Bulk Tunneling at Integer Quantum Hall Transitions

The tunneling into the {\em bulk} of a 2D electron system (2DES) in strong magnetic field is studied near the integer quantum Hall transitions. We present a nonperturbative calculation of the tunneling density of states (TDOS) for both Coulomb and short-ranged electron-electron interactions. In the case of Coulomb interaction, the TDOS exhibits a 2D quantum Coulomb gap behavior, \nu(\ve)=C_Q\ave/e^4, with $C_Q$ a nonuniversal coefficient of quantum mechanical origin. For short-ranged interactions, we find that the TDOS at low bias follows \nu(\ve)/\nu (0)=1+(\ave/\ve_0)^\gamma, where $\gamma$ is a universal exponent determined by the scaling dimension of short-ranged interactions.Comment: 4 pages, revtex, final version to appear in Phys. Rev. Let

Edge state transmission, duality relation and its implication to measurements

The duality in the Chalker-Coddington network model is examined. We are able to write down a duality relation for the edge state transmission coefficient, but only for a specific symmetric Hall geometry. Looking for broader implication of the duality, we calculate the transmission coefficient $T$ in terms of the conductivity $\sigma_{xx}$ and $\sigma_{xy}$ in the diffusive limit. The edge state scattering problem is reduced to solving the diffusion equation with two boundary conditions $(\partial_y-(\sigma_{xy})/(\sigma_{xx})\partial_x)\phi=0$ and $[\partial_x+(\sigma_{xy}-\sigma_{xy}^{lead})/(\sigma_{xx}) \partial_y]\phi=0$. We find that the resistances in the geometry considered are not necessarily measures of the resistivity and $\rho_{xx}=L/W R/T h/e^2$ ($R=1-T$) holds only when $\rho_{xy}$ is quantized. We conclude that duality alone is not sufficient to explain the experimental findings of Shahar et al and that Landauer-Buttiker argument does not render the additional condition, contrary to previous expectation.Comment: 16 pages, 3 figures, to appear in Phys. Rev.

Mesoscopic conductance and its fluctuations at non-zero Hall angle

We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the edge effects. Analytical results are obtained by perturbation theory in the limit $\sigma_{xx} \gg 1$. For mesoscopic systems the conduction process is dominated by diffusion but we show that, due to the lack of time-reversal symmetry, the boundary condition for diffusion is altered at the reflecting edges. Instead of the usual condition, that the derivative along the direction normal to the wall of the diffusing variable vanishes, the derivative at the Hall angle to the normal vanishes. We demonstrate the origin of this boundary condition from different starting points, using (i) a simplified Chalker-Coddington network model, (ii) the standard diagrammatic perturbation expansion, and (iii) the nonlinear sigma-model with the topological term, thus establishing connections between the different approaches. Further boundary effects are found in quantum interference phenomena. We evaluate the mean bilocal conductivity tensor $\sigma_{\mu\nu}(r,r')$, and the mean and variance of the conductance, to leading order in $1/\sigma_{xx}$ and to order $(\sigma_{xy}/\sigma_{xx})^2$, and find that the variance of the conductance increases with the Hall ratio. Thus the conductance fluctuations are no longer simply described by the unitary universality class of the $\sigma_{xy}=0$ case, but instead there is a one-parameter family of probability distributions. In the quasi-one-dimensional limit, the usual universal result for the conductance fluctuations of the unitary ensemble is recovered, in contrast to results of previous authors. Also, a long discussion of current conservation.Comment: Latex, uses RevTex, 58 pages, 5 figures available on request at [email protected]. Submitted to Phys. Rev.

Efficient and Broadband Emission in Dy³⁺-Doped Glass-Ceramic Fibers for Tunable Yellow Fiber Laser

Yellow lasers are of great interest in biology, medicine and display technology. However, nonlinear emission of near-infrared lasers at yellow still presents particularly complex optical alignment to date. Here, to the best of our knowledge, we demonstrate the fabrication of a NaLa(WO4)2: Dy3+ glass-ceramic fiber (GCF) for the first time. More importantly, the emission band of the GCF, which is around 575 nm, has a wide full-width half maximum (FWHM) of 18~22 nm, which is remarkably larger than that of the Dy3+-doped YAG crystal (<7 nm). The precursor fiber (PF) was drawn using the molten core drawing (MCD) method. In particular, benefiting from the in situ nanocrystals fabricated in the amorphous fiber core after thermal treatment, the resultant glass-ceramic fiber exhibits a five-times enhancement of luminescence intensity around 575 nm, compared with the precursor fiber, while retaining its broadband emission. Overall, this work is anticipated to offer a high potential GCF with prominent bandwidth for the direct access of a tunable yellow laser