Spintronics and Berry Phase Effects in Solids:
Probably the majority of materials of interest to theoretical physicists are those close to or in a Mott insulating state, where the particles (cold atoms, Cooper pairs, electrons) become spontaneously localized due to their mutual interactions. In most cases, such Mott phases break symmetries. Often it is difficult to predict a priori what pattern of symmetry breaking will emerge. Sometimes there may be many "competing" states nearby in energy, so that the material can be easily influenced by perturbations into changing its order. The transitions between different Mott states and from a Mott state to a delocalized one are also major theoretical problems. We are interested in various aspects of this area. Some of our contributions are listed below.
- Z2 topological insulators
- In a remarkable pair of papers, Kane and Mele proposed
a Z2 topological invariant of time-reversal invariant insulators in
two dimensions, showed that the nontrivial ``topological insulator''
phase has an intrinsic spin Hall effect distinct from earlier
proposals, and argued that graphene is a viable
system in which to observe this effect. A
direct and experimentally relevant characterization of the invariant
was given in terms of edge states at the boundary of a 2D insulator:
the topological insulator has an odd number of Kramers pairs of edge
modes, while the ordinary insulator has an even number. Two more
complicated explanations for the invariant as a property of the bulk
band structure were also given.
By a rather different method more akin to the Chern number characterization of integer quantum Hall states in time-reversal broken materials, we (Joel Moore and I)recover the Z2 classification for two-dimensional insulators introduced by Kane and Mele ( here ). We argue that there are also non-trivial Z2 invariant(s) in three-dimensions. Such a 3d topological insulator will have remarkable properties, including a "protected" metallic surface state. This is very exciting, because the requirements for such a topological insulator do not seem very strict! Unlike other known states with topological properties, neither strong electron-electron interactions (necessary for time-reversal invariant quantum spin liquid states heavily studied theoretically), high magnetic fields and low temperatures (necessary for fractional quantum Hall states, which are well-studied experimentally), or low dimensionality (needed for quantum Hall states and one-dimensional non-Fermi liquids) are not needed for the 3d topological insulator. Thus in all likelihood these materials already exist and the topological character has simply not been detected (or looked for)!
If you're interested, please read our paper , but also do look at several more papers in this area, which are excellent. Two recent papers by Roy here and here address the same questions as our own paper, and come to essentially the same conclusions. If you are going to read just one or two papers, though, I would have to recommend this paper by Fu, Kane, and Mele which gives a very physical interpretation of their Z2 invariant in two dimensions, and this paper by Kane and Mele which (two weeks after our paper) not only gives the same classification of 3d topological insulators as our own, but explores much more fully the physical consequences and also presents an explicit microscopic toy model for the effect.
- Artificial electric field in U(1) Fermi liquids
-
It has become well-known in recent years that the geometric
structure (in Hilbert space) of Bloch wavefunctions influences the
dynamics of quasiparticles. For non-interacting electrons, this is
described by the Berry curvature, which plays the role of a dual
(momentum and position interchanged) "artificial magnetic field" in
momentum space. We have found that for interacting electrons, a
counterpart, which we call the "artificial electric field" appears.
Based on the Keldysh formalism, we derived an effective Boltzmann
equation for a quasi-particle associated with a particular Fermi
surface in an interacting Fermi liquid. This provides a many-body
derivation of the Berry curvature effects in electron dynamics with
spin-orbit coupling. Our Fermi liquid formulation completes the
reinvention of modified band dynamics by introducing in addition the
artificial electric field, which is related to Berry curvature in
frequency and momentum space. With Ryuichi Shindou, we showed
explicitly how the artificial electric field affects the
renormalization factor and transverse conductivity of interacting U(1)
Fermi liquids with non-degenerate bands. Accordingly, we also proposed
a method of momentum resolved Berry's curvature detection in terms of
angle resolved photoemission spectroscopy (ARPES). Analogous
extensions to SU(2) Fermi liquids with doubly degenerate bands were
also briefly mentioned.
Read cond-mat/0603089 .
- Spin relaxation in a Rashba 2DEG in a strong magnetic field
- In this paper , we calculated the oscillations of the spin relaxation rate with a perpendicular magnetic field in a two-dimensional electron gas with Rashba spin-orbit interaction and disorder. This is an extension of the well-known Dyakanov-Perel mechanism of spin relaxation, and we described behavior consistent with existing experiments in the Awschalom group at UCSB. In general, we feel that such microscopic understanding of the mechanisms of spin relaxation and decoherence is an important theoretical problem.
- Anomalous Hall effect in the hopping regime
- Prompted by intriguing experiments by Prof. Elizabeth Gwinn and collaborators, we studied the anomalous Hall effect in diluted magnetic semiconductors in the hopping transport regime. Since the Hall effect is ubiquitously used to experimentally determine hole concentrations in these materials, an understanding of the anomalous Hall effect is very important in interpreting these measurements. The strong spin-orbit coupling of the heavy and light hole bands in Ga1-xMnxAs is believed theoretically to lead to a strong anomalous contribution in clean samples. The majority of samples are, however, rather insulating, and display hopping-type conductivity over a broad range of temperatures. In this paper , Anton Burkov and I showed that in the hopping regime, the anomalous Hall contribution is large and is not directly proportional to the carrier density. In fact, it is proportional to the derivative of the density of states. Thus we predicted a mechanism for a sign change in the anomalous Hall conductivity if the Fermi level is moved through the center of the impurity band.
