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Register a new userBound states in semi-Dirac semi-metals
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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.
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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 instability towards forming these ordered phases. The charge density wave phase is similar as that of a Weyl semimetal while the nematic phase is unique for Dirac semimetals. Gapless zero modes are found in the vortex core formed by nematic order parameters, indicating the topological nature of nematic phases. The nematic phase can be observed experimentally using scanning tunnelling microscopy.
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 but equal electron and hole filling factors $| u_{pm}|=1/m$ ({it m} odd). Here, we propose a Laughlin-like correlated liquid wavefunction, at the charge neutrality point, that exhibits fractionally charged quasi-particle/hole pair excitation of opposite parity. Using a bosonized one-dimensional edge state theory, we show that the longitudinal conductance of this state, $sigma_{xx} = 2e^2/(m h)$, is robust to short-ranged inter-mode interactions.
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 current jets forming along the magnetic field when currents pass through point-like constrictions. Occurring accidentally at imperfect current injection contacts, the phenomenon of current jetting plagues the research of longitudinal magneto-resistance which is particularly important in topological conductors. Here we demonstrate the controlled generation of tightly focused electron beams in a new class of micro-devices machined from crystals of the Dirac semi-metal Cd3As2. The current beams can be guided by tilting a magnetic field and their range tuned by the field strength. Finite element simulations quantitatively capture the voltage induced at faraway contacts when the beams are steered towards them, supporting the picture of controlled electron jets. These experiments demonstrate the first direct control over the highly nonlocal signal propagation unique to 3D semi-metals in the current jetting regime, and may lead to novel applications akin to electron optics in free space.
We prove the existence of ground states for the semi-relativistic Schrodinger-Poisson-Slater energy $$I^{alpha,beta}(rho)=inf_{substack{uin H^frac 12(R^3) int_{R^3}|u|^2 dx=rho}} frac{1}{2}|u|^2_{H^frac 12(R^3)} +alphaintint_{R^{3}timesR^{3}} frac{| u(x)|^{2}|u(y)|^2}{|x-y|}dxdy-betaint_{R^{3}}|u|^{frac{8}{3}}dx$$ $alpha,beta>0$ and $rho>0$ is small enough. The minimization problem is $L^2$ critical and in order to characterize of the values $alpha, beta>0$ such that $I^{alpha, beta}(rho)>-infty$ for every $rho>0$, we prove a new lower bound on the Coulomb energy involving the kinetic energy and the exchange energy. We prove the existence of a constant $S>0$ such that $$frac{1}{S}frac{|varphi|_{L^frac 83(R^3)}}{|varphi|_{dot H^frac 12(R^3)}^frac 12}leq left (intint_{R^3times R^3} frac{|varphi(x)|^2|varphi(y)|^2}{|x-y|}dxdyright)^frac 18 $$ for all $varphiin C^infty_0(R^3)$. Eventually we show that similar compactness property fails provided that in the energy above we replace the inhomogeneous Sobolev norm $|u|^2_{H^frac 12(R^3)}$ by the homogeneous one $|u|_{dot H^frac 12(R^3)}$.
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 into two parts in the energy spectrum, one part is in the direct gap, the other part including the crossing point of surface state Dirac cone is submerged in the valence band. We also show how uni-axial strain induces an insulating band gap and raises the crossing point from the valence band into the band gap, making the system a true topological insulator. We predict existence of helical edge states and spin Hall effect in the thin film topological semi-metals, which could be tested with future experiment. Disorder is found to significantly enhance the spin Hall effect in the valence band of the thin films.
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