Masses and Majorana fermions in graphene

We review the classification of all the 36 possible gap-opening instabilities in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac Hamiltonian when the spin, valley, and superconducting channels are included. We then show that in graphene it is possible to realize an odd number of Majorana fermions attached to vortices in superconducting order parameters if a proper hierarchy of mass scales is in place.Comment: Contribution to the Proceedings of the Nobel symposium on graphene and quantum matte

Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry

We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these particle-hole symmetric systems the topological phases are characterized by an even-numbered winding number $\nu$. At a two-dimensional (2D) surface the topological properties of this quantum state manifest themselves through the presence of $\nu$ flavors of gapless Dirac fermion surface states, which are robust against localization from random impurities. We construct a tight-binding model on the diamond lattice that realizes a topologically nontrivial phase, in which the winding number takes the value $\nu =\pm 2$. Disorder corresponds to a (non-localizing) random SU(2) gauge potential for the surface Dirac fermions, leading to a power-law density of states $\rho(\epsilon) \sim \epsilon^{1/7}$. The bulk effective field theory is proposed to be the (3+1) dimensional SU(2) Yang-Mills theory with a theta-term at $\theta=\pi$.Comment: 5 pages, 3 figure

Constraining the Emissivity of Ultrahigh Energy Cosmic Rays in the Distant Universe with the Diffuse Gamma-ray Emission

Ultra-high cosmic rays (UHECRs) with energies >10^19 eV emitted at cosmological distances will be attenuated by cosmic microwave and infrared background radiation through photohadronic processes. Lower energy extra-galactic cosmic rays (~10^18-10^19 eV) can only travel a linear distance smaller than ~Gpc in a Hubble time due to the diffusion if the extra-galactic magnetic fields are as strong as nano Gauss. These prevent us from directly observing most of the UHECRs in the universe, and thus the observed UHECR intensity reflects only the emissivity in the nearby universe within hundreds of Mpc. However, UHECRs in the distant universe, through interactions with the cosmic background photons, produce UHE electrons and gamma-rays that in turn initiate electromagnetic cascades on cosmic background photons. This secondary cascade radiation forms part of the extragalactic diffuse GeV-TeV gamma-ray radiation and, unlike the original UHECRs, is observable. Motivated by new measurements of extragalactic diffuse gamma-ray background radiation by Fermi/LAT, we obtained upper limits placed on the UHECR emissivity in the distant universe by requiring that the cascade radiation they produce not exceed the observed levels. By comparison with the gamma-ray emissivity of candidate UHECR sources (such as GRBs and AGNs) at high-redshifts, we find that the obtained upper limit for a flat proton spectrum is ~10^1.5 times larger than the gamma-ray emissivity in GRBs and ~10 times smaller than the gamma-ray emissivity in BL Lac objects. In the case of iron nuclei composition, the derived upper limit of the UHECR emissivity is a factor of 3-5 times higher. Robust upper limit on the cosmogenic neutrino flux is further obtained, which is marginally reachable by the Icecube detector and the next-generation detector JEM-EUSO.Comment: 14 pages, 8 figures, Replaced to match the published versio

Superlattices based on van der Waals 2D materials

Two-dimensional (2D) materials exhibit a number of improved mechanical, optical, electronic properties compared to their bulk counterparts. The absence of dangling bonds in the cleaved surfaces of these materials allows combining different 2D materials into van der Waals heterostructures to fabricate p-n junctions, photodetectors, 2D-2D ohmic contacts that show unexpected performances. These intriguing results are regularly summarized in comprehensive reviews. A strategy to tailor their properties even further and to observe novel quantum phenomena consists in the fabrication of superlattices whose unit cell is formed either by two dissimilar 2D materials or by a 2D material subjected to a periodical perturbation, each component contributing with different characteristics. Furthermore, in a 2D materials-based superlattice, the interlayer interaction between the layers mediated by van der Waals forces constitutes a key parameter to tune the global properties of the superlattice. The above-mentioned factors reflect the potential to devise countless combinations of van der Waals 2D materials based superlattices. In the present feature article, we explain in detail the state-of-the-art of 2D materials-based superlattices and we describe the different methods to fabricate them, classified as vertical stacking, intercalation with atoms or molecules, moir\'e patterning, strain engineering and lithographic design. We also aim to highlight some of the specific applications for each type of superlattices.Comment: Perspective article. 6 Figures. 133 reference

Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sln)E_{\tau,\eta}(sl_n) and its applications

We study the tensor product of the {\it higher spin representations} (see the definition in Sect. 2.2) of the elliptic quantum group $E_{\tau,\eta}(sl_n)$. The transfer matrices associated with the $E_{\tau,\eta}(sl_n)$-module are exactly diagonalized by the nested Bethe ansatz method. Some special cases of the construction give the exact solution for the $Z_n$ Belavin model and for the elliptic $A_{n-1}$ Ruijsenaars-Schneider model.Comment: 23 pages, latex file, to appear in Nucl. Phys.

Effective mass theory of monolayer \delta-doping in the high-density limit

Monolayer \delta-doped structures in silicon have attracted renewed interest with their recent incorporation into atomic-scale device fabrication strategies as source and drain electrodes and in-plane gates. Modeling the physics of \delta-doping at this scale proves challenging, however, due to the large computational overhead associated with ab initio and atomistic methods. Here, we develop an analytical theory based on an effective mass approximation. We specifically consider the Si:P materials system, and the limit of high donor density, which has been the subject of recent experiments. In this case, metallic behavior including screening tends to smooth out the local disorder potential associated with random dopant placement. While smooth potentials may be difficult to incorporate into microscopic, single-electron analyses, the problem is easily treated in the effective mass theory by means of a jellium approximation for the ionic charge. We then go beyond the analytic model, incorporating exchange and correlation effects within a simple numerical model. We argue that such an approach is appropriate for describing realistic, high-density, highly disordered devices, providing results comparable to density functional theory, but with greater intuitive appeal, and lower computational effort. We investigate valley coupling in these structures, finding that valley splitting in the low-lying \Gamma band grows much more quickly than the \Gamma-\Delta band splitting at high densities. We also find that many-body exchange and correlation corrections affect the valley splitting more strongly than they affect the band splitting