Competing phases in the kagome magnet FeGe from functional renormalization

The discovery of a charge density wave in FeGe extends the discussion of the nature of charge order in kagome metals to a magnetic compound. Motivated by this observation, we combine density functional theory (DFT) and functional-renormalization-group calculations to study interaction-induced Fermi-surface instabilities of the magnetic state of FeGe. We argue that the leading intra-band contribution to electronic correlations are approximately two-dimensional (2D) and come from Van Hove points at the projected <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>M</a:mi> </a:math> points. By varying parameters around DFT values, we determine a phase diagram for the quasi-2D scenario as function of on-site and nearest-neighbor interactions. We discuss universal aspects in the electronic mechanisms for the resulting phases, as well as the role of SU(2) symmetry breaking. We find FeGe to be in a regime of strong competition between <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>p</b:mi> </b:math> -wave charge density wave, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>f</c:mi> </c:math> -wave pairing, and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>d</d:mi> </d:math> -wave spin Pomeranchuk instabilities. This interplay can be influenced in favor of superconducting pairing for slightly increased nearest-neighbor interaction, suggesting a potential to induce superconductivity in FeGe.