Skutterudites are built up from binary compounds with the chemical composition CoAs3. Binary CoAs3 was discovered as a minaral on the farm Skutterud (Norway) in 1772 and served as the basis for the precious blue pigment used in luxury goods like fine china. CoAs3 is a diamagnetic semiconductor characterised by a large void in its crystal structure. Co can be exchanged by Rh or Ir, while As can be substituted by P and Sb without changing the crystalline unit cell. The cavities of skutterudites can be filled up by electropositive elements like monovalent earth alkali (e.g., Na), divalent alkali (like Ba) or trivalent rare earth elements (La). Since these electropositive elements are just loosely bound, heat carrying phonons are intensely scattered on the resulting „rattling modes“. As a consequence, lattice thermal conductivity is dramatically reduced (by about one order of magnitude) driving a similar enhancement of the thermoelectric figure of merit.

Our research activities in this field are focused on:



x+y=4 αℏ
x0+y=4 αℏ
das ist ein Test x0=∞ obs im Text steht

∑ 1 2 1k = 1,5

<hr />
<p>WOPTIC calculates the optical conductivity of interacting systems in a maximally-localized Wannier basis from the expression<br />
<br />
σ<sub>αβ</sub>(<em>Ω</em>)=e<sup>2</sup>ℏ/(2π)<sup>2</sup>∫d<sup>3</sup><em>k</em>∫d<em>ω w</em>(<em>ω;Ω</em>)tr[<em>A</em>(<em>k</em>,<em>ω</em>)V<sup>α</sup>(k)<em>A</em>(<em>k</em>,<em>ω</em>+<em>Ω</em>)V<sup>β</sup>(<em>k</em>)]<br />
<br />
where σ<sup>αβ</sup>(Ω) is the (α,β) element of the optical conductivity tensor (α,β∈{x,y,z} at external frequency Ω, w(ω;Ω)=[f(ω)−f(ω+Ω)]/Ω is a weight in terms of the Fermi functions f, A=i(G−G<sup>†</sup>)/(2π) the generalized spectral function, and V<sup>α</sup> the group velocity in direction α. The numerical bottleneck in evaluating σ<sup>αβ</sup> is the k-summation, since usually many k-points are required to obtain converged results.</p>



woptic: optical conductivity with Wannier functions and adaptive k-mesh refinement

E. Assmann, P. Wissgott, J. Kuneš, A. Toschi, P. Blaha, and K. Held, arXiv:1507.04881, öffnet eine externe URL in einem neuen Fenster (to appear in Computer Physics Communications)

WOPTIC calculates the optical conductivity of interacting systems in a maximally-localized Wannier basis from the expression

σαβ(Ω)=e2ℏ/(2π)2∫d3k∫dω w(ω;Ω)tr[A(k,ω)Vα(k)A(k,ω+Ω)Vβ(k)]


Computational Materials Science

Dynamical mean field theory and its extensions

Dynamical mean field theory (DMFT) and its numerous extensions represent a big step forward in our efforts to develop reliable methods for describing electronic correlations. Depending on the strength of the electronic correlation, these non-perturbative methods correctly yield a weakly correlated metal, a strongly correlated metal, or a Mott insulator. Applied to model Hamiltonians, DMFT was a big success and advanced our understanding of correlation effects like the Mott-Hubbard metal-insulator transition. More recently, extensions of DMFT such as the so-called quantum cluster theories as well as other extensions based on diagrammatic approaches have been quickly unveiling the missing aspects of the complete picture, where also non-local physics beyond DMFT is treated.

DMFT has been successfully merged with conventional bandstructure calculations in the local density approximation (LDA), thereby allowing for the realistic calculation of materials with strong electronic correlations such as transition metal oxides or heavy Fermion systems, which was hitherto not possible.

Electronic Structure Calculations with DMFT

One of the most important challenges of theoretical physics is the development of tools for the accurate calculation of material properties. In solid state theory, we already know our ''theory of everything'', which consists of three terms: the kinetic energy, the lattice potential, and the Coulomb interaction between electrons:



Here, ri and Rl denote the position of electron i and ion l with charge e and Zl e, respectively, Î is the Laplace operator of the kinetic energy, 00 and are the vacuum dielectric and Planck constant, see Fig. 1 for an illustration. Despite knowing the Hamiltonian, it is impossible to solve, even numerically, if more than a very few electrons are involved. This is due to the last term, the Coulomb interaction, which correlates the movement of every electron i with every other electron j.

Since electrons have to be described quantum-mechanically, the numerical effort grows exponentially with the number of electrons.


Figure 1:






Solid State Hamiltonian 
To calculate a material, one has to take into account three terms: the kinetic energy favoring the electrons to move through the crystal (black), the lattice potential of the ions (green), and the Coulomb interaction between the electrons (red). Due to the latter, the first electron is repelled by the second, and it is energetically favorable to hop somewhere else, as depicted. Hence, the movement of every electron is correlated with that of every other, which prevents even a numerical solution.

LDA approximation 
LDA is an approximation which allows to calculate material properties but which dramatically simplifies the electronic correlations: every electron moves independently, i.e., uncorrelated, within a time-averaged local density of the other electrons.


In this situation, one can either dramatically simplify the Hamiltonian (1), hoping that the simplified model allows for a qualitative understanding including correlation (many-body) effects, or employ equally dramatic approximations to deal with (1). These two paths have been followed by the two big communities of solid state theory, the many-body model-Hamiltonian and the density functional community.

Within density functional theory, the local density approximation (LDA) turned out to be unexpectedly successful, and established itself as the method for realistic solid state calculations in the last century. This is surprising because LDA is a serious approximation to the Coulomb interaction. Basically, an electron at ri sees a time-averaged density of the other electrons r (ri), with a corresponding local LDA potential, VLDA(r (ri))  see Fig. 1. This reduces the problem to a single electron calculation.

The success of LDA shows, that this treatment is actually sufficient for many materials, both for calculating ground state energies and bandstructures, implying that electronic correlations are rather weak in these materials. But, there are important classes of materials where LDA fails, such as transition metal oxides or heavy fermion systems. In these materials the valence orbitals are the 3d and 4f orbitals. For two electrons in these orbitals the distance *ri - rj* is particularly short, and electronic correlations particularly strong.

Many such transition metal oxides are Mott insulators, where, the on-(lattice-)site Coulomb repulsion U splits the LDA bands into two sets of Hubbard bands. One can envisage the lower Hubbard band as consisting of all states with one electron on every lattice site and the upper Hubbard band as those states where two electrons are on the same lattice site. Since it costs an energy U to have two electrons on the same lattice sites, the latter states are completely empty and the former completely filled with a gap of size U in-between, see Fig. 2. Other transition metal oxides and heavy fermion systems are strongly correlated metals, with heavy quasiparticles at the Fermi energy, described by an effective mass or inverse weight  m/m0=1/Z o1, see Fig. 2.



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