Abstract:
Using advanced ab-initio calculations, we describe the formation and confinement of a two-dimensional electron gas in short-period ($\simeq$4 nm) Nb-doped SrTiO$_3$ superlattices as function of Nb doping. We predict complete two-dimensional confinement for doping concentrations higher than 70%. In agreement with previous observations, we find a large thermopower enhancement at room temperature. However, this effect is primarily determined by dilution of the mobile charge over a multitude of weakly occupied bands. As a general rule, we conclude that thermopower in similar heterostructures will be more enhanced by weak, rathern than tight spatial confinement.

Abstract:
Electrodynamic properties of La-doped SrTiO3 thin films with controlled elemental vacancies have been investigated using optical spectroscopy and thermopower measurement. In particular, we observed a correlation between the polaron formation and thermoelectric properties of the transition metal oxide (TMO) thin films. With decreasing oxygen partial pressure during the film growth (P(O2)), a systematic lattice expansion was observed along with the increased elemental vacancy and carrier density, experimentally determined using optical spectroscopy. Moreover, we observed an absorption in the mid-infrared photon energy range, which is attributed to the polaron formation in the doped SrTiO3 system. Thermopower of the La-doped SrTiO3 thin films could be largely modulated from -120 to -260 {\mu}V K-1, reflecting an enhanced polaronic mass of ~3 < mpolron/m < ~4. The elemental vacancies generated in the TMO films grown at various P(O2) influences the global polaronic transport, which governs the charge transport behavior, including the thermoelectric properties.

Abstract:
An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behavior of the effective mass as a function of the electron-phonon coupling. By increasing the strength of the inter-molecular forces the crossover becomes smoother and occurs at higher {\it e-ph} couplings. These effects are more evident in three dimensions. We show that our Modified Lang-Firsov method starts to capture the occurence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order $\sim 5 - 40$ times the bare band mass according to dimensionality and value of the adiabatic parameter. Modified Lang-Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime.

Abstract:
The crossover from quasi free electron to small polaron in the Holstein model for a single electron is studied by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice, in order to understand the role of dimensionality in such a crossover. We show that a small polaron ground-state occurs when both strong coupling ($\lambda>1$) and multiphonon ($\alpha^2 >1$) conditions are fulfilled leading to different relevant coupling constants ($\lambda$) in adiabatic and ($\alpha^2$) anti adiabatic region of the parameters space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover.

Abstract:
We use analytic techniques and the dynamical mean field method to study the crossover from fermi liquid to polaron behavior in models of electrons interacting with dispersionless classical phonons.

Abstract:
The Hubbard-Holstein model is studied including double-exchange interaction and superexchange interaction using a variational phonon basis obtained through the modified Lang-Firsov (MLF) transformation followed by the squeezing transformation. The kinetic energy, polaron crossover and magnetic transition are investigated as a function of electron-phonon ($e$-ph) coupling and electron concentration for different values of antiferromagnetic superexchange interaction ($J$) between the core spins. The polaron crossover, magnetic transition and the suppression of ferromagnetic transition with $J $ are discussed for the model.

Abstract:
The electronic symmetry of the SrTiO3/LaAlO3 interface was investigated by optical second harmonic generation, using superlattices with varying periodicity to study the evolution of the electronic reconstruction while avoiding substrate contributions. The superlattices show large perpendicular optical nonlinearity, which abruptly increases when the sublattice thickness goes above 3 unit cells, revealing substantial effects of the polar-nonpolar interface. The nonlinear 'active' area is primarily in SrTiO3, develops with increasing thickness, and extends up to 8 unit cells from the interface.

Abstract:
A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction ($J$) between the core spins and the hopping ($t$) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of $J/t$, the magnetic field has very pronounced effect on the transport.

Abstract:
We have investigated two-dimensional thermoelectric properties in transition metal oxide heterostructures. In particular, we adopted an unprecedented approach to direct tuning of the 2D carrier density using fractionally {\delta}-doped oxide superlattices. By artificially controlling the carrier density in the 2D electron gas that emerges at a LaxSr1-xTiO3 {\delta}-doped layer, we demonstrate that a thermopower as large as 408 {\mu}V K-1 can be reached. This approach also yielded a power factor of the 2D carriers 117 {\mu}Wcm-1K-2, which is one of the largest reported values from transition metal oxide based materials. The promising result can be attributed to the anisotropic band structure in the 2D system, indicating that {\delta}-doped oxide superlattices can be a good candidate for advanced thermoelectrics.

Abstract:
Motivated by the remarkable experimental realizations of $f$-electron superlattices, e.g. CeIn$_3$/LaIn$_3$- and CeCoIn$_5$/YbCoIn$_5$- superlattices, we analyze the formation of heavy electrons in layered $f$-electron superlattices by means of the dynamical mean field theory. We show that the spectral function exhibits formation of heavy electrons in the entire system below a temperature scale $T_0$. However, in terms of transport, two different coherence temperatures $T_x$ and $T_z$ are identified in the in-plane- and the out-of-plane-resistivity, respectively. Remarkably, we find $T_z < T_x \sim T_0$ due to scatterings between different reduced Brillouin zones. The existence of these two distinct energy scales implies a crossover in the dimensionality of the heavy electrons between two and three dimensions as temperature or layer geometry is tuned. This dimensional crossover would be responsible for the characteristic behaviors in the magnetic and superconducting properties observed in the experiments.