LinReTraCe

The Linear Response Transport Centre (LinReTraCe) — FWF stand-alone project P 30213 (01.09.2017-31.08.2021)

LinReTraCe is available at https://github.com/linretrace and described in detail in SciPost Phys. Codebases 16 (2023). 



Methodological Objectives
In this project we developed a highly efficient methodology for the precise description of transport properties of correlated materials. This had so far been elusive: the charge propagation in correlated materials invalidates semi-classical Boltzmann-theory, and a full quantum many-particle treatment is often computationally too demanding. Our main hypothesis is that for transport properties the essential many-particle effects can be described to a high accuracy by assuming 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 and increasing numerical precision drastically.

Discoveries
With the LinReTraCe package, we were able to access previously challenging regions of phase-space. For the prime target class of materials (correlated narrow-gap semiconductors) we discovered that finite lifetimes of intrinsic carriers cause a rich temperature profile in various transport quantities. Most notably, we provide a new microscopic scenario for the low-temperature saturation of the resistivity in Kondo insulators and d-electron intermetallic semiconductors. The crucial insight is that the scattering rate (inverse lifetime) of valence and conduction electrons is a relevant energy scale that can have an intricate interplay/competition with other scales of the problem, such as the charge gap and temperature. The relevance of incoherent transport of charge and energy is a signature of quantum effects (not included in Boltzmann approaches). Previous attempts at modelling the temperature profiles of resistivity and the coefficients of Hall, Seebeck, and Nernst had to resort to ad hoc extrinsic in-gap impurity levels at specific energies to introduce characteristic temperature features. We demonstrated that the characteristic temperature profiles emerge intrinsically as a result of said interplay of energy scales.

Key publications

LinReTraCe: The Linear Response Transport Centre
M. Pickem, E. Maggio, J. M. Tomczak
SciPost Physics Codebases 16 (2023)
arXiv:2206.06097

The "Linear Response Transport Centre" (LinReTraCe) is a package for the simulation of transport properties of solids. LinReTraCe captures quantum (in)coherence effects beyond semi-classical Boltzmann techniques, while incurring similar numerical costs. The enabling algorithmic innovation is a semi-analytical evaluation of Kubo formulae for resistivities and the coefficients of Hall, Seebeck and Nernst. We detail the program's architecture, its interface and usage with electronic-structure packages such as WIEN2k, VASP, and Wannier90, as well as versatile tight-binding settings. 

Prototypical many-body signatures in
transport properties of semiconductors
M. Pickem, E. Maggio, J. M. Tomczak
Phys. Rev. B 105, 085139 (2022)
arXiv:2112.07604

We devise a methodology for charge, heat, and entropy transport driven by carriers with finite lifetimes. Combining numerical simulations with analytical expressions for low temperatures, we establish a comprehensive and thermodynamically consistent phenomenology for transport properties in semiconductors. We demonstrate that the scattering rate (inverse lifetime) is a relevant energy scale: It causes the emergence of several characteristic features in each transport observable. The theory is capable to reproduce—with only a minimal input electronic structure—the full temperature profiles measured in correlated narrow-gap semiconductors. In particular, we account for the previously elusive low-T saturation of the resistivity and the Hall coefficient, as well as the (linear) vanishing of the Seebeck and Nernst coefficient in systems, such as FeSb2, FeAs2, RuSb2 and FeGa3.

Resistivity saturation in Kondo insulators
M. Pickem, E. Maggio, J.M. Tomczak
Commun. Phys. 4, 226 (2021)

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 semi-classical Boltzmann picture. Then, finite lifetimes of intrinsic carriers drive residual conduction, impose the existence of a crossover T*, and control—now on par with the gap—the quantum regime emerging below it. Assisted by realistic many-body simulations, we showcase the mechanism for the Kondo insulator Ce3Bi4Pt3, for which residual conduction is a bulk property, and elucidate how its saturation regime evolves under external pressure and varying disorder. Deriving a phenomenological formula for the quantum regime, we also unriddle the ill-understood bulk conductivity of SmB6—demonstrating a wide applicability of our mechanism in correlated narrow-gap semiconductors. 

Data available at zenodo.org/record/4355597#.YdQ5NGiZOt8

All associated publications