Semiclassical theory of transport in a random magnetic field

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$.Comment: 22 pages REVTEX, 14 figure

The Discovery of a Highly Accreting, Radio-loud Quasar at z = 6.82

Radio sources at the highest redshifts can provide unique information on the first massive galaxies and black holes, the densest primordial environments, and the epoch of reionization. The number of astronomical objects identified at z > 6 has increased dramatically over the last few years, but previously only three radio-loud (R 2500 = f ν,5 GHz/f ν,2500 Å > 10) sources had been reported at z > 6, with the most distant being a quasar at z = 6.18. Here we present the discovery and characterization of PSO J172.3556+18.7734, a radio-loud quasar at z = 6.823. This source has an Mg ii-based black hole mass of ∼3 × 108 M o˙ and is one of the fastest accreting quasars, consistent with super-Eddington accretion. The ionized region around the quasar is among the largest measured at these redshifts, implying an active phase longer than the average lifetime of the z ⪆ 6 quasar population. From archival data, there is evidence that its 1.4 GHz emission has decreased by a factor of two over the last two decades. The quasar's radio spectrum between 1.4 and 3.0 GHz is steep (α = -1.31). Assuming the measured radio slope and extrapolating to rest-frame 5 GHz, the quasar has a radio-loudness parameter R 2500 ∼ 90. A second steep radio source (α = -0.83) of comparable brightness to the quasar is only 23.″1 away (∼120 kpc at z = 6.82; projection probability <2%), but shows no optical or near-infrared counterpart. Further follow-up is required to establish whether these two sources are physically associated. © 2021. The Author(s). Published by the American Astronomical Society..Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]