• Corpus ID: 122796793

# Dirac and Majorana edge states in graphene and topological superconductors

@inproceedings{Akhmerov2011DiracAM,
title={Dirac and Majorana edge states in graphene and topological superconductors},
author={A. Akhmerov},
year={2011}
}
This dissertation is about transport and electronic properties of two types of electronic states occuring at the edges, which are protected by symmetry between positive and negative energies. One type of these states is shown to occur universally in graphene. It is also described how another type of edge states, Majorana fermions, can be used for topological quantum computation.
2 Citations
Broken Mirrors: The breakdown of the law of reflection in bilayer graphene
As long as a wave has a large enough wavelength, it should reflect off of smooth surfaces specularly: that is what the law of reflection states. This phenomenon is widely known, and used in for
Introduction to Graphene-Based Nanomaterials: From Electronic Structure to Quantum Transport Luis E.F. Foa Torres, Stephan Roche, and Jean-Christophe Charlier
• Physics
• 2014
Beginning with an introduction to carbon-based nanomaterials, their electronic properties, and general concepts in quantum transport, this detailed primer describes the most effective theoretical and

## References

SHOWING 1-10 OF 223 REFERENCES
Detection of valley polarization in graphene by a superconducting contact.
• Physics
Physical review letters
• 2007
This work shows how Andreev reflection can be used to detect the valley polarization of edge states produced by a magnetic field, in the absence of intervalley relaxation.
Topological quantum computation away from the ground state using Majorana fermions
We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within
Boundary conditions for Dirac fermions on a terminated honeycomb lattice
• Physics
• 2008
We derive the boundary condition for the Dirac equation corresponding to a tight-binding model on a two-dimensional honeycomb lattice terminated along an arbitrary direction. Zigzag boundary
Theory of the valley-valve effect in graphene nanoribbons
• Physics
• 2008
A potential step in a graphene nanoribbon with zigzag edges is shown to be an intrinsic source of intervalley scattering -- no matter how smooth the step is on the scale of the lattice constant a.
Effects of disorder on the transmission of nodal fermions through a d-wave superconductor
• Physics
• 2011
The bulk microwave conductivity of a dirty d-wave superconductor is known to depend sensitively on the range of the disorder potential: long-range scattering enhances the conductivity, while short-
Universal temperature dependence of the conductivity of a strongly disordered granular metal
• Physics
• 2006
A disordered array of metal grains with large and random intergrain conductances is studied within the one-loop accuracy renormalization group approach. While, at low level of disorder, the
Valley-isospin dependence of the quantum Hall effect in a graphene p − n junction
• Physics
• 2007
We calculate the conductance $G$ of a bipolar junction in a graphene nanoribbon, in the high-magnetic-field regime where the Hall conductance in the $p$-doped and $n$-doped regions is $2{e}^{2}∕h$.
Theory of non-Abelian Fabry-Perot interferometry in topological insulators
• Physics
Physical Review B
• 2010
Interferometry of non-Abelian edge excitations is a useful tool in topological quantum computing. In this paper we present a theory of a non-Abelian edge-state interferometer in a three-dimensional
Pseudodiffusive conduction at the Dirac point of a normal-superconductor junction in graphene
• Physics
• 2007
A ballistic strip of graphene (width $W⪢\text{length}$ $L$) connecting two normal metal contacts is known to have a minimum conductivity of $4{e}^{2}∕\ensuremath{\pi}h$ at the Dirac point of charge
Quantum Goos-Hänchen effect in graphene.
• Physics
Physical review letters
• 2009
It is shown that the GH effect at a p-n interface in graphene depends on the pseudospin (sublattice) degree of freedom of the massless Dirac fermions, and a sign change of sigma at angle of incidence alpha=arcsin sqrt[sinalpha{c] determined by the critical angle alpha{c} for total reflection.