Direct observation of a magnetic-field-induced Wigner crystal.

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2-11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

Electrical Control of Spin and Valley in Spin-Orbit Coupled Graphene Multilayers.

Electrical control of magnetism has been a major technological pursuit of the spintronics community, owing to its far-reaching implications for data storage and transmission. Here, we propose and analyze a new mechanism for electrical switching of isospin, using chiral-stacked graphene multilayers, such as Bernal bilayer graphene or rhombohedral trilayer graphene, encapsulated by transition metal dichalcogenide (TMD) substrates. Leveraging the proximity-induced spin-orbit coupling from the TMD, we demonstrate electrical switching of correlation-induced spin and/or valley polarization, by reversing a perpendicular displacement field or the chemical potential. We substantiate our proposal with both analytical arguments and self-consistent Hartree-Fock numerics. Finally, we illustrate how the relative alignment of the TMDs, together with the top and bottom gate voltages, can be used to selectively switch distinct isospin flavors, putting forward correlated Van der Waals heterostructures as a promising platform for spintronics and valleytronics.

Extracting Higher Central Charge from a Single Wave Function.

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_{-} is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_{-} to gapping out the edge. In this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν=1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)_{2} and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_{-}, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.

Energy Gap of the Even-Denominator Fractional Quantum Hall State in Bilayer Graphene.

Bernal bilayer graphene hosts even-denominator fractional quantum Hall states thought to be described by a Pfaffian wave function with non-Abelian quasiparticle excitations. Here, we report the quantitative determination of fractional quantum Hall energy gaps in bilayer graphene using both thermally activated transport and by direct measurement of the chemical potential. We find a transport activation gap of 5.1 K at B=12 T for a half filled N=1 Landau level, consistent with density matrix renormalization group calculations for the Pfaffian state. However, the measured thermodynamic gap of 11.6 K is smaller than theoretical expectations for the clean limit by approximately a factor of 2. We analyze the chemical potential data near fractional filling within a simplified model of a Wigner crystal of fractional quasiparticles with long-wavelength disorder, explaining this discrepancy. Our results quantitatively establish bilayer graphene as a robust platform for probing the non-Abelian anyons expected to arise as the elementary excitations of the even-denominator state.

Joint L2,p-norm and random walk graph constrained PCA for single-cell RNA-seq data.

The development and widespread utilization of high-throughput sequencing technologies in biology has fueled the rapid growth of single-cell RNA sequencing (scRNA-seq) data over the past decade. The development of scRNA-seq technology has significantly expanded researchers' understanding of cellular heterogeneity. Accurate cell type identification is the prerequisite for any research on heterogeneous cell populations. However, due to the high noise and high dimensionality of scRNA-seq data, improving the effectiveness of cell type identification remains a challenge. As an effective dimensionality reduction method, Principal Component Analysis (PCA) is an essential tool for visualizing high-dimensional scRNA-seq data and identifying cell subpopulations. However, traditional PCA has some defects when used in mining the nonlinear manifold structure of the data and usually suffers from over-density of principal components (PCs). Therefore, we present a novel method in this paper called joint L2,p-norm and random walk graph constrained PCA (RWPPCA). RWPPCA aims to retain the data's local information in the process of mapping high-dimensional data to low-dimensional space, to more accurately obtain sparse principal components and to then identify cell types more precisely. Specifically, RWPPCA combines the random walk (RW) algorithm with graph regularization to more accurately determine the local geometric relationships between data points. Moreover, to mitigate the adverse effects of dense PCs, the L2,p-norm is introduced to make the PCs sparser, thus increasing their interpretability. Then, we evaluate the effectiveness of RWPPCA on simulated data and scRNA-seq data. The results show that RWPPCA performs well in cell type identification and outperforms other comparison methods.

Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact.

One-dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the single-electron tunneling density of states at low voltages. The scaling exponent is predicted to be quantized when tunneling into a single isolated chiral edge state of the fractional quantum Hall effect. We report conductance measurements across a point contact linking integer and fractional quantum Hall edge states (at fillings 1 and [Formula: see text], respectively). At weak coupling, we observe the predicted universal quadratic scaling with temperature and voltage. At strong coupling, we demonstrate perfect Andreev reflection of fractionalized quasiparticles at the point contact. We use the strong coupling physics to realize a nearly dissipationless direct current voltage step-up transformer, whose gain arises directly from topological fractionalization of electrical charge.

Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene.

Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are strong. We further elucidate how the inter-valley Hund's coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Remarkably, if the normal state is spin-unpolarized, we find that a ferromagnetic Hund's coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing.

Hypoglossal acupuncture for acute chemotherapy-induced dysgeusia in patients with breast cancer: study protocol of a randomized, sham-controlled trial.

BACKGROUND: Distortion of taste sensations is a common chemotherapy-induced side effect; however, treatment evidence is limited. Pilot data indicated that acupuncture might be able to improve symptoms of dysgeusia. Thus, the aim of this study is to investigate the effects and side effects of hypoglossal acupuncture in the treatment of dysgeusia in patients with breast cancer undergoing chemotherapy. METHODS/DESIGN: The study is a randomized controlled trial comparing a single verum acupuncture treatment with two active comparators: sham acupuncture and dietary recommendations. Sample size calculation revealed a total of 75 patients pending an alpha of 0.05, a power of 0.8, and an estimated effect size of 0.80. Patients with breast cancer undergoing platinum- or taxane-based chemotherapy will be included if they present with phantogeusia (abnormal taste sensations without an external oral stimulus) with an intensity of 4 points or above on an 11-point numeric rating scale (NRS). The primary outcome is phantogeusia; secondary outcomes include parageusia (abnormal taste of food), hypogeusia (reduced taste sensations), hypergeusia (increased taste sensations), xerostomia (dry mouth), stomatitis, appetite, and functional impairment. All outcomes will be assessed at baseline and prior to the next chemotherapy administration using an 11-point NRS for each. All adverse events will be recorded. DISCUSSION: The results of this study will demonstrate the extent to which hypoglossal acupuncture may influence the intensity of and functional impairment due to chemotherapy-induced dysgeusia. TRIAL REGISTRATION: Clinical Trials.gov, NCT02304913 . Registered on 19 November 2014.