Coupled Spin and Pseudo-magnetic Field in Graphene Nanoribbons

Pseudo-magnetic field becomes an experimental reality after the observation of zero-field Landau level-like quantization in strained graphene, but it is not expected that the time-reversal symmetric pseudo-magnetic fields will have any effect on the spin degree of freedom of the charge carriers. Here, we demonstrate that spin-orbit coupling (SOC) could act as a bridge between pseudo-magnetic field and spin. In quantum spin Hall (QSH) states, the direction of the spin of edge states is tied to their direction of motion because of the SOC. The pseudo-magnetic field affects the clockwise and counter-clock-wise edge currents of the QSH states, and consequently lifts the degenerate edge states of opposite spin orientation. Because of opposite signs of the pseudo-magnetic field in two valleys of graphene, the one-dimensional charge carriers at the two opposite edges have different group velocities, and in some special cases the edge states can only propagate at one edge of the nanoribbon and the group velocity at the other edge becomes zero.Comment: 4 figure

A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm

A4A_4 Group and Tri-bimaximal Neutrino Mixing -- A Renormalizable Model

The tetrahedron $A_4$ group has been widely used in studying neutrino mixing matrix. It provides a natural framework of model building for the tri-bimaximal mixing matrix. In this class of models, it is necessary to have two Higgs fields, $\chi$ and $\chi'$, transforming under $A_4$ as 3 with one of them having vacuum expectation values for the three components to be equal and another having only one of the components to be non-zero. These specific vev structures require separating $\chi$ and $\chi'$ from communicating with each other. The clash of the different vev structures for $\chi$ and $\chi'$ is the so called sequestering problem. In this work, I show that it is possible to construct renormalizable supersymmetric models producing the tri-bimaximal neutrino mixing with no sequestering problem.Comment: 4 page