Professor Chapelier begins the tutorial by announcing a shift or a theme
that he'd be returning to throughout the talk regarding the question posed,
presumably by the organizers, for the discussion section to happen later
today: "How can one distinguish atomic and electronic inhomogeneities in
real materials?" (paraphrased). The speaker admits not understanding the
question or whether it is one that can be answered and has tried to examine
the field with this question in mind.
His tutorial is organized in three parts, the last of which is a discussion
with questions expanding on the proposed discussion question (above). The
first two parts are I. STM/STS review and II. Applications to highly
disordered superconductors.
Part I. STM/STS review
An STM consists of a metallic tip on a piezo electric tube that allows for
very fine manipulation of the tip near the surface of a sample. A bias is
applied between the sample and the tip, which creates a tunneling current
through the vacuum from sample to tip (or vice versa). The experimenter
measures this tunneling current. Difficulties in low temperature are
related to vibrations. The speaker specifically mentioned the difficulty in
having a high resolution over large (micon) areas because of stronger
vibrations experienced when the piezo is able to scan large areas.
Now we look at some "textbook systems." The first is NbSe2. Where we see
atomic resolution in the microscopy images with an overlaying modulation.
Charge density wave or artifact? Modulation depends on applied bias. Need to
study this superstructure carefully and know things about the tip, like that
its DOS doesn't change with bias.
The slide is interrupted by a computer problem. The speaker claims that the
problem is not on his computer. The organizer accuses the speaker of
stealing a computer. A few cable switches and we're up again.
Now the DOS is studied locally through the IV curves at different spatial
locations on the sample. (Microscopy is done at a fixed V). A kink in the
DOS at the edge of the superconducting gap turns out to be important and was
studied in detail by Guillam (PRB 2008). The kink is more pronounced between
Se atoms. Back to the question regarding different levels of inhomogeneity:
which kind(s) of inhomogeneity are the superstructure and the kink related
to? Blogger doesn't think this question is answered here.
Speaker describes using STM to measure the vortex lattice in
superconductors. References Hess, PRL 1989. The experimenter sits at a bias
voltage that corresponds to the tip of the coherence peak in the
superconductor, then watches coherence disappear periodically with the
spatial scan, revealing an array of vortices in a triangular lattice.
Blogger interprets the discussion to indicate that NbSe2 is especially
well-suited to measuring the vortex lattice. Measurements in BSCCO show much
less contrast between vortex cores and superconducting lattice. A
checkerboard pattern also appears inside the vortex core (which
inhomogeneity is this pattern due to?). (Hoffman data)
The last "textbook system" described is hybrid nanostructures of, for
example, Au overlapping Nb. Experimenters (Vinet, LeSuer) have probed the
DOS spectra at different positions and found a lot of different kinds of
spectra. The behavior of the gap and the coherence peaks appears to be very
complicated, but may also be well understood (?).
Part II. Highly disordered Superconductors
The disorder-driven SITs of granular films are compared to those of
homogeneous films. Homogeneous SITs have a sharp transition where insulators
give way directly to superconductors whereas granular SITs show more
features near the transition, like reentrance and kinks in the R(T).
Next, the disorder driven SIT of sputtered TiN films is shown, and shows
similarities to both the homogeneous and granular SITs previously shown. The
question of whether these films are granularly or homogeneously disordered
motivates the STM experiments.
STM measurements show superconducting grains embedded in an insulating
material. The spectra in a line across the grain edge shows a nice gap in
the superconductor that fills in with shrinking coherence peaks as you move
into the insulator. Curiously the gap width does not change. This does not
seem to be understood.
TiN films made by Atomic Layer Deposition (a la Baturina) seem to be a
totally different story. These films have very small nano-crystalline
grains, but are homogeneously disordered within the grain. Tc changes with
disorder in a way that roughly matches predictions of Finkelstein's model.
Additionally, the spectral measurements fits BCS rather well at low T and
low bias. However, these spectrum are not spatially homogeneous and vary
quite a lot from place to place (for ~100nm distances).
Some similarities are drawn to Trivedi's work: Tc goes to zero before the
gap disappears with increasing disorder. Also, something of a gap persists
far above Tc. Can plot this 'anomalous conductance' (at zero bias) with
temperature and find deltaG/G~ln(T/Tc), which the blogger understood to be
consistent with predictions due to superconducting fluctuations from
Varlamov and Dorin, JETP 1983 (not familiar with this work). Deciding
carefully on Tc to the accuracy of <50mK is important to getting this linear
dependence. Experimentally, Tc is very close to R(T)-->0.
This analysis brings up a conundrum, between microscopic (superconducting
fluctuations) and macroscopic (Tc) quantities which the blogger did not
completely understand.
Part III.
The speaker repeats the discussion question about atomic versus electronic
inhomogeneities. It seems no one wants to supply an answer as the audience
questions are all unrelated. Perhaps it will be addressed in tomorrow's
discussion section.
Blogged by Shawna Hollen (Brown)
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