Session A38: Metal-Insulator Phase Transitions - Theory I

Monday, March 21, 2005

The evolution from an anomalous metallic phase to a Mott insulator within the two-dimensional Hubbard model is investigated by means of the Cellular Dynamical Mean-Field Theory. We show that the density-driven Mott metal-insulator transition is approached in a non-uniform way in different regions of the momentum space. This gives rise to a breakup of the Fermi surface and to the formation of {\it hot} and {\it cold} regions, whose position depends on the hole or electron like nature of the carriers in the system.   

Monday, March 21, 2005

We consider a two-dimensional electron system with Coulomb interaction between particles at a finite temperature $T$. The Kohn singularity in the response function leads to a linear- in-$T$ correction to the quasiparticle $g$-factor and the spin susceptibility. We show that the universal linear temperature correction is a generic property of a strongly interacting electron system.   

Monday, March 21, 2005

A dynamical mean-field theory formalism is developed to exactly solve the non-equilibrium properties of the conduction electrons in the Falicov-Kimball model. We study the response of the conduction electrons on a hypercubic lattice in the half-filled case when an external spatially uniform time-dependent electric field is applied. The single-particle response functions and the electric conductivity are calculated as functions of time for different cases of the time-dependent electric field and for different values of the on-site repulsion parameter U. In particular, the most interesting case occurs when U is close to the Mott-insulator transition value.   

Monday, March 21, 2005

The f-electron spectral function of the Falicov-Kimball model is calculated within the dynamical mean-field theory using the numerical renormalization group method as the impurity solver. Both the Bethe lattice and the hypercubic lattice are considered at half filling. For small U we obtain a single-peaked f-electron spectral function, which --for zero temperature-- exhibits an algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \rightarrow 0$. The characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation U. This X-ray singularity cannot be observed when using alternative (Keldysh-based) many- body approaches. With increasing U $\alpha$ decreases and it vanishes for sufficiently large U when the f-electron spectral function develops a gap and a two-peak structure (metal-insulator transition).   

Monday, March 21, 2005

We solve the one dimensional spinless Falicov-Kimball model with hybridization between the conduction and localized electrons for partial band filling. Using a bosonization technique we derive an effective model for the occupation of the localized orbitals and find a crossover from a mixed-valence metallic state to a charge-ordered insulating state with increasing on-site Coulomb interaction.   

Monday, March 21, 2005

A detailed study of linear-wave dynamics on a family of finitely ramified, hierarchical lattices that includes the modified rectangle of Dhar shows that the spectrum contains only a continuum with a smooth local density of states. This is in contrast with the typical spectrum associated with linear-wave models on finitely ramified fractals, like the Sierpi\'{n}ski lattice, that consist of a Cantor-like portion with a sequence of isolated eigenvalues sitting in the gaps of the Cantor set. In addition, at random energy the Greenwood-Peierls conductance shows metallic behavior rather than tending to zero with increasing lattice size either exponentially (strong localization or superlocalization faster than exponential) or as a power law (weak localization). Both the modified rectangle of Dhar and modified cube demonstrate these novel properties and suggest the possibility of cross-over as a function of energy between metallic and insulating regimes.   

Monday, March 21, 2005

Scaling arguments imply that quantum critical points exhibit universal non-linear responses to external probes. We investigate the origins of such non-linearities in transport, which is especially problematic since the system is neccessarily driven far from equilibrium. We argue that for a wide class of systems the new ingredient that enters is the Schwinger mechanism---the production of carriers from the vacuum by the applied field--- which is then balanced against a scattering rate which is itself set by the field. We show by explicit computation how this works for the case of the superfluid-Mott insulator transition of bosons at commensurate fillings.   

Monday, March 21, 2005

The Anderson model for independent electrons in a disordered potential transforms analytically and exactly to an ordered lattice of spins interacting through an itinerant electron, a variant of augmented space [see Phys. Rev. B 66, 155121]. Anderson transitions are clear in this representation where the sector of augmented space dominating the asymptotics of states changes at critical disorders. There are also critical energies or mobility edges which depend on the disorder and separate band states from defect states. The critical disorders together with improved approximations for critical energies produce an analytic phase diagram which can be largely reconciled with the results of single-parameter scaling and numerical scaling.   

Monday, March 21, 2005

Total energies and electronic spectral functions for Americium are calculated using novel dynamical mean field based spectral density functional approach. Pressure dependence as a function of volume and bulk modules for different phases of Am will be studied by this many body calculation and compared to the predictions of experiment. Volume dependent spectral functions will be extracted and discussed in connection to the anomalous resistivity behavior showing its almost one order of magnitude increase under pressure. Electron-phonon interactions estimated in the presence of electronic correlations using linear response method shed a new light on superconductivity of this actinide.   

Monday, March 21, 2005

Recent experiment [1] revealed an unusual feature of the electron effective mass ($m^*$) in Si MOSFETs: while $m^*$ exhibits a strong dependence on the electron density ($r_s$), it does not depend on the degree of spin polarization. Also, the masses of electrons with up- and down spins are the same. These findings are in an apparent contradiction with the Fermi-liquid theory, which predicts two different and polarization-dependent masses in a partially spin-polarized regime, both in the weak- and strong-coupling limits. We show that the effective mass of the Coulomb gas in the large-N limit (for Si MOSFET, $N=4$) is renormalized primarily to a polaronic effect: emission/absorption of high energy plasmons. As plasmons are classical objects, the quantum degeneracy, and hence polarization, does not affect the effective mass to the leading order in $1/N$. Polarization dependence shows up at the next-to-leading orders. We find that for $r_s=2-6$ the change in effective mass between unpolarized and fully polarized states is within $1-3\%$, which is consistent with the experiment. [1] A. A. Shashkin, M. Rahimi, S. Anissimova, S. V. Kravchenko, V. T. Dolgopolov, and T. M. Klapwijk, Phys. Rev. Lett. \textbf{91}, 046403   

Monday, March 21, 2005

We establish the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons (amorphous semiconductors or granular metals, e.g.). We map the model to an effective single site problem, treating the correlations between electrons in a self-consistent manner. We find that in the case of strong disorder a continuous glass transition takes place whose Landau expansion is identical to that of the Sherrington-Kirkpatrick spin glass. We show that the marginal stability of the glass phase controls the physics of these systems: it results in slow dynamics and leads to the formation of the Efros-Shklovskii Coulomb gap.   

Monday, March 21, 2005

Using a simple model for interacting electrons with random disorder in two dimensions, we show in simulations that a transition from a Wigner liquid to a Wigner glass occurs as a function of electron density. The conduction noise power increases strongly at the crossover and the characteristics of the $1/f^{\alpha}$ noise change. When the temperature is increased, the noise power decreases. We compare these results with recent noise measurements in systems with two-dimensional metal-insulator transitions. [1] C. Reichhardt and C.J. Olson Reichhardt, PRL 93, 176405 (2004).