Density functional theory of superconductivity and non-collinear magnetism, within and far from equilibrium

The basic idea of “functional theories” is to describe nature in terms of a simple, reduced quantity rather than the full many-body wave function. Prominent examples of functional theories are density-functional theory (DFT) as well as Green's-function-functional theory (better known as many-body perturbation theory). In this lecture, the description of quantum phases, such as superconductivity and magnetism, within functional theories will be addressed. The basic idea is to include the order parameter describing the respective quantum phases or the corresponding propagator explicitly in the formalism as an additional density or an additional Green’s function. The exchange-correlation (xc) energy of DFT then becomes a functional of the density and the respective order parameter. Approximations for the xc functional will be presented, both for phonon-driven superconductors [1] and for non-collinear magnetism [2]. The accuracy of results for material-specific properties, such as the critical temperature and the magnetic moment will be critically assessed. The same strategy is followed for driven systems far from thermal equilibrium. As an example, real-time TDDFT simulations of the ultrafast laser-induced spin dynamics [3,4] in magnetic materials will be presented, and first steps will be taken towards the description of laser-driven superconductivity [5]. Finally, the relation between DFT and Green's-function-based approaches will be analyzed [6].



[1] A. Sanna, C. Pellegrini, E.K.U. Gross, Phys.Rev.Lett. 125, 057001 (2020).

[2] S. Sharma, E.K.U. Gross, A. Sanna, J.K. Dewhurst, J. Chem. Theory Comput. 14, 1247 (2018).

[3] J.K. Dewhurst, P. Elliott, S. Shallcross, E.K.U. Gross, S. Sharma , Nano Lett. 18,1842 (2018).

[4] K. Krieger, J.K. Dewhurst, P. Elliott, S.Sharma, E.K.U. Gross, J. Chem. Theory Comput. 11, 4870 (2015).

[5] C.Y. Wang, S. Sharma, T. Mueller, E.K.U. Gross, J.K. Dewhurst, Phys. Rev. B 105, 174509 (2022).

[6] S. Crisostomo, E.K.U. Gross, K. Burke, Phys. Rev. Lett. 133, 086401 (2024).