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Register a new userConfining massless Dirac particles in two-dimensional curved space
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Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.
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We predict from DFT based electronic structure calculations that a monolayer made up of Carbon and Arsenic atoms, with a chemical composition (CAs3) forms an energetically and dynamically stable system. The optimized geometry of the monolayer is slightly different from the buckled geometric configuration observed for silicene and germanene. The results of electronic structure calculations predict that it is a semi-metal. Interestingly, the electronic band structure of this material possesses a linear dispersion and a Dirac cone at the Fermi level around the high symmetric K point in the reciprocal lattice. Thus, at low energy excitation (up to 105 meV), the charge carriers in this system behave as massless Dirac-Fermions. Detailed analysis of partial density of state suggests that the 2pz orbital of C atoms plays vital role in determining the nature of the states, which has a linear dispersion and hence the Dirac cone, around the Fermi level. Thus, the electronic properties of CAs3 monolayer are similar to those of graphene and other group IV based monolayers. In addition, we have also investigated the influence of mechanical strain on the properties of CAs3 monolayer. The buckled configuration becomes the planar configuration for a tensile strain beyond 18%. Our results indicate that the monolayer possesses linear dispersion in the electronic band structure for a wide range of mechanical strain from -12 to 20%, though the position of Dirac point may not lie exactly at the Fermi level. The linear dispersion disappears for a compressive strain beyond -12% & it is due to the drastic changes in the geometrical environment around C atom. Finally, we wish to point out that CAs3 monolayer belongs to the class of Dirac materials where the behaviour of particles, at low energy excitations, are characterized by the Dirac-like Hamiltonian rather than the Schrodinger Hamiltonian.
We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Poschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.
In a Dirac material we investigated the confining properties of massive and massless particles subjected to a potential well generated by a purely electrical potential, that is, an electric quantum dot. To achieve this in the most exhaustive way, we have worked on the aforementioned problem for charged particles with and without mass, limited to moving on a plane and whose dynamics are governed by the Dirac equation. The bound states are studied first and then the resonances, the latter by means of the Wigner time delay of the dispersion states as well as through the complex eigenvalues of the outgoing states, in order to obtain a complete picture of the confinement. One of the main results obtained and described in detail is that electric quantum dots for massless charges seem to act as sinks (or sources in the opposite direction) of resonances, while for massive particles the resonances and bound states are conserved with varying position depending on the depth of the well.
We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent going from real to complex as the coupling constant is increased. This change of behavior is manifested in the antisymmetric response, which displays power law behavior at small wavevectors reminiscent of a critical state, and a change in this power law from real to complex that is accompanied by poles in the response function for finite size systems, suggesting a phase transition for strong enough interactions. The density-density response is also calculated, for which no critical behavior is found. We demonstrate that exciton correlations enhance the cusp in the irreducible polarizability at $2k_F$, leading to a strong increase in the amplitude of Friedel oscillations around a charged impurity.
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realising an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
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