Resistivity saturation in Kondo insulators

Resistivities of heavy-fermion insulators typically saturate below a characteristic temperature $T^*$. For some, metallic surface states, potentially from a non-trivial bulk topology, are a likely source of residual conduction. Here, we establish an alternative mechanism: At low temperature, in addition to the charge gap, the scattering rate turns into a relevant energy scale, invalidating the semiclassical Boltzmann picture. Finite lifetimes of intrinsic carriers limit conduction, impose the existence of a crossover $T^*$, and control - now on par with the gap - the quantum regime emerging below it. We showcase the mechanism with realistic many-body simulations and elucidate how the saturation regime of the Kondo insulator Ce$_3$Bi$_4$Pt$_3$, for which residual conduction is a bulk property, evolves under external pressure and varying disorder. Using a phenomenological formula we derived for the quantum regime, we also unriddle the ill-understood bulk conductivity of SmB$_6$ - demonstrating that our mechanism is widely applicable to correlated narrow-gap semiconductors.Comment: 8 pages, 6 figure

Self-consistent ladder DΓ\GammaA approach

We present and implement a self-consistent D$\Gamma$A approach for multi-orbital models and ab initio materials calculations. It is applied to the one-band Hubbard model at various interaction strengths with and without doping, to the two-band Hubbard model with two largely different bandwidths, and to SrVO$_3$. The self-energy feedback reduces critical temperatures compared to dynamical mean-field theory, even to zero temperature in two-dimensions. Compared to a one-shot, non-self-consistent calculation the non-local correlations are significantly reduced when they are strong. In case non-local correlations are weak to moderate as for SrVO$_3$, one-shot calculations are sufficient.Comment: 21 Pages, 20 Figure

Dynamische Vertex Approximation für SrVO3: Effekte von nicht lokaler Wechelwirkung, Temperatur und Dimensionalität Dynamical vertex approximation for SrVO3: Effects of non-local interactions, temperature and dimensionality

Abweichender Titel nach Übersetzung der Verfasserin/des VerfassersStrong electronic correlations have been in the focus of solid state research for quite some time. Many interesting phenomena such as the Mott metal-to-insulator transition, superconductivity (both conventional and unconventional) or heavy-fermion systems can only be explained when taking correlation effects into account. In this regard there has always been the hope that applications exploiting these correlation effects will one day replace or enhance current technologies. One of the most promising group of materials with respect to applicability are transition metal oxides which are at the center of this thesis. In order to be able to describe the involved physics we will, in the first part of this thesis, construct the bridge from the many-body problem in first quantization to the Green’s function formalism and subsequently Feynman diagrammatic. With this formalism we are able to introduce the state-of-the-art density functional theory (DFT) + dynamical mean-field theory (DMFT) approach both from a physical point of view and, more importantly, diagrammatically. This technique allows for an accurate description of genuine (local) correlation effects. However due to the underlying mean-field approach in the spatial domain non-local effects are out of its reach. These non-local correlations play an essential role in two-dimensional structures (e.g. ultra-thin films) or near phase transitions. For this reason many theories and techniques have been developed which extend DMFT to capture both the local correlations of DMFT and non-local correlations beyond. The dynamical vertex approximation (DΓA) represents one of the diagrammatic extensions of DMFT and will be our main focus point in this thesis. With it, in the second part of this thesis, we will further investigate a common testbed material used in electronic structure calculations, namely strontium vanadate (SrVO 3 ). More specifically we will study the effects of temperature and non-local interactions in bulk SrVO 3 as well as the effects of the previously mentioned reduced dimensionality. The latter is based on recent findings that two-layered SrVO 3 on a substrate of strontium titanate (SrTiO 3 ) could be potentially used as a so-called ‘Mott transistor’ where the involved Mott metal-to-insulator transition can be triggered via different external perturbations, such as a gate voltage, pressure or temperature.11