2 Control of the interlayer twist angle in two-dimensional (2D) van der Waals (vdW)heterostructures enables one to engineer a quasiperiodic moiré superlattice of tunable length scale 1-7 . In twisted bilayer graphene (TBG), the simple moiré superlattice band description suggests that the electronic band width can be tuned to be comparable to the vdW interlayer interaction at a 'magic angle' 8 , exhibiting strongly correlated behavior. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favoring interlayer commensurability, which competes with the intralayer lattice distortion 9-15 . Here we report the atomic scale reconstruction in TBG and its effect on the electronic structure. We find a gradual transition from incommensurate moiré structure to an array of commensurate domain structures as we decrease the twist angle across the characteristic crossover angle, θc ~1°. In the twist regime smaller than θc where the atomic and electronic reconstruction become significant, a simple moiré band description breaks down. Upon applying a transverse electric field, we observe electronic transport along the network of onedimensional (1D) topological channels that surround the alternating triangular gapped domains, providing a new pathway to engineer the system with continuous tunability.In the absence of atomic scale reconstruction, a small rigid rotation of the vdW layers relative to each other results in a moiré pattern, whose long wavelength periodicity is determined by the twist angle. For unreconstructed TBG, atomic registry varies continuously across the moiré period between three distinct types of symmetric stacking configurations: energetically favorable AB and BA Bernal stacking and unfavorable AA stacking (Fig. 1a). This quasiperiodic moiré superlattice, associated with the incommensurability of the twisted layers, modifies the band structure significantly. In the small twist regime, low-energy flat bands appear at a series of magic angles ( ≤ 1.1°) where the diverging density of states (DOS) and vanishing Fermi velocity, associated with strong electronic correlation, are predicted 8 . The recent experiment demonstrated the presence of the first magic angle near ~1.1° where Mott insulator and unconventional superconductivity were observed 6,7 . The TBG moiré band calculation, however, assumes a rigid rotation of layers ignoring atomic scale reconstruction. Despite the weak nature of vdW interaction and the absence of dangling bonds, recent experimental works on similar material systems suggestthere is substantial lattice reconstruction at vdW interfaces, especially at small twist angle close to global commensuration between two adjacent layers 9,10 . Atomic scale reconstruction at vdW B 92, 155438 (2015).

DNA sequencing using solid-state nanopores is, in part, impeded by the relatively high noise and low bandwidth of the current state-of-the-art translocation measurements. In this Letter, we measure the ion current noise through sub 10 nm thick Si3N4 nanopores at bandwidths up to 1 MHz. At these bandwidths, the input-referred current noise is dominated by the amplifier's voltage noise acting across the total capacitance at the amplifier input. By reducing the nanopore chip capacitance to the 1-5 pF range by adding thick insulating layers to the chip surface, we are able to transition to a regime in which input-referred current noise (∼ 117-150 pArms at 1 MHz in 1 M KCl solution) is dominated by the effects of the input capacitance of the amplifier itself. The signal-to-noise ratios (SNRs) reported here range from 15 to 20 at 1 MHz for dsDNA translocations through nanopores with diameters from 4 to 8 nm with applied voltages from 200 to 800 mV. Further advances in bandwidth and SNR will require new amplifier designs that reduce both input capacitance and input-referred amplifier noise.

The artificial stacking of atomically thin crystals suffers from intrinsic limitations in terms of control and reproducibility of the relative orientation of exfoliated flakes. This drawback is particularly severe when the properties of the system critically depends on the twist angle, as in the case of the dodecagonal quasicrystal formed by two graphene layers rotated by 30°. Here we show that large-area 30°-rotated bilayer graphene can be grown deterministically by chemical vapor deposition on Cu, eliminating the need of artificial assembly. The quasicrystals are easily transferred to arbitrary substrates and integrated in high-quality hBN-encapsulated heterostructures, which we process into dual-gated devices exhibiting carrier mobility up to 10 5 2 cm 2 /Vs. From low-temperature magnetotransport, we find that the graphene quasicrystals effectively behave as uncoupled graphene layers, showing 8-fold degenerate quantum Hall states: this result indicates that the Dirac cones replica detected by previous photo-emission experiments do not contribute to the electrical transport. KEYWORDS. twisted bilayer graphene, CVD, dodecagonal quasicrystals, quantum Hall effectTwisted bilayer graphene (TBG), a system made of two stacked single-layer graphene (SLG) with misaligned crystallographic orientation, is providing an incredibly rich platform for novel physical phenomena [1,2]. In the limit of small twist angle (<10°), the long-range moiré superpotential determines important modifications to the structural and electronic properties [3][4][5]. On the other hand, TBG falls in a weak coupling regime for large twisting, with the electronic properties resembling those of two SLG conducting in parallel [6,7]. However, relevant interlayer coupling seems to re-emerge in TBG with a twist angle of precisely 30 degrees, giving rise to multiple Dirac cones replica, as detected by angle-resolved photoemission spectroscopy (ARPES) in two recent experiments [8,9]. In this configuration, TBG forms an incommensurate structure with 12-fold rotational symmetry -although lacking of translational symmetry -known as dodecagonal quasicrystal (QC). In addition to the cones' multiplication, QC-TBG is predicted to host spiral Fermi surfaces resulting in novel quantum oscillations [10], van Hove singularities [11,12] and semi-localized electronic states following the dodecagonal tiling [11], which strongly motivates further experimental investigation, in particular low-temperature electrical transport in highmobility devices. However, the QC-TBG is extremely sensitive to small variation in the twist angle, which makes it highly challenging to realize with the common hBN-mediated "tear-and-13

Solid-state membranes are finding use in many applications in nanoelectronics and nanomedicine, from single molecule sensors to water filtration, and yet many of their electronics applications are limited by the relatively high current noise and low bandwidth stemming from the relatively high capacitance (>10 pF) of the membrane chips. To address this problem, we devised an integrated fabrication process to grow and define circular silicon nitride membranes on glass chips that successfully lower the chip capacitance to below 1 pF. We use these devices to demonstrate low-noise, high-bandwidth DNA translocation measurements. We also make use of this versatile, low-capacitance platform to suspend other thin, two-dimensional membrane such as graphene.

Direct visualization of nanometer-scale properties of moiré superlattices in van der Waals heterostructure devices is a critically needed diagnostic tool for study of the electronic and optical phenomena induced by the periodic variation of atomic structure in these complex systems. Conventional imaging methods are destructive and insensitive to the buried device geometries, preventing practical inspection. Here we report a versatile scanning probe microscopy employing infrared light for imaging moiré superlattices of twisted bilayers graphene encapsulated by hexagonal boron nitride. We map the pattern using the scattering dynamics of phonon polaritons launched in hexagonal boron nitride capping layers via its interaction with the buried moiré superlattices. We explore the origin of the double-line features imaged and show the mechanism of the underlying effective phase change of the phonon polariton reflectance at domain walls. The nano-imaging tool developed provides a non-destructive analytical approach to elucidate the complex physics of moiré engineered heterostructures.