Recently, the most intensely studied objects in the electronic theory of
solids have been strongly correlated systems and graphene. However, the fact
that the Dirac bands in graphene are made up of $sp^{2}$-electrons, which are
subject to neither strong Hubbard repulsion $U$ nor strong Hund's rule coupling
$J$ creates certain limitations in terms of novel, interaction-induced physics
that could be derived from Dirac points. Here we propose
GaCu$_{3}$(OH)$_{6}$Cl$_{2}$ (Ga-substituted herbertsmithite) as a correlated
Dirac-Kagome metal combining Dirac electrons, strong interactions and
frustrated magnetism. Using density functional theory (DFT), we calculate its
crystallographic and electronic properties, and observe that it has
symmetry-protected Dirac points at the Fermi level. Its many-body physics is
excitingly rich, with possible charge, magnetic and superconducting
instabilities. Through a combination of various many-body methods we study
possible symmetry-lowering phase transitions such as Mott-Hubbard, charge or
magnetic ordering, and unconventional superconductivity, which in this compound
assumes an $f$-wave symmetry
A monolayer of jacutingaite (Pt2HgSe3) has recently been identified as a novel quantum spin Hall insulator. By first-principles calculations, we study its Fermiology in the doped regime and unveil a type-I and type-II van Hove singularity for hole and electron doping, respectively. We find that the common link between the propensity for a topological band gap at pristine filling and unconventional superconductivity at finite doping roots in the longer ranged hybridization integrals on the honeycomb lattice. In a combined effort of random phase approximation and functional renormalization group, we find chiral d-wave order for the type-I and odd-parity f -wave order for the type-II regime.
Microscopic details such as interactions and Fermiology determine the structure of superconducting pairing beyond the spatial symmetry classification along irreducible point group representations. From the effective pairing vertex, the pairing wave function related to superconducting order unfolds in its orbital-resolved Fourier profile which we call the harmonic fingerprint (HFP). The HFP allows to formulate a concise connection between microsopic parameter changes and their impact on superconductivity. From a random phase approximation analysis of twisted bilayer graphene (TBG) involving d + id, s±, and f -wave order, we find that nonlocal interactions, which unavoidably enter the low-energy electronic description of TBG, not only increase the weight of higher lattice harmonics but also have a significant effect on the orbital structure of these pairing states. For gapped unconventional superconducting order such as s± and d + id, a change in HPF induces enhanced gap anisotropies. Experimental implications to distinguish the different gaps and HPFs are also discussed.
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