Near-Zero Modes in Superconducting Graphene

Vortices in the simplest superconducting state of graphene contain very low energy excitations, whose existence is connected to an index theorem that applies strictly to an approximate form of the relevant Bogoliubov-deGennes equations. When Zeeman interactions are taken into account, the zero modes required by the index theorem are (slightly) displaced. Thus the vortices acquire internal structure, that plausibly supports interesting dynamical phenomena.Comment: 9 pages, to appear in Proceedings of the Nobel Symposium on Graphene and Quantum Matte

Magnification of signatures of a topological phase transition by quantum zero point motion

FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOWe show that the zero point motion of a vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level, and the corresponding effects are manifest in the density of states at energies which are on the order of the vortex fluctuation frequency. Although the electronic energy gap in the spectrum generated by a stationary vortex is but a small fraction of the bulk superconducting gap, the vortex fluctuation frequency may be much larger. As a result, this quantum zero point motion can induce a discontinuous change in the spectral features of the system at the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. This discontinuous change is exclusive to superconducting systems in which we have a topological phase transition. Moreover, the phenomena studied in this paper present effects of Magnus forces on the vortex spectrum which are not present in the ordinary s-wave superconductors. Finally, we demonstrate explicitly that the vortex in this system is equivalent to a Kitaev chain. This allows for the mapping of the vortex fluctuating scenario in three dimensions into similar one-dimensional situations in which one may search for other novel signatures of topological phase transitions.We show that the zero point motion of a vortex in superconducting doped topological insulators leads to significant changes in the electronic spectrum at the topological phase transition in this system. This topological phase transition is tuned by the doping level, and the corresponding effects are manifest in the density of states at energies which are on the order of the vortex fluctuation frequency. Although the electronic energy gap in the spectrum generated by a stationary vortex is but a small fraction of the bulk superconducting gap, the vortex fluctuation frequency may be much larger. As a result, this quantum zero point motion can induce a discontinuous change in the spectral features of the system at the topological vortex phase transition to energies which are well within the resolution of scanning tunneling microscopy. This discontinuous change is exclusive to superconducting systems in which we have a topological phase transition. Moreover, the phenomena studied in this paper present effects of Magnus forces on the vortex spectrum which are not present in the ordinary s-wave superconductors. Finally, we demonstrate explicitly that the vortex in this system is equivalent to a Kitaev chain. This allows for the mapping of the vortex fluctuating scenario in three dimensions into similar one-dimensional situations in which one may search for other novel signatures of topological phase transitions.926113FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOFAPESP [2009/18336-0]2009/18336-

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

Dynamical Gate Tunable Supercurrents in Topological Josephson Junctions

Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has been attributed to a transition where the topologically trivial 2DEG at the surface is nearly depleted, causing a shift in the spatial location and change in nature of the helical surface states. We present measurements that support this picture by revealing qualitative changes in the temperature and magnetic field dependence of the critical current across this transition. In particular, we observe pronounced fluctuations in the critical current near total depletion of the 2DEG that demonstrate the dynamical nature of the supercurrent transport through topological low energy ABSs.Comment: 6 pages, 6 figure

Fractional topological phases and broken time reversal symmetry in strained graphene

We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strained induced pseudo magnetic fields are oppositely oriented in the two valleys [1-3] and can be as large as 60-300 Tesla as reported in recent experiments [4,5]. For strained graphene at neutrality, a spin or a valley polarized state is predicted depending on the value of the onsite Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley polarized Fractional Quantum Hall liquid which spontaneously breaks time reversal symmetry. Motivated by artificial graphene systems [5-8], we consider tuning the short range part of interactions, and demonstrate that exotic valley symmetric states, including a valley Fractional Topological Insulator and a spin triplet superconductor, can be stabilized by such interaction engineering.Comment: 5 pages + supplementary, 4 figures. Version accepted to Physical Review Letter

Lambda phage nanoparticles for targetomics

The emerging aim of drug delivery requires the bioactive or therapeutic molecule to be protected from degradation and reach its target cell and intracellular location. Target specificity of nanoparticles is a prerequisite to attain the concentration of therapeutic agent required for therapeutic efficacy in the target tissue while minimising adverse effects on other parts of the body. Therefore, there is an urgent need for improvement of more effective drug delivery systems to direct the anticancer drugs to cancer cells, specifically. In the paper, we have described advantages of Lambda bacteriophage over other drug delivery vectors and proposed it as promising drug delivery vehicle. © 2012 Asian Network for Scientific Information

Huygens description of resonance phenomena in subwavelength hole arrays

We develop a point-scattering approach to the plane-wave optical transmission of subwavelength metal hole arrays. We present a real space description instead of the more conventional reciprocal space description; this naturally produces interfering resonant features in the transmission spectra and makes explicit the tensorial properties of the transmission matrix. We give transmission spectra simulations for both square and hexagonal arrays; these can be evaluated at arbitrary angles and polarizations.Comment: 5 pages, 3 figure

Nanodiagnostic method for colorimetric detection of Mycobacterium tuberculosis 16S rRNA

A nanodiagnostic method using nucleic acid sequence-based amplification (NASBA) and gold nanoparticle probes (AuNP probes) was developed for colorimetric detection of Mycobacterium tuberculosis. The primers targeting 16S rRNA were used for the amplification of mycobacterial RNA by the isothermal NASBA process. The amplicons were hybridized with specific gold nanoparticle probes. The RNA-DNA hybrids were colorimetrically detected by the accumulation of gold nanoparticles. Using this method, 10 CFU ml-1 of M. tuberculosis was detected within less than 1 h. Results obtained from the clinical specimens showed 94.7% and 96% sensitivity and specificity, respectively. No interference was encountered in the amplification and detection of M. tuberculosis in the presence of non-target bacteria, confirming the specificity of the method. © 2009 Humana Press Inc