Simulating Transport Properties of Correlated Materials

Conventional materials such as copper and silicon form the bulk of todays electronic devices. Detailed theoretical understandings of these materials, in which electronic conduction is governed by weakly interacting charge carriers, have made designing complex functional structures by computer simulations possible. Correlated materials, systems in which electrons interact strongly, represent another vast untapped resource with tremendous potential for transformative technical innovations. Akin to La Ola, in which each football fans cheer is coordinated into a stadium-wide wave, the motion of one electron in these materials is correlated to the motions of all others. Owing to this synchronized behavior, these materials are highly sensitive to external stimuli, making them prime candidates for technical developments of sensors, switches, transistors, and memory storage. Yet realizing the full potential of these materials requires a thorough understanding of their physical behaviors and the ability to efficiently screen a huge pool of materials for promising functionalities, particularly electronic and thermoelectric transport properties. Here we propose to develop a highly efficient methodology for an accurate description of transport properties of correlated materials. This has so far been elusive: the charge propagation in correlated materials invalidates semi-classical Boltzmann-theory, and a full quantum many-particle treatment is too computationally demanding. We hypothesize that for transport properties the essential many-particle effects can be described to a high accuracy by a simple form of the electron dynamics. This will effectively replace one of the most time-consuming steps by an analytical evaluation, speeding up the simulation by at least 100-fold. We will first develop a full-fledged algorithm for realistic materials calculations. Next we will apply this novel methodology to the strongly correlated semiconductor FeSi to describe the still elusive microscopic mechanism behind its Hall and Nernst effect. We will also calculate the transport properties of transition metal dichalcogenides, scrutinizing if, and how, different dopings affect their thermoelectrical properties. Next we will devise a complete architecture that will, for the first time, make high-throughput simulations of correlated materials affordable, without sacrificing any salient features of the many-particle correlations. From the massive amount of data we will generate, we will be able to extract guiding principles for designing high-performance thermoelectrics for waste-heat recovery or maintenance-free refrigerators. Finally we will implement a user-friendly interface oriented to experimentalists that will allow them to make comparisons between phenomenological models and experimental data easily. This project will catalyze interdisciplinary exchange between theoreticians and experimentalists. Our methodology will enable highly efficient identifications of materials with desired properties and establish design guidelines to maximize functionalities. By screening a huge array of materials much larger than what is feasible by experimental surveys, we hope to guide experimentalist towards materials of the future.

A common way to characterize a material is to study how it conducts electricity and heat. These properties can be quantified in transport coefficients that link an external perturbation (an electric or magnetic field, a difference in temperature) to a current (of charge or energy). Besides fundamental insight, transport also describes useful functionalities: For instance, in thermoelectric devices, temperature differences are converted into electricity or vice versa. Hence, an understanding of transport properties and how they can be predicted and optimized is of practical interest. In the Linear Response Transport Centre (LinReTraCe) project, we devised and implemented a physically accurate and numerically efficient methodology for the simulation of various transport properties. A key advance is the capability to capture quantum effects, in particular incoherence, that are beyond dominantly used semi-classical techniques. Roughly speaking, incoherence means that (unlike a classical particle) an electronic state in a solid does not have a sharply defined energy, but its energy follows a more or less broadened probability distribution. An equivalent viewpoint is to say that an electronic state has a finite lifetime. Our algorithm incorporates these effects with no or little additional numerical cost: LinReTraCe is a conceptual upgrade from semi-classical Boltzmann theories and an efficient alternative to sometimes prohibitively expensive full Kubo approaches, allowing us to access previously challenging settings. So where do these quantum effects come to play? We found them to be particularly important in a class of materials relevant for technological applications: narrow-gap semiconductors. There, we discovered that finite lifetimes of intrinsic carriers cause a rich temperature dependence in all transport quantities. Most notably, we provide a new microscopic scenario for the previously puzzling low-temperature saturation of the resistivity in Kondo insulators and d-electron intermetallic semiconductors. The crucial insight is that (one over) the lifetime of valence and conduction electrons is a relevant energy scale that can have an intricate interplay with other scales of the system (the charge gap or temperature). Previous attempts at modelling resistivity and the coefficients of Hall, Seebeck, and Nernst in these systems had to resort to ad hoc extrinsic in-gap impurity levels. The latters energetic positions then controlled much of the temperature dependence. In our more complete theory, characteristic temperatures naturally emerge from the intrinsic electronic structure, providing a new interpretation of experimental measurements. In all, the LinReTraCe software allows simulating and predicting transport properties as well as extracting microscopic information from experiment. With that, we hope to inform the theoretical-experimental dialogue and facilitate the discovery and optimization of material functionalities.