A Simple Method to Measure the Interaction Potential of Dielectric Grains in a Dusty Plasma

A simple minimally perturbative method is introduced which provides the ability to experimentally measure both the radial confining potential and the interaction potential between two individual dust particles, levitated in the sheath of a radio-frequency (RF) argon discharge. In this technique, a single dust particle is dropped into the plasma sheath to interact with a second individual dust particle already situated at the system's equilibrium point, without introducing any external perturbation. The resulting data is analyzed using a method employing a polynomial fit to the particle displacement(s), X(t), to reduce uncertainty in calculation. Employing this technique, the horizontal confinement is shown to be parabolic over a wide range of pressures and displacements from the equilibrium point. The interaction potential is also measured and shown to be well-described by a screened Coulomb potential and to decrease with increasing pressure. Finally, the charge on the particle and the effective dust screening distance are calculated. It is shown for the first time experimentally that the charge on a particle in the sheath of an RF plasma decreases with increasing pressure, in agreement with theoretical predictions. The screening distance also decreases with increasing pressure as expected. This technique can be used for rapid determination of particle parameters in dusty plasma

Two-Dimensional Topological Insulator State and Topological Phase Transition in Bilayer Graphene

We show that gated bilayer graphene hosts a strong topological insulator (TI) phase in the presence of Rashba spin-orbit (SO) coupling. We find that gated bilayer graphene under preserved time-reversal symmetry is a quantum valley Hall insulator for small Rashba SO coupling $\lambda_{\mathrm{R}}$, and transitions to a strong TI when $\lambda_{\mathrm{R}} > \sqrt{U^2+t_\bot^2}$, where $U$ and $t_\bot$ are respectively the interlayer potential and tunneling energy. Different from a conventional quantum spin Hall state, the edge modes of our strong TI phase exhibit both spin and valley filtering, and thus share the properties of both quantum spin Hall and quantum valley Hall insulators. The strong TI phase remains robust in the presence of weak graphene intrinsic SO coupling.Comment: 5 pages and 4 figure

Topological phases in gated bilayer graphene: Effects of Rashba spin-orbit coupling and exchange field

We present a systematic study on the influence of Rashba spin-orbit coupling, interlayer potential difference and exchange field on the topological properties of bilayer graphene. In the presence of only Rashba spin-orbit coupling and interlayer potential difference, the band gap opening due to broken out-of-plane inversion symmetry offers new possibilities of realizing tunable topological phase transitions by varying an external gate voltage. We find a two-dimensional $Z_2$ topological insulator phase and a quantum valley Hall phase in $AB$-stacked bilayer graphene and obtain their effective low-energy Hamiltonians near the Dirac points. For $AA$ stacking, we do not find any topological insulator phase in the presence of large Rashba spin-orbit coupling. When the exchange field is also turned on, the bilayer system exhibits a rich variety of topological phases including a quantum anomalous Hall phase, and we obtain the phase diagram as a function of the Rashba spin-orbit coupling, interlayer potential difference, and exchange field.Comment: 15 pages, 17figures, and 1 tabl

A Combinatorial Approach to Robust PCA

We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional subspace $U \subseteq \mathbb{R}^d$, and $s$ randomly chosen coordinates of each data point fall into the control of an adversary. This setting models the scenario of learning from high-dimensional yet structured data that are transmitted through a highly-noisy channel, so that the data points are unlikely to be entirely clean. Our main result is an efficient algorithm that, when $ks^2 = O(d)$, recovers every single data point up to a nearly-optimal $\ell_1$ error of $\tilde O(ks/d)$ in expectation. At the core of our proof is a new analysis of the well-known Basis Pursuit (BP) method for recovering a sparse signal, which is known to succeed under additional assumptions (e.g., incoherence or the restricted isometry property) on the underlying subspace $U$. In contrast, we present a novel approach via studying a natural combinatorial problem and show that, over the randomness in the support of the sparse signal, a high-probability error bound is possible even if the subspace $U$ is arbitrary.Comment: To appear at ITCS 202