Anchored Critical Percolation Clusters and 2-D Electrostatics

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find that they are given by simple functions of the potentials of 2-D electrostatic dipoles, and that a kind of superposition {\it cum} factorization applies. Our results broaden this connection, already known from previous studies, and we present evidence that it is more generally valid. An exact result similar to the Kirkwood superposition approximation emerges.Comment: 4 pages, 1 (color) figure. More numerics, minor corrections, references adde

Twist operator correlation functions in O(n) loop models

Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure

Single-shot single-gate RF spin readout in silicon

For solid-state spin qubits, single-gate RF readout can help minimise the number of gates required for scale-up to many qubits since the readout sensor can integrate into the existing gates required to manipulate the qubits (Veldhorst 2017, Pakkiam 2018). However, a key requirement for a scalable quantum computer is that we must be capable of resolving the qubit state within single-shot, that is, a single measurement (DiVincenzo 2000). Here we demonstrate single-gate, single-shot readout of a singlet-triplet spin state in silicon, with an average readout fidelity of $82.9\%$ at a $3.3~\text{kHz}$ measurement bandwidth. We use this technique to measure a triplet $T_-$ to singlet $S_0$ relaxation time of $0.62~\text{ms}$ in precision donor quantum dots in silicon. We also show that the use of RF readout does not impact the maximum readout time at zero detuning limited by the $S_0$ to $T_-$ decay, which remained at approximately $2~\text{ms}$. This establishes single-gate sensing as a viable readout method for spin qubits

Phase diagram of the metal-insulator transition in 2D electronic systems

We investigated the interdependence of the effects of disorder and carrier correlations on the metal-insulator transition in two-dimensional electronic systems. We present a quantitative metal-insulator phase diagram. Depending on the carrier density we find two different types of metal-insulator transition - a continuous localization for rs=<8 and a discontinuous transition at higher rs. The critical level of disorder at the transition decreases with decreasing carrier density. At very low carrier densities we find that the system is always insulating. The value of the conductivity at the transition is consistent with recent experimental measurements. The self-consistent method which we have developed includes the effects of both disorder and correlations on the transition, using a density relaxation theory with the Coulomb correlations determined from numerical simulation data.Comment: 4 pages, RevTeX + epsf, 5 figures. New comments on conducting phase and on the conductivity. References updated and correcte

Fermi-liquid behaviour of the low-density 2D hole gas in GaAs/AlGaAs heterostructure at large values of r_s

We examine the validity of the Fermi-liquid description of the dilute 2D hole gas in the crossover from 'metallic'-to-'insulating' behaviour of R(T).It has been established that, at r_s as large as 29, negative magnetoresistance does exist and is well described by weak localisation. The dephasing time extracted from the magnetoresistance is dominated by the T^2 -term due to Landau scattering in the clean limit. The effect of hole-hole interactions, however, is suppressed when compared with the theory for small r_s.Comment: 4 pages ReVTeX, 4 ps figure

Classical versus Quantum Effects in the B=0 Conducting Phase in Two Dimensions

In the dilute two-dimensional electron system in silicon, we show that the temperature below which Shubnikov-de Haas oscillations become apparent is approximately the same as the temperature below which an exponential decrease in resistance is seen in B=0, suggesting that the anomalous behavior in zero field is observed only when the system is in a degenerate (quantum) state. The temperature dependence of the resistance is found to be qualitatively similar in B=0 and at integer Landau level filling factors.Comment: 3 pages, 3 figure

Optical Linear Polarization of Late M- and L-Type Dwarfs

(Abridged). We report on the linear polarimetric observations in the Johnson I filter of 44 M6-L7.5 ultracool dwarfs (2800-1400 K). Eleven (10 L and 1 M) dwarfs appear to have significant linear polarization (P = 0.2-2.5%). We have compared the M- and L-dwarf populations finding evidence for a larger frequency of high I-band polarization in the coolest objects, supporting the presence of significant amounts of dust in L-dwarfs. The probable polarizing mechanism is related to the presence of heterogeneous dust clouds nonuniformly distributed across the visible photospheres and the asymmetric shape of the objects. In some young ultracool dwarfs, surrounding dusty disks may also yield polarization. For polarimetric detections, a trend for slightly larger polarization from L0 to L6.5 may be present in our data, suggesting changes in the distribution of the grain properties, vertical height of the clouds, metallicity, age, and rotation speed. One of our targets is the peculiar brown dwarf (BD) 2MASS J2244+20 (L6.5), which shows the largest I-band polarization degree. Its origin may lie in a surrounding dusty disk or rather large photospheric dust grains. The M7 young BD CFHT-BD-Tau 4 and the L3.5 field dwarf 2MASS J0036+18 were also observed in the Johnson R filter. Our data support the presence of a circum(sub)stellar disk around the young accreting BD. Our data also support a grain growth in the submicron regime in the visible photosphere of J0036+18 (1900 K). The polarimetric data do not obviously correlate with activity or projected rotational velocity. Three polarized early- to mid-L dwarfs display I-band light curves with amplitudes below 10 mmag.Comment: Accepted for publication in ApJ (March 2005), 35 pages, 5 figure

Weak anisotropy and disorder dependence of the in-plane magnetoresistance in high mobility (100) Si-inversion layers

We report studies of the magnetoresistance (MR) in a two-dimensional electron system in (100) Si-inversion layers, for perpendicular and parallel orientations of the current with respect to the magnetic field in the 2D-plane. The magnetoresistance is almost isotropic; this result does not support the suggestion of the orbital origin of the MR in Si-inversion layer. In the hopping regime, however, the MR contains a weak anisotropic component that is non-monotonic in magnetic field. We found that the field, at which the MR saturates, for different samples varies by a factor of two, being lower or higher than the field of complete spin polarization of free carriers. Therefore, the saturation of the MR can not be identified with the spin polarization of free carriers.Comment: 4 pages, 4 figures; New data adde

Comment on "Theory of metal-insulator transitions in gated semiconductors" (B. L. Altshuler and D. L. Maslov, Phys. Rev. Lett. 82, 145 (1999))

In a recent Letter, Altshuler and Maslov propose a model which attributes the anomalous temperature and field dependence of the resistivity of two-dimensional electron (or hole) systems to the charging and discharging of traps in the oxide (spacer), rather than to intrinsic behavior of interacting particles associated with a conductor-insulator transition in two dimensions. We argue against this model based on existing experimental evidence.Comment: 1 page; submitted to PR

Kondo Effect in a Quantum Antidot

We report Kondo-like behaviour in a quantum antidot (a submicron depleted region in a two-dimensional electron gas) in the quantum-Hall regime. When both spin branches of the lowest Landau level encircle the antidot in a magnetic field ($\sim 1$ T), extra resonances occur between extended edge states via antidot bound states when tunnelling is Coulomb blockaded. These resonances appear only in alternating Coulomb-blockaded regions, and become suppressed when the temperature or source-drain bias is raised. Although the exact mechanism is unknown, we believe that Kondo-like correlated tunnelling arises from skyrmion-type edge reconstruction. This observation demonstrates the generality of the Kondo phenomenon.Comment: 9 pages, 3 figures (Fig.3 in colour), to appear in Phys. Rev. Let