Marc A. Kastner

When a Chern band is partially filled, a fractional Chern insulator (FCI)—the lattice analog of a fractional quantum Hall state—can arise. Though the full range of possible scenarios for producing such a state is not established, the most tractable models combine strong electronic interactions with the quantum geometry of the parent Chern band meeting specific criteria. In twisted bilayer graphene, the importance of interactions can be tuned by varying the interlayer twist. Here, we study a sample with twist near 1.4 ^° , large enough to suppress the zero-field correlated states. We find that applying a strong magnetic field restores the importance of electron–electron interactions: at nearly half a magnetic flux quantum per moiré unit cell, deep in the Hofstadter regime, odd-denominator fractional states appear in multiple Hofstadter subbands. These fractional states persist over larger ranges of density, and are more robustly quantized, than nearby integer states, opposite to what is seen in other fractional quantum Hall and FCI systems.

The electronic properties of moiré heterostructures depend sensitively on the relative orientation between layers of the stack. For example, near-magic-angle twisted bilayer graphene (TBG) commonly shows superconductivity, yet a TBG sample with one of the graphene layers rotationally aligned to a hexagonal Boron Nitride (hBN) cladding layer provided experimental observation of orbital ferromagnetism. To create samples with aligned graphene/hBN, researchers often align edges of exfoliated flakes that appear straight in optical micrographs. However, graphene or hBN can cleave along either zig-zag or armchair lattice directions, introducing a 30 ° ambiguity in the relative orientation of two flakes. By characterizing the crystal lattice orientation of exfoliated flakes prior to stacking using Raman and second-harmonic generation for graphene and hBN, respectively, we unambiguously align monolayer graphene to hBN at a near- 0 ° , not 30 ° , relative twist angle. We confirm this alignment by torsional force microscopy of the graphene/hBN moiré on an open-face stack, and then by cryogenic transport measurements, after full encapsulation with a second, nonaligned hBN layer. This work demonstrates a key step toward systematically exploring the effects of the relative twist angle between dissimilar materials within moiré heterostructures.

Scanning probe techniques are popular, nondestructive ways to visualize the real space structure of Van der Waals moirés. The high lateral spatial resolution provided by these techniques enables extracting the moiré lattice vectors from a scanning probe image. We have found that the extracted values, while precise, are not necessarily accurate. Scan-to-scan variations in the behavior of the piezos that drive the scanning probe and thermally driven slow relative drift between probe and sample produce systematic errors in the extraction of lattice vectors. In this Letter, we identify the errors and provide a protocol to correct for them. Applying this protocol to an ensemble of ten successive scans of near-magic-angle twisted bilayer graphene, we are able to reduce our errors in extracting lattice vectors to less than 1%. This translates to extracting twist angles with a statistical uncertainty less than 0.001° and uniaxial heterostrain with uncertainty on the order of 0.002%.

In a stack of atomically thin van der Waals layers, introducing interlayer twist creates a moiré superlattice whose period is a function of twist angle. Changes in that twist angle of even hundredths of a degree can dramatically transform the system’s electronic properties. Setting a precise and uniform twist angle for a stack remains difficult; hence, determining that twist angle and mapping its spatial variation is very important. Techniques have emerged to do this by imaging the moiré, but most of these require sophisticated infrastructure, time-consuming sample preparation beyond stack synthesis, or both. In this work, we show that torsional force microscopy (TFM), a scanning probe technique sensitive to dynamic friction, can reveal surface and shallow subsurface structure of van der Waals stacks on multiple length scales: the moirés formed between bi-layers of graphene and between graphene and hexagonal boron nitride (hBN) and also the atomic crystal lattices of graphene and hBN. In TFM, torsional motion of an Atomic Force Microscope (AFM) cantilever is monitored as it is actively driven at a torsional resonance while a feedback loop maintains contact at a set force with the sample surface. TFM works at room temperature in air, with no need for an electrical bias between the tip and the sample, making it applicable to a wide array of samples. It should enable determination of precise structural information including twist angles and strain in moiré superlattices and crystallographic orientation of van der Waals flakes to support predictable moiré heterostructure fabrication.

Anisotropic hopping in a toy Hofstadter model was recently invoked to explain a rich and surprising Landau spectrum measured in twisted bilayer graphene away from the magic angle. Suspecting that such anisotropy could arise from unintended uniaxial strain, we extend the Bistritzer–MacDonald model to include uniaxial heterostrain and present a detailed analysis of its impact on band structure and magnetotransport. We find that such strain strongly influences band structure, shifting the three otherwise-degenerate van Hove points to different energies. Coupled to a Boltzmann magnetotransport calculation, this reproduces previously unexplained nonsaturating B 2 magnetoresistance over broad ranges of density near filling ν = ± 2 and predicts subtler features that had not been noticed in the experimental data. In contrast to these distinctive signatures in longitudinal resistivity, the Hall coefficient is barely influenced by strain, to the extent that it still shows a single sign change on each side of the charge neutrality point—surprisingly, this sign change no longer occurs at a van Hove point. The theory also predicts a marked rotation of the electrical transport principal axes as a function of filling even for fixed strain and for rigid bands. More careful examination of interaction-induced nematic order versus strain effects in twisted bilayer graphene could thus be in order.

Nanostructured topological insulators (TIs) have the potential to impact a wide array of condensed matter physics topics, ranging from Majorana physics to spintronics. However, the most common TI materials, the Bi2Se3 family, are easily damaged during nanofabrication of devices. In this paper, we show that electron beam lithography performed with a 30 or 50 kV accelerating voltage—common for nanopatterning in academic facilities—damages both nonmagnetic TIs and their magnetically doped counterparts at unacceptable levels. We additionally demonstrate that electron beam lithography with a 10 kV accelerating voltage produces minimal damage detectable through low-temperature electronic transport. Although reduced accelerating voltages present challenges in creating fine features, we show that with careful choice of processing parameters, particularly the resist, 100 nm features are reliably achievable.

Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental quantum anomalous Hall systems elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that the measured potentials at multiple locations within a device at elevated temperature are well described by solution of Laplace’s equation, assuming spatially uniform conductivity, suggesting nonequilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the bulk rather than, as had been assumed, through edge modes. An argument for bulk current flow previously applied to quantum Hall systems supports this picture.