## Single Atom (Mostly Proton) Embedded in the Electron Gas: Kondo Problem from First Principles

Yasutami Takada

Institute for Solid State Physics, University of Tokyo, Kashiwa, Japon.

E-mail: takada@issp.u-tokyo.ac.jp

Lundi 17 Février 2014, 11^{h}00

bibliothèque LCT, tour 12 - 13, 4e étage

There is a long history of research for the electronic structure in the system of a single atom embedded in the electron gas, mostly because this is a typical problem of an impurity in metals, being an ideal system for investigating nonlinear screening and embedding energy, leading to “the effective-medium theory” as discussed in, for example, the old work of Norskov [J. K. Norskov, PRB**20**, 446 (1979)]. Another reason for the study of this system is due to the expectation that very useful information might be provided for the improvement of the local-density approximation (LDA) to the exchange-correlation energy functional in the density functional theory, if we can obtain the very accurate profile for the electron density *n*(**r**), combined with, for example, the inverse Kohn Sham scheme.

I began thinking of this problem in 2002 when I visited Santa Barbara as a visiting professor associated with Professor W. Kohn. Since then, I have studied this system with employing various theoretical tools, but recently Professor R. Maezono and I have succeeded in obtaining a rather accurate *n*(**r**) for a proton embedded in the electron gas in the wide range of the densities (the *r*_{s} parameter ranging from 1 to 15) by diffusion Monte Carlo (DMC). The obtained results show interesting transitions of three typical states by decreasing the metallic electron density; (i) the state H^{+} of metallic nonlinear screening by itinerant electrons, (ii) Kondo resonance state, and (iii) H^{-} state in the metallic environment. Among them, the concept of the Kondo resonance state has not been considered so far in this system, but I find it a key in correctly understanding the state appearing in the intermediate density region (2 < *r*_{s} < 10).

In the seminar, I will make a rather detailed discussion on the above point with adding some basic knowledge on the Kondo resonance state unveiled by the study of the impurity Anderson model. I also mention the preliminary results for the atoms in the second row of the elements in the periodic table embedded in the electron gas [for example, V. U. Nazarov, C. S. Kim, and YT, PRB**72**, 233205 (2005)] explained in the light of a multi-channel Kondo problem. In the final part of the seminar, I mention on our recent trial to improve on the GGA-PBE exchange-correlation energy functional on the basis of the information of the accurate *n*(**r**).