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Register a new userQualitative analysis of magnetic waveguides for two-dimensional Dirac fermions
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We focus on the confinement of two-dimensional Dirac fermions within the waveguides created by realistic magnetic fields. Understanding of their band structure is of our main concern. We provide easily applicable criteria, mostly depending only on the asymptotic behavior of the magnetic field, that can guarantee existence or absence of the energy bands and provide valuable insight into the systems where analytical solution is impossible. The general results are employed in specific systems where the waveguide is created by the magnetic field of a set of electric wires or magnetized strips.
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We use the Wick-rotated time-dependent supersymmetry to construct models of two-dimensional Dirac fermions in presence of an electrostatic grating. We show that there appears omnidirectional perfect transmission through the grating at specific energy. Additionally to being transparent for incoming fermions, the grating hosts strongly localized states.
We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $epsilon=(3-d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an emph{enlarged} $O(S_1+S_2)$ chiral symmetry. Such a fixed point acts as an exotic quantum multi-critical point (MCP), governing the emph{continuous} semimetal-insulator as well as insulator-insulator (for example antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $O(S_1)$ or $O(S_2)$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher dimensional Dirac fermions is also outlined.
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak-disorder expansion in the parameter g/m^2, where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non-uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.
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.
Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable electronic, optical, mechanical and chemical properties of 2D Dirac materials. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of SOC. Here we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC. Through $mu$-ARPES measurements we observe Dirac-like band dispersions in $alpha$-bismuthene. The nonsymmorphic lattice symmetry is confirmed by $mu$-LEED and STM. Our first-principles simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results open the door for the search of symmetry enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.
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