### Transport

On transport we mostly focused on contributions of the nodal states to the long wavelength transport properties.

- We have developed a method to investigate the doped local electronic properties of topological insulators that allow us to predict the gap closure of the magnetically doped Topological Insulators and hence to predict the existence of the mobility gaps and not real gaps in doped TI. This prediction would have implications for the applications of the Anomalous Quantum Hall effect, one of the hall marks of magnetic Tis. We expect that most magnetically doped TI do not have gaps and hence exhibit a mixture of the delocalized states that are responsible for transport and states that are localized and form mobility gaps. [Phys. Rev. B 91, 201411 (2015)]
- We have investigated the Josephson coupling between superconducting grans deposited on graphene. [Supercond. Sci. Technol. 29, 054004 (2016)]
- We have proved that even for purely potential scattering the interference effects produce a significant Density of states at arbitrarily low energies. The implication of this result is that impurity band engineering will induce a near perfect back scattering in TI. [Phys. Rev. B 90, 241409(R) (2014)]
- We developed as theory of angular magnetoresistance oscillations (AMRO) in Dirac double layers. For the first time, demonstrated that Berry phase modifies the magic angles in AMRO. We calculate the energy spectrum of a Dirac double layer in the presence of a tilted magnetic field and small interlayer tunneling and show that the energy splitting between the Landau levels has an oscillatory dependence on the in-plane magnetic field and vanishes at a series of special tilt angles of the magnetic field. The interlayer tunneling conductance exhibits an oscillatory dependence on the magnetic field tilt angle. Our results are applicable to graphene double layers and thin films of topological insulators. [Phys. Rev. B 91, 085418 (2015)]
- Using model Hamiltonians that replicate various two-dimensional massive Dirac materials, we show that inversion of the mass term generates topologically protected interface states that can carry valley or spin currents. This has application in spintronics and in developing novel switching mechanisms. [ New J. Phys. 16, 065012 (2014)]
- We pursued optics of stacked graphene to demonstrate generation of additional Dirac points due to Moire pattern formation. [Phys. Rev. B 92, 115430 (2015)]

We also pursue the stated goal of developing nanoscale science and nanotechonology of Dirac Materials. The parameter that allows a control of properties of graphene is doping and functionalization by controlled nanoscale manipulation of the atoms and defects.

### Local properties

- We have developed a theory of local negative U centers for Dirac materials like TI and graphene and we find that these centers can induce SC for high enough concentration. We also found the phase diagram for SC phase in this model. This model would allow us to work on IETS in the future with prior expertise using negative U centers as test. [Phys. Rev. B 90, 104517 (2014)]
- We have extended earlier scattering theory developed for Dirac materials to Weyl semimetals. [New J. Phys. 15 (2013) 123019]

In addition to the immediate focus we have spent time looking for other realizations of Dirac physics in condensed matter systems:

- We studied interrelation between magnetoelectric current and spin-polarization of the Majorana fermions in engineered topological superconductors. [Phys. Rev. B 92, 214501 (2015)]
- We demonstrated the strong magnetoelectric currents in superconductors with the spin-orbit coupling. [Phys. Rev. Lett. 115, 116602 (2015)]

In addition to the papers focused on DM we had been involved in other projects that allow us to be agile and respond to new developments where Dirac Materials are not the essential player but more is a platform to generate new functionalities. Examples include the case of majorana fermions generated in p wave superconductors and interactions between these majorana excitations. While this work is not the central part it does allow us to connect to the ongoing interesting developments in the field. These projects are also important for the carrier development of PD and students.