In the conventional quantum theory of the electronic structure of
solids the interacting and the free spectra are adiabatically connected,
the strong bare couplings are significantly renormalized and the resulting
state is that of a weakly interacting gas of excitations.
This approach, known as the "Fermi-liquid theory'', has been extraordinarily
successful at describing the properties of metals and semiconductors.
However, in the last two decades a large number of materials has
been discovered in which the Fermi-liquid paradigm breaks down.
Among the systems in question one finds the fractional quantum Hall
effect, high mobility semiconducting devices which appear to show
metal-insulator transition in two dimensions, the cuprate high-temperature
superconductors, and other oxides, including the ruthenates, the
nickelates and the colossal magnetoresistance materials - the manganites.
There is a clear need for new theoretical principles and techniques
to deal with the wealth of novel behaviors that these systems exhibit.
I take part in the search for such principles.
In my work I have focused my attention on two problems in particular.
The first is the interacting two-dimensional electron gas in a strong
magnetic field. This system exhibits a plethora of exotic phenomena
such as the fractional quantum Hall effect and the existence of
excitations with fractional charge and statistics. In addition to that,
the edges of such samples offer a realization of
a peculiar state of matter, the "Luttinger liquid", made
out of interacting electrons moving in one dimension. I have been
interested in its properties and the way it is born out of the physics
that governs the bulk of the sample.
I have carried my interest in low-dimensional interacting systems
to the field of high temperature superconductivity which currently
constitutes my prime field of study. One concept that has emerged
in this context is the electronic stripe phase in which
the charge carriers spontaneously segregate into one-dimensional
"rivers of charge". There is a growing body of
experimental evidence supporting the existance of such phases
in the cuprate high temperature superconductors and other systems,
most recently in quantum Hall samples.
Stripes occur commonly in systems with short range attractive
interactions and long range repulsive forces.
In the cuprates, which become superconductors upon doping of holes
into an antiferromagnet, the holes tend to phase separate in order
to reduce the energetic penalty associated with their motion
through the antiferromagnetic background. However, owing to the
presence of long range Coulomb forces complete phase separation
is averted and stripes emerge as the best compromise.
I am pursuing an understanding of the electronic properties of
stripe phases and their relation to the phenomenology
of the high temperature superconductors.
"From the Chern-Simons
Theory for the Fractional Quantum Hall Effect to the Tomonaga-Luttinger
Model of Its Edges'', D. Orgad, Phys. Rev. Lett. 79,
Crossover in Quasi-One-Dimensional and High T_c Superconductors'',
E. W. Carlson, D. Orgad, S. A. Kivelson and V. J. Emery, Phys. Rev.
B 62, 3422 (2000).
for Electron Fractionalization From Photoemission Spectra in the
High Temperature Superconductors'', D. Orgad, S. A. Kivelson,
E. W. Carlson, V. J. Emery, X. J. Zhou and Z. X. Shen, Phys. Rev.
Lett. 86, 4362 (2001).
High Temperature Superconductivity", E. W. Carlson, V. J. Emery,
S. A. Kivelson and D. Orgad, review chapter in
"The Physics of Superconductors: Superconductivity in Nanostructures,
High-Tc and Nivel Superconductors", Vol 2, p. 275-452,
edited by K. H. Bennemann and J. B. Ketterson (Springer-Verlag 2004).
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