When two sheets of graphene are stacked at a small twist angle, the resulting flat superlattice minibands are expected to strongly enhance electron-electron interactions. Here, we present evidence that near three-quarters (34) filling of the conduction miniband, these enhanced interactions drive the twisted bilayer graphene into a ferromagnetic state. In a narrow density range around an apparent insulating state at34, we observe emergent ferromagnetic hysteresis, with a giant anomalous Hall (AH) effect as large as 10.4 kilohms and indications of chiral edge states. Notably, the magnetization of the sample can be reversed by applying a small direct current. Although the AH resistance is not quantized, and dissipation is present, our measurements suggest that the system may be an incipient Chern insulator.

For centuries, practitioners of origami ('ori', fold; 'kami', paper) and kirigami ('kiru', cut) have fashioned sheets of paper into beautiful and complex three-dimensional structures. Both techniques are scalable, and scientists and engineers are adapting them to different two-dimensional starting materials to create structures from the macro- to the microscale. Here we show that graphene is well suited for kirigami, allowing us to build robust microscale structures with tunable mechanical properties. The material parameter crucial for kirigami is the Föppl-von Kármán number γ: an indication of the ratio between in-plane stiffness and out-of-plane bending stiffness, with high numbers corresponding to membranes that more easily bend and crumple than they stretch and shear. To determine γ, we measure the bending stiffness of graphene monolayers that are 10-100 micrometres in size and obtain a value that is thousands of times higher than the predicted atomic-scale bending stiffness. Interferometric imaging attributes this finding to ripples in the membrane that stiffen the graphene sheets considerably, to the extent that γ is comparable to that of a standard piece of paper. We may therefore apply ideas from kirigami to graphene sheets to build mechanical metamaterials such as stretchable electrodes, springs, and hinges. These results establish graphene kirigami as a simple yet powerful and customizable approach for fashioning one-atom-thick graphene sheets into resilient and movable parts with microscale dimensions.

Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators, that are spaced apart by a few hundred nanometers and are coupled through an optical cavity radiation field. The tunability of the optical coupling between the oscillators enables one to externally control the dynamics and switch between coupled and individual oscillation states. These results pave a path toward reconfigurable synchronized oscillator networks.

We simulated the behavior of suspended carbon nanotube resonators over a broad range of temperatures to explore the physics of semiflexible polymers in underdamped environments. We find that thermal fluctuations induce strong coupling between resonance modes. This effect leads to spectral fluctuations that readily account for the experimentally observed quality factors Q ∼ 100 at 300 K. Using a mean-field approach to describe fluctuations, we analytically calculate Q and frequency shifts in tensioned and buckled carbon nanotubes and find excellent agreement with simulations.nanomechanics | stochastic dynamics | nonlinear vibrations | mesoscopic physics T he effects of thermal fluctuations can completely alter the mechanical properties of reduced dimensional systems. For example, the shape and elasticity of a DNA molecule are entirely dominated by thermal fluctuations of transverse degrees of freedom, completely altering both physical behavior and biological function. In overdamped environments such as liquids, these entropic effects have been studied for decades (1), but the behavior of reduced elastic objects in underdamped environments is largely unexplored. For example, consider a resonator made from an atomically thin membrane or polymer. How will thermal fluctuations affect the vibrational spectrum, and how will thermally driven nonlinear effects influence the decay widths of the resonance modes?Carbon nanotube (CNT) resonators, with their nanometerscale cross-section (2) and very small bending rigidity for flexural modes (3) present a unique opportunity to probe these questions. Experimental work has shown CNT resonators to be highly tunable (4) as well as functional as rf transceivers (5) and atomic mass detectors (6, 7), but these resonators have consistently exhibited much broader than expected decay widths (4, 8). Specifically, the quality factor Q, the key parameter measuring the degree to which an oscillating mode is decoupled from its environment, which is inferred from the decay width, is typically less than Q ∼ 100 at room temperature. These low Qs are not consistent with known dissipation mechanisms seen in other nanomechanical resonator systems (9). Analytical phonon-phonon scattering studies establish a theoretical upper bound on Q in CNTs that is well above experimental values, with Q ( 50,000 at 300 K (10, 11). Moleculardynamics simulations of short CNTs (L ∼ 50 nm) show interesting behaviors in cantilevered and free CNT segments (12-15) due to anharmonic atomic potentials, and those that make an explicit determination of quality factor in thermal equilibrium (13,14) give Q ∼ 1,000 at room temperature. Typically, however, experiments are performed on CNTs with L T 1 μm, and the anharmonic elastic effects that dominate in short-length CNTs do not contribute as significantly at this longer length scale.An alternative explanation for these altered properties comes from the field of polymer physics, where the effects of fluctuations on the physics of 1D elastic objects have a long and storied his...

Ballistic electrons in solids can have mean free paths far larger than the smallest features patterned by lithography. This has allowed development and study of solid-state electron-optical devices such as beam splitters and quantum point contacts, which have informed our understanding of electron flow and interactions. Recently, high-mobility graphene has emerged as an ideal two-dimensional semimetal that hosts unique chiral electron-optical effects due to its honeycomb crystalline lattice. However, this chiral transport prevents the simple use of electrostatic gates to define electron-optical devices in graphene. Here we present a method of creating highly collimated electron beams in graphene based on collinear pairs of slits, with absorptive sidewalls between the slits. By this method, we achieve beams with angular width 18° or narrower, and transmission matching classical ballistic predictions.