Arbitrage in Stock Index Futures One and Two Dimensional Problems

Master'sMASTER OF SCIENC

Spin Polarized and Valley Helical Edge Modes in Graphene Nanoribbons

Inspired by recent progress in fabricating precisely zigzag-edged graphene nanoribbons and the observation of edge magnetism, we find that spin polarized edge modes with well-defined valley index can exist in a bulk energy gap opened by a staggered sublattice potential such as that provided by a hexagonal Boron-Nitride substrate. Our result is obtained by both tight-binding model and first principles calculations. These edge modes are helical with respect to the valley degree of freedom, and are robust against scattering, as long as the disorder potential is smooth over atomic scale, resulting from the protection of the large momentum separation of the valleys.Comment: 4 pages, 4 figure

Edge states in Graphene: from gapped flat band to gapless chiral modes

We study edge-states in graphene systems where a bulk energy gap is opened by inversion symmetry breaking. We find that the edge-bands dispersion can be controlled by potentials applied on the boundary with unit cell length scale. Under certain boundary potentials, gapless edge-states with valley-dependent velocity are found, exactly analogous to the spin-dependent gapless chiral edge-states in quantum spin Hall systems. The connection of the edge-states to bulk topological properties is revealed

Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects

We investigate the possibility of realizing quantum anomalous Hall effect in graphene. We show that a bulk energy gap can be opened in the presence of both Rashba spin-orbit coupling and an exchange field. We calculate the Berry curvature distribution and find a non-zero Chern number for the valence bands and demonstrate the existence of gapless edge states. Inspired by this finding, we also study, by first principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result.Comment: 4 papges, 5 figure

Magnetic control of the valley degree of freedom of massive Dirac fermions with application to transition metal dichalcogenides

We study the valley-dependent magnetic and transport properties of massive Dirac fermions in multivalley systems such as the transition metal dichalcogenides. The asymmetry of the zeroth Landau level between valleys and the enhanced magnetic susceptibility can be attributed to the different orbital magnetic moment tied with each valley. This allows the valley polarization to be controlled by tuning the external magnetic field and the doping level. As a result of this magnetic field induced valley polarization, there exists an extra contribution to the ordinary Hall effect. All these effects can be captured by a low energy effective theory with a valley-orbit coupling term.Comment: 9 pages, 6 figure

Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and Novel 2D Emergent Fermions

Tunable quantum phase transitions and novel emergent fermions in solid state materials are fascinating subjects of research. Here, we propose a new stable two-dimensional (2D) material, the blue phosphorene oxide (BPO), which exhibits both. Based on first-principles calculations, we show that its equilibrium state is a narrow-bandgap semiconductor with three bands at low energy. Remarkably, a moderate strain can drive a semiconductor-to-semimetal quantum phase transition in BPO. At the critical transition point, the three bands cross at a single point at Fermi level, around which the quasiparticles are a novel type of 2D pseudospin-1 fermions. Going beyond the transition, the system becomes a symmetry-protected semimetal, for which the conduction and valence bands touch quadratically at a single Fermi point that is protected by symmetry, and the low-energy quasiparticles become another novel type of 2D double Weyl fermions. We construct effective models characterizing the phase transition and these novel emergent fermions, and we point out several exotic effects, including super Klein tunneling, supercollimation, and universal optical absorbance. Our result reveals BPO as an intriguing platform for the exploration of fundamental properties of quantum phase transitions and novel emergent fermions, and also suggests its great potential in nanoscale device applications.Comment: 23 pages, 5 figure