the Quantum Hall regime.
Vg
ReW, 70 mK, Vg=-7..4V,
B=7,5 T, no offset!
B
ReW, 55 mK, Vg=0,
offset by 100 Ω
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
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
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
quasi-classical
picture
 ideal, fully transparent S-N interface: 2G0
 incoming electron edge state scatters into 2 Andreev edgestates (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)
LandauerBüttiker
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,
of conductance
With only
the E=0doubling
Landau level
populated (ν = 2):
measurement:
1.1xS-G
increase
SC statestrong
conductance of the
interfaceinonly
depends on the angle θ
intervalley
between thescattering
valley polarizations
of incoming and outgoing
edge-state
N=1, 2 Landau levels’ edge states are valley degenerate
(unlike N=0):
less sensitive to disorder+further from edgesstronger
conductance
enhancement
Identical opposite
edges, ν = 2:
Deviations are due to intervalley scattering
(If the superconductor covers a single edge, ϴ= 0 and no
current
canedges,
enter the
superconductor
(without
intervalley
For
clean
conductance
doubling
would
be
scattering,for
for all
ν = LLs
2). )
expected
Phys. Rev. Lett. 2007, 98, 157003
probably strong
intervalley scattering
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