Singlelayer graphene flake used in this experiment

1
Normal-Metal/Graphene/Superconductor Tunnel
Junctions
Nan Sun,1 Kristof Tahy,2 Huili Xing,2 Debdeep
Jena,2 Gerald Arnold,1 and Steven
Ruggiero1  1Department of Physics, University of
Notre Dame, Notre Dame, IN 46556 2Department of
Electrical Engineering, University of Notre Dame,
Notre Dame, IN 46556
Klein Paradox and Graphene Band Structure
Graphene is a planar hexagonal mat of carbon
atoms. The band-structure of graphene comprises
aligned, conical electron and hole bands. This
unique situation provides for a dispersion of the
form , and the coupling of electron
and hole carriers. This can give rise to Klein
tunneling whereby a wavefunction can propagate
within a barrier as opposed to decaying
exponentially with distance.  
Single-layer graphene flake used in this
experiment
Andreev Reflection at N/G/S Interfaces
Theory
?
?
If we introduce normal and superconducting
contacts along the length of a graphene sheet,
Andreev reflection (AR) will occur at the
normal-metal/graphene and graphene/superconductor
interfaces as depicted above. Noting the picture
to the right, an incident electron (e-) with an
energy below the superconducting energy gap ?
cannot propagate into the superconductor. AR
occurs instead the incident electron is
reflected as a hole (h), such that a pair of
charges (2e-) are transferred into the
superconductor and form a Cooper pair at the
Fermi level. In addition, if the Dirac point is
inside the gap, a new phenomenon will appear
Specular AR whereby the reflected hole from the
valence band follows the trajectory of a normally
reflected electron.
Linder et al. have shown that for N/G/S systems
of lateral dimension w, conductance oscillations
will appear below the superconducting energy gap
?. Furthermore, they show that if the
oscillations are generally constant or increasing
with bias, the superconducting coupling in the
graphene is s-like, whereas for attenuated
oscillations the coupling should be d-like.  
Device Design and Fabrication
Experimental Results
Shown are results for both the low-temperature (
) device current normalized by the
room-temperature current and the low-temperature
conductance normalized
by the room-temperature conductance, versus
normalized bias voltage, where ?Nb 1.4meV. For
these measurements, the back-gate potential was
adjusted to place the Fermi level at the Dirac
point. The observed oscillations have equal
energy spacing, and are in general accord with
the Linder model, exhibiting a series of
resonances at energies
. Using the measured width w 5.5µm, we
obtain energy spacings of 0.52meV, implying a
Fermi velocity of 1.38106 m/s. The energy
dependence of the oscillation amplitude suggests
an s-wave nature for the coupling in the graphene
film.
The fabrication of our N/G/S system began with a
commercially prepared exfoliated graphene flake
(50?m in length) on SiO2 (300nm). Au (200nm) and
Nb (300nm) contacts were separately deposited on
the flake, and patterned using e-beam
lithography. The lateral spacings, w, between Au
and Nb fingers ranged from 0.5-6?m.
eVbias/?Nb
Simplified Model
Conclusion
We have observed current oscillations for
Normal-Metal/Graphene/Superconductor structures
suggesting an association with Klein effects. As
such, our results would imply that the induced
superconductivity in our graphene layers is
s-wave in nature.
APS March Meeting, March 16-20, 2009 Pittsburgh,
PA USA