Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice

Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes the combined operation of space-inversion P and time-reversal T, it is extremely important and intriguing to completely classify exotic PT-invariant topological metals and to physically realize them. Here we, for the first time, establish a rigorous classification of topological metals that are protected by the PT symmetry using KO-theory. As a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D Brillouin zone is constructed, whose topological stability is revealed through its PT-symmetry-protected nontrivial Z2 topological charge. Based on these exact results, we propose an experimental scheme to realize and to detect tunable PT-invariant topological NL states with ultracold atoms in an optical lattice, in which atoms with two hyperfine spin states are loaded in a spin-dependent 3D OL and two pairs of Raman lasers are used to create out-of-plane spin-flip hopping with site-dependent phase. Such a realistic cold-atom setup can yield topological NL states, having a tunable ring-shaped band-touching line with the two-fold degeneracy in the bulk spectrum and non-trivial surface states. The states are actually protected by the combined PT symmetry even in the absence of both P and T symmetries, and are characterized by a Z2-type invariant (a quantized Berry phase). Remarkably, we demonstrate with numerical simulations that (i) the characteristic NL can be detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation; (ii) the topological invariant may be measured based on the time-of-flight imaging; and (iii) the surface states may be probed through Bragg spectroscopy. The present proposal for realizing topological NL states in cold atom systems may provide a unique experimental platform for exploring exotic PT-invariant topological physics.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

Black phosphorus (P) has emerged as a layered semiconductor with a unique crystal structure featuring corrugated atomic layers and strong in-plane anisotropy in its physical properties. Here, we demonstrate that the crystal orientation and mechanical anisotropy in free-standing black P thin layers can be precisely determined by spatially resolved multimode nanomechanical resonances. This offers a new means for resolving important crystal orientation and anisotropy in black P device platforms in situ beyond conventional optical and electrical calibration techniques. Furthermore, we show that electrostatic-gating-induced straining can continuously tune the mechanical anisotropic effects on multimode resonances in black P electromechanical devices. Combined with finite element modeling (FEM), we also determine the Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and armchair directions, respectively.Comment: Main Text: 13 Pages, 4 Figures; Supplementary Information: 5 Pages, 2 Figures, 2 Table

Graphite Nanoeraser

We present here a method for cleaning intermediate-size (5~50nm) contamination from highly oriented pyrolytic graphite. Electron beam deposition causes a continuous increase of carbonaceous material on graphene and graphite surfaces, which is difficult to remove by conventional techniques. Direct mechanical wiping using a graphite nanoeraser is observed to drastically reduce the amount of contamination. After the mechanical removal of contamination, the graphite surfaces were able to self-retract after shearing, indicating that van der Waals contact bonding is restored. Since contact bonding provides an indication of a level of cleanliness normally only attainable in a high-quality clean-room, we discuss potential applications in preparation of ultraclean surfaces.Comment: 10 pages, two figure

Environmental, Thermal, and Electrical Susceptibility of Black Phosphorus Field Effect Transistors

Atomic layers of black phosphorus (P) isolated from its layered bulk make a new two-dimensional (2D) semiconducting crystal with sizable direct bandgap, high carrier mobility, and promises for 2D electronics and optoelectronics. However, the integrity of black P crystal could be susceptible to a number of environmental variables and processes, resulting in degradation in device performance even before the device optical image suggests so. Here, we perform a systematic study of the environmental effects on black P electronic devices through continued measurements over a month under a number of controlled conditions, including ambient light, air, and humidity, and identify evolution of device performance under each condition. We further examine effects of thermal and electrical treatments on inducing morphology and, performance changes and failure modes in black P devices. The results suggest that procedures well established for nanodevices in other 2D materials may not directly apply to black P devices, and improved procedures need to be devised to attain stable device operation.Comment: in Journal of Vacuum Science & Technology B (2015