118621064
Dirac fermions in graphene and analogues: magnetic field and topological properties
This is a short review of two-dimensional Dirac fermions in graphene and similar systems such as boron nitride, quasi-2D organic salts $\alpha$-(BEDT-TTF)$_2$I$_3$, artificial graphene with cold atoms in optical lattices, etc. The emphasis is on magnetic field properties (semi-classical quantization of cyclotron orbits, Landau levels, quantum Hall effect, magneto-plasmons, magneto-phonon resonance, magneto-transport, etc.) and on topological properties (Berry phase, winding number, inter-band effects, merging transition of Dirac points, etc.).
118685069
Klein tunneling in graphene: optics with massless electrons
Abstract
This article provides a pedagogical review on Klein tunneling in graphene, i.e. the
peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two
simple situations in detail: a massless Dirac electron incident either on a potential step
or on a potential barrier and use elementary quantum wave mechanics to obtain the
transmission probability. We emphasize the connection to related phenomena in optics, such
as the Snell-Descartes law of refraction, total internal reflection, Fabry-Pérot
resonances, negative refraction index materials (the so called meta-materials), etc. We
also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not
necessarily involve passing through a classically forbidden region via evanescent waves. A
crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin,
which is discussed in detail. A major consequence is the absence of backscattering at
normal incidence, of which we give a new shorten proof. The current experimental status is
also thoroughly reviewed. The Appendix contains the discussion of a one-dimensional toy
model that clearly illustrates the difference in Klein tunneling between mono- and
bi-layer graphene.

121959537
Physical State Conditions and Supersymmetry Breaking in Quantum Mechanics
It is shown, by giving an explicit example, how the conditions imposed on physically admissible states can affect the pattern of supersymmetry breaking and, as a consequence, the values of physically interesting quantities such as the Witten index. As a by‐product an unusual kind of explicit supersymmetry breaking is observed, where the supersymmetry algebra still holds formally, as well as a spontaneous breakdown of supersymmetry, which is not induced by instantons.
119529680
Braiding in conformal field theory and solvable lattice models
Abstract Braiding matrices in rational conformal field theory are considered. The braiding matrices for any two-block four-point function are computed, in general, using the holomorphic properties of the blocks and the holomorphic properties of rational conformal field theory. The braidings involving the defining representation of SU( N ) k are evaluated and are used as examples. Solvable interaction round the face lattice models are constructed from these braiding matrices, and their Boltzmann weights are given. This allows, in particular, for the derivation of the Boltzmann weights of such solvable height models.
120054522
RATIONAL HOPF ALGEBRAS: POLYNOMIAL EQUATIONS, GAUGE FIXING, AND LOW-DIMENSIONAL EXAMPLES
Rational Hopf algebras, i.e. certain quasitriangular weak quasi-Hopf algebras whose representations form a tortile modular C* category, are expected to describe the quantum symmetry of rational field theories. In this paper the essential structure (hidden by a large gauge freedom) of rational Hopf algebras is revealed. This allows one to construct examples of rational Hopf algebras starting only from the corresponding fusion ring. In particular we classify all solutions for fusion rules with not more than three sectors, as well as for the level 3 affine fusion rules.