

 Theory of hightemperature superconductivity
 Nanoscale superconductivity
 Strong electron correlations in solids
 The Electronphonon Interaction in Solids
 Spin currentinduced Spinflip interactions
All five of these topics are closely related; nonetheless a separate description
is provided for each:
1. Theory of hightemperature
superconductivity
There is no general consensus on the mechanism of superconductivity
in the high temperature oxide materials. Our work has focused
on understanding various anomalous superconducting and normal state properties
of these materials, both in terms of the conventional electronphonon mechanism
of superconductivity, and in terms of other novel mechanisms. Primary
amongst these has been the socalled "holemechanism" of superconductivity,
first proposed by J.E. Hirsch.
We have written a number of papers since
the late 1980's, which work out many of the consequences of this
mechanism. Ongoing work is directed towards discovering the "smoking
gun" signature which will point towards the correct theory for high temperature
superconductivity.
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2. Nanoscale Superconductivity
In 1959, Richard Feynman wrote, in a remarkably prophetic account,
entitled "There's
Plenty of Room at the Bottom" that in the future it would be
possible to read and write information on a tiny scale. Much of what he foresaw
has now been realized in the last two decades of the 20th century. Our group has
begun to examine the process of miniaturization on superconductivity. What has
to be modified? First, the Bardeen, Cooper, and Schrieffer (BCS) Theory
of Superconductivity is based on the grand canonical ensemble. Since present day experiments can detect the difference between an even and an odd number of electrons in
ultrasmall
superconducting
grains
the grand canonical ensemble is clearly not adequate. We have investigated the
predictions of a CANONICAL formulation of BCS theory (link
to paper), where even/odd effects, for example, emerge naturally. A
next obvious requirement for a proper description of superconductivity in small
nanograins is a correct description of surfaces and impurities. There
are several formulations one can use; we have adopted the Bogoliubovde Gennes
formalism. These calculations resemble BCS calculations, except that
the order parameter (and other quantities of interest) are allowed to
acquire a spatial dependence. Thus, even the occurence of surfaces results in
a dramatic change in the order parameter (link
to paper), particularly in the case where the order parameter has dwave
symmetry. We have also examined the effects of single impurities,
where, locally, they give rise to a strong suppression of the order parameter.
As our ability to fabricate small superconducting nanograins improves,
and our probes for observing the effect of superconductivity in these
grains (for example the scanning tunnelling microscope (STM)) improve in resolution,
the theory will have to keep pace to critically examine the many fascinating
properties of these grains.
Such a formalism is also required to properly describe the results
of surfacesensitive probes of the high temperature superconductors,
such as recent STM work and photoemission spectroscopy.
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3. Strong Electron Correlations in Solids
The motivation for this work comes from the hightemperature superconductors,
though, in many ways this represents a longstanding unsolved problem
in general. Perhaps because of the quasitwodimensional nature of the
cuprates, or perhaps because of the high critical temperatures
involved, fluctuations appear to play an important role in these systems
above Tc. One possible source of these fluctuations is the tendency to pair
itself, a contribution that can be summarized by the ladder diagrams
in the particleparticle channel. In collaboration with Robert
Gooding our group has been examining a systematic approach to this problem
in the low density limit. This requires going beyond the simple ladder
sum of diagrams, i.e. including renormalization or selfconsistent effects.
As a first step, long range order is suppressed properly in two dimensions
by including selfconsistent feedback on the single electron Green functions.
We are currently tackling the dynamics, and have already utilized a variety
of promising techniques (link
to paper A) (link to
paper B) (link to paper
C). The long term goal will be to have a completely controlled diagrammatic
theory in the low density limit.
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4. The Electronphonon Interaction in
Solids
(a) conventional superconductors
In collaboration with Jules
Carbotte we have examined various possible signatures of the electronphonon
interaction in conventional electronphonon superconductors. The primary
source of evidence for this interaction comes from the tunneling inversion
procedure (McMillan and Rowell, in Superconductivity (edited by Parks), 1969).
We have recently extended early work by Allen, Phys. Rev. B3, 305 (1971)
and Farnworth and Timusk Phys. Rev. B10, 2799 (1974), to show how the optical conductivity can also be inverted, in the normal state, for K_{3}C_{60}, to infer the electronphonon interaction in the fullerene family.
(b) polarons
In more extreme cases of very strong electronphonon interaction,
the electrons and phonons form quasiparticles called polarons.
Recent advances have been made using numerical diagonalization and strong coupling
techniques. Examples of work in this area are The Spectral Function
of a OneDimensional Holstein Polaron, by F. Marsiglio, in Phys. Lett.
A180, 280284 (1993) and Pairing in the Holstein Model in the Dilute Limit,
in Physica C244, 2134 (1995). In this latter paper retardation
effects are examined in the HolsteinHubbard Hamiltonian.
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5. Spin currentinduced Spinflip interactions
Much of the computer hard drive memory business
relies on the ability to flip magnetic spins quickly. One
new approach, often discussed in the past decade, is to use spin currents
to perform the flipping. This process can be described by the
LandauLifshitzGilbertbased
approach, a semiclassical formalism that works reasonably well in certain
parameter regimes. However, to gain further insight and to probe regimes where the
semiclassical approach is likely to break down, we have performed fully quantum
mechanical calculations to describe the spinflip process of Heisenbergcoupled
spins subjected to spin current wave packets. A densitymatrixbased approach is
required to avoid entanglement difficulties. Recent work is in
(
EPL paper) and in (PRB paper
), and references therein.
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