Delta-function-potential junctions with quasiparticles occupying tilted bands with quadratic-in-momentum dispersion

We continue our explorations of the transport characteristics in junction-configurations comprising semimetals with quadratic band-crossings, observed in the bandstructures of both two- and three-dimensional materials. Here, we consider short potential barriers/wells modelled by delta-function potentials. We also generalize our analysis by incorporating tilts in the dispersion. Due to the parabolic nature of the spectra, caused by quadratic-in-momentum dependence, there exist evanescent waves, which decay exponenWe continue our explorations of the transport characteristics in junction-configurations comprising semimetals with quadratic band-crossings, observed in the bandstructures of both two- and three-dimensional materials. Here, we consider short potential barriers/wells modelled by delta-functions. We also generalize our analysis by incorporating tilts in the dispersion. Due to the parabolic nature of the spectra, caused by quadratic-in-momentum dependence, there exist evanescent waves, which decay exponentially as we move away from the junction represented by the location of the delta-function potential. Investigating the possibility of the appearance of bound states, we find that their energies appear as pairs of $\pm |E_b |$, reflecting the presence of the imaginary-valued wavevectors at both positive and negative values of energies of the propagating quasiparticles.