Transcript Packard Poster-2 - Northwestern University Mesoscopic Physics

Coherent Nonlocal Effects in Superconducting Nanostructures
Paul Cadden-Zimansky, Jian Wei and Venkat Chandrasekhar
Department of Physics and Astronomy, Northwestern University, Evanston, IL
Motivation
Microscopic objects that have become quantum
mechanically entangled exhibit novel behavior that violates
many of our classical intuitions.
The exploitation of
entangled quantum objects is at the heart of a number of
recently developed subfields in physics – quantum
computation, quantum cryptography, quantum information,
etc. Perhaps the simplest entangled object is two electrons
of opposite spin bound in a singlet state.
Nonlocal quantum coherence between normal probes placed on a superconductor is
predicted to occur through two microscopic processes. In crossed Andreev reflection
(a) the electrons forming a Cooper pair in the superconductor break up, with each
electron entering a different probe.
This entanglement occurs in many
materials which are cooled to low enough
temperatures to become superconductors
(S).
In this phase transition singlet
Cooper pairs of electrons are naturally
created. Though the constituent electrons
of these pairs form a single quantum
object, they are spatially separated by a
coherence length x which can extend
several hundred nanometers.
As this length scale is now easily accessible to
modern nanolithographic techniques, we ask the
question: is it possible to use the Cooper pairs in a
superconductor to quantum mechanically couple
two normal metal (N) probes placed on it? In
particular, can the quantum phase of electrons in
one probe be coherently communicated to the
other, without any current being passed between
the probes?
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.
Nonlocal Coherence Experiment
To demonstrate that a nonlocal signal between
two probes can communicate information about
the quantum phase of the electrons, a phasedependent current I(F) from one probe into the
superconductor needs to be established. The
nonlocal voltage VN can then be monitored as the
phase is tuned on a second probe located less
than a superconducting coherence length from the
first. To create the current, one of the normal
probes is embedded in a hybrid normal metalsuperconducting loop known as an Andreev
interferometer. The phase of electrons around this
loop are tuned by threading a magnetic flux F
through it. As this phase is altered, shifting
quantum interference effects are observed, such
as symmetric, periodic oscillations in the
resistance of the interferometer.
These
oscillations are periodic in the Fo=h/2e
superconducting quantum of flux. By creating a
nonequilibrium distribution of electrons in the
normal arm of the interferometer, such as by
sending a small DC current into its center along
with an AC measurement current, one can
produce the phase-tunable I(F) current. The
voltages generated by this current are monitored
on probes at the top and bottom corners of the
loop as well as the nonlocal probes just off it.
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Nonlocal Signals
Crossed Andreev Reflection & Elastic Cotunneling
Injecting a current from a gold normal metal
lead (I+) into an aluminum superconductor
(I-) the nonlocal voltages on spatially
separated normal probes (V1-6) are
measured relative to the superconductor
potential (V-).
Just below the 0.6 K
superconducting transition, peaks in the
nonlocal resistance are observed due to
single
electron
excitations
in
the
superconductor (charge imbalance). These
excitations are frozen out at the lowest
temperature revealing a remnant nonlocal
resistance that decays rapidly as the
distance to each nonlocal probe is
increased. The decay length of this lowtemperature, zero-bias resistance is several
hundred nanometers, comparable to the
superconducting coherence length.
1 mm
Cadden-Zimansky et al., Physical Review
Letters (2006)
In elastic cotunneling (b) the spatially extended Cooper pair mediates a long-range
tunneling of electrons from one probe to another. These two processes should only
occur if the normal metal probe separation is on the order of x, and can be observed
when electrons are injected from one probe into the superconductor and a nonlocal
voltage is monitored on the second probe.
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Observation of Nonlocal Phase Coherence
Phase coherent signals are observed both at the corners of the loop and also
nonlocally. The amplitude of the nonlocal signals are reduced sixfold from those
measured on the corners, consistent with rapid decay over the superconducting
coherence length.
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Coexistence of Normal Current and Supercurrent
One paradox regarding the supercurrent
traveling around the hybrid loop is that
the loop still has a finite resistance. This
paradox can be resolved by showing that
a normal metal can simultaneously
support a resistive normal current and a
resistanceless supercurrent.
1 mm
Measurements of an SNS wire are made with
two different sets of probes. Superconducting
probes are used to measure the resistance of
the whole wire while normal probes are used to
measure a part of the normal section at its
center.
At low enough temperatures a
supercurrent across the whole wire shows no
resistance while the normal part is still resistive.
The fact that the oscillations at the top and bottom of the loop are of opposite
polarities despite the symmetry of the device about its horizontal axis indicates that
the sign of the voltages are determined by a flux-induced supercurrent that
circulates around the interferometer loop.
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The apparent drop in the normal part
resistance when the supercurrent is
established is due to the fact that the
measurement current injected at point A now
has two paths to exit the wire at point B: the
usual path along the normal wire and a
second path that uses the resistanceless
channel from one superconductor to the
other.
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