# P7: Interplay of screening and structure at interfaces of correlated electron systems

## Project Description

The effective electron-electron interaction in low-energy models for electrons in solids depends on the number and energies of screening bands away from the Fermi surface. In material-specific studies, the screening mechanism is nowadays often treated in the so-called cRPA approximation (constrained random phase approximation) that is based

on the ab-initio band structure^{(1)(2)}. Generally, the screening leads to a reduction of the interaction energy of the effective model with respect to the bare Coulomb integrals, with modulations of both the onsite and non-local parts

(see, e.g., (3)). Varying the crystal structure may change the screening and may hence lead to different interaction contributions to the total energy of the system. A large energy gain by a reduced repulsion may have a direct influence on the structure, i.e. the whole system might adapt or reorganize itself in order to reduce the interaction energy most efficiently. For instance, at an interface between two layers made from materials with different strength of correlations, the reduction of the interaction energy of a more correlated side of the interface might induce structural changes on the less correlated side, so as to provide the most efficient screening. Quantitatively, such a novel phenomenon in correlated electron interface physics should be possible, as both binding energies and Coulomb repulsions are of the order of electron volts.

To explore this effect in an elementary and transparent way, in this project we plan, as first step, to study correlated toy models on fixed lattices. The simplest system contains two layers, a less correlated 'screening' layer A and a more strongly correlated layer B. They are coupled either by single-particle hopping or via density-density interactions. Now, different lattice configurations of the screening layer A (mimicking different possible lattice structures with different binding energies) will be integrated out formally on the level of the RPA. This leads to an effective action (in some approximation describable by an effective Hubbard model) for the strongly correlated layer B from which the effect on the effective interactions in layer B can be determined. Then the strongly correlated layer B will be solved, e.g. by exact diagonalization (ED) or dynamical mean-field theory (DMFT), in order to assess which configuration of the screening layer is energetically most advantageous. After this basic exploration, a more realistic picture will be investigated, with the use of DFT techniques that allow for a more precise treatment of the structural part of the problem. The student working on this subject will acquire in-depth knowledge of various methods for strongly correlated electron physics (DMFT and or ED, functional integral formalism, and RPA) and ab-initio techniques. Furthermore, this project opens the chance investigate to a novel aspect of correlated electron physics in a foundational way. This project has some overlap with P1, P3, and P6.

(1) F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann and A. I. Lichtenstein,

Phys. Rev. B **70**, 195104 (2004)

(2) M. Imada and T. Miyake, J. Phys. Soc. Jpn. **79**, 112001 (2010)

(3) T. Wehling, E.Şaşıoğlu, C. Friedrich, A.I. Lichtenstein, M. I. Katsnelson and S. Blügel,

Phys. Rev. Lett. **106**, 236805 (2011)