Interdimensional effects in systems with quasirelativistic fermions

We examine the Green function and the density of states for fermions moving in three-dimensional Dirac materials with interfaces which affect the propagation properties of particles. Motivation for our research comes from interest in materials that exhibit quasirelativistic dispersion relations. By modifying Dirac-type contributions to the Hamiltonian in an interface we are able to calculate the Green function and the density of states. The density of states inside the interface exhibits interpolating behavior between two and three dimensions, with two-dimensional behavior at high energies and three-dimensional behavior at low energies, provided that the shift in the mass parameter in the interface is small. We also discuss the impact of the interpolating density of states on optical absorption in Dirac materials with a two-dimensional substructure.

Figure 1

Density of states in the interface for $\ell =3$ nm, $m{c}^2=82.5$ meV, and $\mathrm{\Delta }m{c}^2=0$. The three-dimensional density of states in Eq. (43) is included in blue (upper curve) for comparison.

Figure 2

Density of states in the interface for $\ell =3$ nm, $m{c}^2=82.5$ meV, and $\mathrm{\Delta }m{c}^2=0$. The corresponding two-dimensional limit plus the logarithmic correction in Eq. (45) is included in blue (upper curve) for comparison.

Figure 3

Density of states in the interface for $\ell =3$ nm, $E>{\mathrm{\Delta }}_g$, and gap shift $\mathrm{\Delta }m{c}^2=-{\mathrm{\Delta }}_g$, where ${\mathrm{\Delta }}_g=82.5$ meV.