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The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate pattern formation on the observable surface. This rich spatial structure contains information about interactions, dimensionality, and disorder -- a spatial encoding of the Hamiltonian driving the pattern formation. Image recognition techniques from machine learning are an excellent tool for interpreting information encoded in the spatial relationships in such images. Here, we develop a deep learning framework for using the rich information available in these spatial correlations in order to discover the underlying Hamiltonian driving the patterns. We first vet the method on a known case, scanning near-field optical microscopy on a thin film of VO2. We then apply our trained convolutional neural network architecture to new optical microscope images of a different VO2 film as it goes through the metal-insulator transition. We find that a two-dimensional Hamiltonian with both interactions and random field disorder is required to explain the intricate, fractal intertwining of metal and insulator domains during the transition. This detailed knowledge about the underlying Hamiltonian paves the way to using the model to control the pattern formation via, e.g., tailored hysteresis protocols. We also introduce a distribution-based confidence measure on the results of a multi-label classifier, which does not rely on adversarial training. In addition, we propose a new machine learning based criterion for diagnosing a physical system's proximity to criticality.

The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other.

Twisted van der Waals multilayers are widely regarded as a rich platform to access novel electronic phases, thanks to the multiple degrees of freedom such as layer thickness and twist angle that allow control of their electronic and chemical properties. Here, we propose that the stacking domains that form naturally due to the relative twist between successive layers act as an additional "knob" for controlling the behavior of these systems, and report the emergence and engineering of stacking domain-dependent surface chemistry in twisted few-layer graphene. Using mid-infrared near-field optical microscopy and atomic force microscopy, we observe a selective adhesion of metallic nanoparticles and liquid water at the domains with rhombohedral stacking configurations of minimally twisted double bi- and tri-layer graphene. Furthermore, we demonstrate that the manipulation of nanoparticles located at certain stacking domains can locally reconfigure the moir\'e superlattice in their vicinity at the {\mu}m-scale. In addition, we report first-principles simulations of the energetics of adhesion of metal atoms and water molecules on the stacking domains in an attempt to elucidate the origin of the observed selective adhesion. Our findings establish a new approach to controlling moir\'e-assisted chemistry and nanoengineering., Comment: 11 pages, 3 figures

We visualized negative refraction of phonon polaritons, which occurs at the interface between two natural crystals. The polaritons—hybrids of infrared photons and lattice vibrations—form collimated rays that display negative refraction when passing through a planar interface between the two hyperbolic van der Waals materials: molybdenum oxide (MoO 3 ) and isotopically pure hexagonal boron nitride (h 11 BN). At a special frequency ω 0 , these rays can circulate along closed diamond-shaped trajectories. We have shown that polariton eigenmodes display regions of both positive and negative dispersion interrupted by multiple gaps that result from polaritonic-level repulsion and strong coupling.

We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The conversion is activated by applying a dc electric field that induces a density gradient or a current across the ribbon. Another scheme is degenerate four-wave mixing where the counter-propagating plasmons are emitted at the pump frequency. This third-order nonlinear process does not require a symmetry-breaking dc field. We suggest nano-optical experiments for measuring position-momentum entanglement of the emitted plasmon pairs. We estimate the critical pump fields at which the plasmon generation rates exceed their dissipation, leading to parametric instabilities., Comment: 11 pages, 8 figures