A Spectroscopic Study of Electronic Correlations in Twisted Bilayer Graphene by Scanning Tunneling Microscopy

Twisted bilayer graphene around the magic angle has shown variety of correlated phases such as superconductivity, correlated insulators, and magnetism due to its flat band structure. The unconventional nature of the superconductivity and its pos- sible relation to high temperature superconductors have sparked a lot of theoretical and experimental efforts to understand the properties of the magic angle twisted bilayer graphene. While electrical transport measurements revealed the interesting phases, spectroscopic understanding is strongly needed to connect the phases with theoretical calculations. We present the spectroscopic studies of gate-tunable magic angle twisted bilayer graphene using scanning tunneling microscopy. We report that the band structure is significantly modified even at charge neutrality due to exchange interaction. We apply a perpendicular magnetic field and develop a novel method that enables scanning tunneling microscopy to reveal Landau fan diagrams. We discover topologically non-trivial states appearing at finite magnetic field, and from spectroscopy we are able to identify the mechanism. Finally, we verify inter- action driven band flattening experimentally in twisted bilayer graphene, which is responsible for creating strong correlations.</p

Unsupervised Legendre-Galerkin Neural Network for Stiff Partial Differential Equations

Machine learning methods have been lately used to solve differential equations and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques such as deep neural networks and statistical learning are applied to classical problems of applied mathematics. Because neural networks provide an approximation capability, computational parameterization through machine learning and optimization methods achieve noticeable performance when solving various partial differential equations (PDEs). In this paper, we develop a novel numerical algorithm that incorporates machine learning and artificial intelligence to solve PDEs. In particular, we propose an unsupervised machine learning algorithm based on the Legendre-Galerkin neural network to find an accurate approximation to the solution of different types of PDEs. The proposed neural network is applied to the general 1D and 2D PDEs as well as singularly perturbed PDEs that possess boundary layer behavior.Comment: 29 pages, 8 figure

Examination of benefits sought by hiking tourists: a comparison of impact - range performance analysis and impact asymmetry analysis

This study assesses the benefits of hiking for visitors to the Jeju Olle Trail on Jeju Island in Korea, which has been designated as a World Heritage Site. Data were collected from a total of 318 tourists visiting the Jeju Olle Trail. The study focused on comparing the benefits sought by first-time visitors and those of repeat visitors. Analytical results found that first-time visitors and repeat visitors sought different benefits from their hiking experiences. First-time visitors sought to observe nature and interact with people. For first-time visitors, benefits that delighted them were buying unique souvenirs and enjoying educational experiences, whereas repeat visitors demonstrated a good assessment on interactions with new people and buying unique souvenirs

Superconductivity in metallic twisted bilayer graphene stabilized by WSe₂

Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1 degrees, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic and topological phases. Correlated insulators and superconductivity have been previously observed only for angles within 0.1 degree of the magic angle and occur in adjacent or overlapping electron-density ranges; nevertheless, the origins of these states and the relation between them remain unclear, owing to their sensitivity to microscopic details. Beyond twist angle and strain, the dependence of the TBG phase diagram on the alignment and thickness of the insulating hexagonal boron nitride (hBN) used to encapsulate the graphene sheets indicates the importance of the microscopic dielectric environment. Here we show that adding an insulating tungsten diselenide (WSe₂) monolayer between the hBN and the TBG stabilizes superconductivity at twist angles much smaller than the magic angle. For the smallest twist angle of 0.79 degrees, superconductivity is still observed despite the TBG exhibiting metallic behaviour across the whole range of electron densities. Finite-magnetic-field measurements further reveal weak antilocalization signatures as well as breaking of fourfold spin–valley symmetry, consistent with spin–orbit coupling induced in the TBG via its proximity to WSe₂. Our results constrain theoretical explanations for the emergence of superconductivity in TBG and open up avenues towards engineering quantum phases in moiré systems

Correlation-driven topological phases in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron–electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when ±1, ±2 and ±3 electrons occupy each moiré unit cell, and lead to the formation of various correlated phases. Although some phases have been shown to have a non-zero Chern number, the local microscopic properties and topological character of many other phases have not yet been determined. Here we introduce a set of techniques that use scanning tunnelling microscopy to map the topological phases that emerge in MATBG in a finite magnetic field. By following the evolution of the local density of states at the Fermi level with electrostatic doping and magnetic field, we create a local Landau fan diagram that enables us to assign Chern numbers directly to all observed phases. We uncover the existence of six topological phases that arise from integer fillings in finite fields and that originate from a cascade of symmetry-breaking transitions driven by correlations. These topological phases can form only for a small range of twist angles around the magic angle, which further differentiates them from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions, exhibits prominent electron–hole asymmetry, and features an unexpectedly large splitting between zero Landau levels (about 3 to 5 millielectronvolts). Our results show how strong electronic interactions affect the MATBG band structure and lead to correlation-enabled topological phases