Condensed Matter Theory Office: CP-387D Phone: (859) 257-4729
Research Interests
Much of my recent work is in the area of
``strongly correlated electron systems'', in which the interactions
between electrons play a dominant role in selecting the ground state
and low-energy excitations of the system. Usually Nature reorganizes
the strongly interacting electrons into weakly interacting
``quasiparticles'', which are collective excitations of the electrons.
Examples are Landau's Fermi liquid theory, where the quasiparticles
have the same quantum numbers as the electron, or the
Bardeen-Cooper-Schreiffer theory of superconductivity, where the gound
state can roughly be described as a collection of Bose-condensed
Cooper pairs (pairs of electrons of opposite spin and momentum). The
collective excitations of this system are fermionic quasiparticles and
bosonic phase fluctuations. More exotic reorganizations occur in
fractional quantum Hall states, where the quasiparticles have a charge
which is a fraction of the electron's charge. The fundamental problem
of strongly correlated systems may be phrased as that of finding the
correct weakly interacting quasiparticles, and the theory that
describes their dynamics. Usually, because of the strong interactions,
this connection between the original electrons and the final
quasiparticles is nonperturbative (that is, the quasiparticle cannot
be understood as a small deviation from a noninteracting
electron). This makes the problem mathematically quite difficult.
The introduction of disorder, ubiquitous in real life in the form of
lattice imperfections or impurity atoms, makes the problem much more
challenging and interesting. Many symmetries of the clean system, such as translation and rotation, are now absent,
and this makes the analysis of disordered systems much harder. More
importantly, qualitatively new phenomena which are not present in
systems without disorder can arise in systems with disorder, even when
the electrons are noninteracting. Of course, real systems are both
disordered and interacting, potentially leading to even more
interesting new phenomena. I believe the interplay of interactions and
disorder will be one of the dominant themes of condensed matter theory
in the years to come, and I have started some investigations into this
subfield. In particular, with my co-workers Herb Fertig, Harsh Mathur, R. Shankar,
and Damir Herman, I have been able to obtain { nonperturbative}
solutions to this problem in certain experimentally interesting
regimes.
Specific topics I am working on are (i) The role of disorder in the bilayer quantum Hall systems, (ii) States with strong correlations and strong quantum fluctuations in mesoscopic systems, and (iii) The effect of disorder on gauge theories.
Education
B.Tech., Physics, Indian Institute of Technology, Madras (1982)
Ph.D., Theoretical Condensed Matter Physics), Yale University (1987)
Selected Recent Publications
G. Murthy, Phys. Rev. Lett. 84, 350 (2000):
``A Composite Fermion Hofstader Problem: Partially Polarized Density
Wave States in the FQHE''.
G. Murthy, Phys. Rev. Lett. 85, 1954 (2000):
``Hall Crystal States at \nu=2 and Moderate Landau Level Mixing''.
G. Murthy, Jour. Phys. Cond. Mat. 12, 10543 (2000) : ``Finite Temperature Magnetism in
Fractional Quantum Hall Systems: Composite Fermion Hartree-Fock and
Beyond''.
G. Murthy, Phys. Rev. B 64, 195310 (2001):
``Hamiltonian theory of the fractional quantum Hall effect: Conserving approximation for in compressible fractions''.
R. Narevich, G. Murthy, and H. A. Fertig, Phys. Rev. B 64, 245326 (2001):
``Hamiltonian Theory of the Composite Fermion Wigner Crystal''.
G. Murthy, Phys. Rev. Lett. 87, 179701 (2001):
``Comment on ``Half-Polarized Quantum Hall States''''.
G. Murthy, Phys. Rev. B 64, 241309 (2001):
``Effects of Disorder on the \nu=1 Quantum Hall State''.
G. Murthy and R. Shankar, Phys. Rev. B 65, 245309 (2002):
``Hamiltonian Theory of the Fractional Quantum Hall Effect: Effect of
Landau Level Mixing''.
G. Murthy and H. Mathur, Phys. Rev. Lett. 89, 126804 (2002):
``Interactions and Disorder in Quantum Dots; Instabilities of the
Universal Hamiltonian''.
G. Murthy and R. Shankar, Phys. Rev. Lett. 90, 066801 (2003):
``Quantum Dots with Disorder and Interactions: A Solvable Large-g Limit''.
G. Murthy and R. Shankar, Rev. Mod. Phys. 75, 1101 (2003):
``Hamiltonian Theory of the Fractional Quantum Hall Effects''.
Y. N. Joglekar, H. K. Nguyen, and G. Murthy, Phys. Rev. B 68, 035332 (2003):
"Edge Reconstructions in Fractional Quantum Hall Systems"
I. F. Herbut, B. H. Seradjeh, S. Sachdev, and G. Murthy, Phys. Rev. B 68, 195110 (2003):
``Absence of U(1) Spin Liquids in Two Dimensions''.
D. Herman, H. Mathur, and G. Murthy, cond-mat/0305364,
Phys. Rev. B 69, 041301 (2004): ``Diamagnetic Persistent Currents and Spontaneous
Time-Reversal Symmetry Breaking in Mesoscopic Structures''.
G. Murthy, R. Shankar, D. Herman, and H. Mathur, cond-mat/0306529, Phys. Rev. B 69, 075321 (2004):
``A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I:
Consequences for Coulomb Blockade''.
H. K. Nguyen, Y. N. Joglekar, and G. Murthy, Phys. Rev. B 70, 035324 (2004):
``Collective edge modes in fractional quantum Hall systems''.
G. Murthy, Phys. Rev. B 70, 153304 (2004):
``Random matrix crossovers and quantum critical crossovers for interacting electrons in quantum dots''.
G. Murthy, Phys. Rev. Lett. 94, 126803 (2005):
``Interplay between the mesoscopic Stoner and Kondo effects in quantum dots''.
G. Murthy, R. Shankar, and H. Mathur, Phys. Rev. B 72, 075364 (2005) :
``Ballistic Quantum Dots with Disorder and Interactions: A numerical study on the
Robnik-Berry billiard''.
I. Rozhkov and G. Murthy, Phys. Rev. B 72, 193311 (2005):
``A nearly closed ballistic billiard with random boundary transmission''
H. A. Fertig and G. Murthy, Phys. Rev. Lett. 95, 156802 (2005):
``A Coherence Network in the Quantum Hall Bilayer''
I. Rozhkov and G. Murthy, Jour. Phys. A 38, 10843-10857 (2005):
``Ballistic dynamics of a convex smooth-wall billiard with finite
escape rate along the boundary''.
R. Shankar and G. Murthy, Phys. Rev. B 72, 224414 (2005):
``Deconfinement in d=1: A closer look''.
