Quantum Spin Hall Effect and Topologically Invariant Chern Numbers

We present a topological description of quantum spin Hall effect (QSHE) in a two-dimensional electron system on honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. We show that the topology of the band insulator can be characterized by a $2\times 2$ traceless matrix of first Chern integers. The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). A spin Chern number is derived from the CNM, which is conserved in the presence of finite disorder scattering and spin nonconserving Rashba coupling. By using the Laughlin's gedanken experiment, we numerically calculate the spin polarization and spin transfer rate of the conducting edge states, and determine a phase diagram for the QSHE.Comment: 4 pages and 4 figure

Spin Hall Effect and Spin Transfer in Disordered Rashba Model

Based on numerical study of the Rashba model, we show that the spin Hall conductance remains finite in the presence of disorder up to a characteristic length scale, beyond which it vanishes exponentially with the system size. We further perform a Laughlin's gauge experiment numerically and find that all energy levels cannot cross each other during an adiabatic insertion of the flux in accordance with the general level-repulsion rule. It results in zero spin transfer between two edges of the sample as each state always evolves back after the insertion of one flux quantum, in contrast to the quantum Hall effect. It implies that the topological spin Hall effect vanishes with the turn-on of disorder.Comment: 4 pages, 4 figures final versio

Tunable Circularly Polarized Terahertz Radiation from Magnetized Gas Plasma

It is shown, by simulation and theory, that circularly or elliptically polarized terahertz radiation can be generated when a static magnetic (B) field is imposed on a gas target along the propagation direction of a two-color laser driver. The radiation frequency is determined by $\sqrt{\omega_p^2+{\omega_c^2}/{4}} + {\omega_c}/{2}$, where $\omega_p$ is the plasma frequency and $\omega_c$ is the electron cyclotron frequency. With the increase of the B field, the radiation changes from a single-cycle broadband waveform to a continuous narrow-band emission. In high-B-field cases, the radiation strength is proportional to $\omega_p^2/\omega_c$. The B field provides a tunability in the radiation frequency, spectrum width, and field strength.Comment: 6 pages, 5 figure

Leibniz 2-algebras and twisted Courant algebroids

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.Comment: 22 pages, to appear in Comm. Algebr

Laser opacity in underdense preplasma of solid targets due to quantum electrodynamics effects

We investigate how next-generation laser pulses at 10 PW $-$ 200 PW interact with a solid target in the presence of a relativistically underdense preplasma produced by amplified spontaneous emission (ASE). Laser hole boring and relativistic transparency are strongly restrained due to the generation of electron-positron pairs and $\gamma$-ray photons via quantum electrodynamics (QED) processes. A pair plasma with a density above the initial preplasma density is formed, counteracting the electron-free channel produced by the hole boring. This pair-dominated plasma can block the laser transport and trigger an avalanche-like QED cascade, efficiently transfering the laser energy to photons. This renders a 1-$\rm\mu m$-scalelength, underdense preplasma completely opaque to laser pulses at this power level. The QED-induced opacity therefore sets much higher contrast requirements for such pulse in solid-target experiments than expected by classical plasma physics. Our simulations show for example, that proton acceleration from the rear of a solid with a preplasma would be strongly impaired.Comment: 5 figure