Interacting type-II semi-Dirac quasiparticles
Type-II semi-Dirac fermions in two dimensions have been proposed to describe topologically nontrivial low-energy excitations in titanium/vanadium oxide heterostructures. These quasiparticles appear at the merger of three Dirac cones, resulting in a non-zero Berry phase. We find, by employing Hartree-Fock, renormalization group and Random Phase Approximation (RPA) techniques, that the spectrum is very sensitive to long-range electron-electron interactions and can undergo a profound transformation. Our results indicate that at the topological phase boundary, long-range correlations stabilize a hybrid electronic phase displaying both Dirac and type-II semi-Dirac qualities, with physical characteristics exhibiting continuously varying critical exponents as a function of the Fermi energy; for example Landau levels in a magnetic field vary with the energy scale: $|\varepsilon_n(B)|\sim (nB)^{1/2} \rightarrow (nB)^{3/4}, n\in \mathbb{N}_0$. The quasiparticle spectrum evolves, driven by interactions, from anisotropic Dirac dispersion at the lowest energies, towards the characteristic type-II semi-Dirac boomerang shape as the energy increases. The corresponding density of states concomitantly varies between linear and power one third ($ρ(\varepsilon) \sim |\varepsilon| \rightarrow |\varepsilon|^{1/3}$). The crossover scale is controlled by the interaction strength $α= e^2/(\hbar v)$ and the specifics of the effective interacting Hamiltonian.