Dynamical Vertex Approximation Approach in Strongly Correlated Electron Systems

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently methods have been developed [1,2] that address this problem by starting with the important local correlations of dynamical mean field theory (DMFT), but further extend it to nonlocal correlations on all length scales. These non-local correlations are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. These diagrammatic extensions of DMFT have been very successfully used to calculate long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality in strongly correlated electron systems [1].

I will start by giving a brief synopsis of these diagrammatic extensions of DMFT, in particular the first such approach, the dynamical vertex approximation (DΓA). For the applications, I will concentrate on spin-fluctuations and how they open a pseudogap and give rise to superconductivity e.g. in nickelates [2,3]. Among others, DΓA has been used to actually predict [4] the phase diagram critical-temperature vs. doping of the novel nickelate superconductors - with a breathtaking accuracy. Also the critical temperature of the recently synthesized pentalayer nickelates [5] nicely concurs with the DΓA calculation and infinite-layer experiments.

[1] G. Rohringer et al., Rev. Mod. Phys. 90, 025003 (2018).

[2] For a first reading cf. K. Held, arXiv:2208.03174.

[3] K. Held et al., Frontiers in Physics 9, 810394 (2022).

[4] M. Kitatani et al., npj Quantum Materials 5, 59 (2020).

[5] P. Worm et al., Phys. Rev. Materials 6, L091801 (2022).