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New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations. Physically relevant sufficient and necessary conditions to guarantee the existence of discrete eigenvalues are derived under rather general assumptions on external fields. One of the most interesting features of the analysis is the evident spectral instability of the systems in the weakly coupled regime. The rigorous theoretical results are illustrated by numerical experiments and predictions for physical experiments are made.
We study the interaction effect in a three dimensional Dirac semimetal and find that two competing orders, charge-density-wave orders and nematic orders, can be induced to gap the Dirac points. Applying a magnetic field can further induce an instabil
The Landau bands of mirror symmetric 2D Dirac semi-metals (for example odd-layers of ABA-graphene) can be identified by their parity with respect to mirror symmetry. This symmetry facilitates a new class of counter-propagating Hall states at opposite
While electrons moving perpendicular to a magnetic field are confined to cyclotron orbits, they can move freely parallel to the field. This simple fact leads to complex current flow in clean, low carrier density semi-metals, such as long-ranged curre
We prove the existence of ground states for the semi-relativistic Schrodinger-Poisson-Slater energy $$I^{alpha,beta}(rho)=inf_{substack{uin H^frac 12(R^3) int_{R^3}|u|^2 dx=rho}} frac{1}{2}|u|^2_{H^frac 12(R^3)} +alphaintint_{R^{3}timesR^{3}} frac{|
We study the topologically non-trivial semi-metals by means of the 6-band Kane model. Existence of surface states is explicitly demonstrated by calculating the LDOS on the material surface. In the strain free condition, surface states are divided int