Many-body instabilities in two-dimensional materials

Abstract

Two-dimensional materials constitute a prominent showplace of competing many-body instabilities such as superconductivity and charge-density waves (CDWs). Even though these phenomena populate rich phase diagrams, the underlying physics can be reduced to well-defined interactions between basic particles. Here, we focus on CDWs in the metallic transition-metal dichalcogenides (TMDCs), whose origin has been controversial for decades. We approach the problem by “downfolding” the full system onto models that are complex enough to capture the relevant processes but at the same time simple enough to be dealt with efficiently. They describe the low-energy electrons, phonons—the vibrations of the lattice—, and their interaction. All model parameters are obtained from first principles, using methods such as density-functional theory and constrained density-functional perturbation theory (cDFPT). In this context, we developed a computational scheme that allows us to calculate how the electrons renormalize the phonons and thus effect said CDWs. Regarding the octahedral TMDC NbSe₂, we find that the presence of a CDW lays the ground on which electronic correlations drive the system into an insulating phase. Independently, we show that in the trigonal–prismatic TMDCs, the electrons and phonons qualitatively behave very similar but that quantitative energy differences finally determine the material specifics. Importantly, our cDFPT results reveal that the CDWs in these materials stem from interactions with the low-energy electrons alone. On this basis, we calculate the CDW phase diagram of TaS₂ and thus explain contradictory experimental findings. Furthermore, introducing the concept of fluctuation diagnostics to electron–phonon physics, we pinpoint the microscopic origin of these CDWs. We can rule out purely electronic mechanisms and confirm the importance of the momentum dependence of the electron–phonon coupling, which we trace back to massive Dirac fermions.