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Charge distribution offers a unique fingerprint of important properties of electronic systems, including dielectric response, charge ordering and charge fractionalization. We develop a new architecture for charge sensing in two-dimensional electronic systems in a strong magnetic field. We probe local change of the chemical potential in a proximitized detector layer using scanning tunneling microscopy (STS), allowing us to infer the chemical potential and the charge profile in the sample. Our technique has both high energy (<0.3 meV) and spatial (<10 nm) resolution exceeding that of previous studies by an order of magnitude. We apply our technique to study the chemical potential of quantum Hall liquids in monolayer graphene under high magnetic fields and their responses to charge impurities. The chemical potential measurement provides a local probe of the thermodynamic gap of quantum Hall ferromagnets and fractional quantum Hall states. The screening charge profile reveals spatially oscillatory response of the quantum Hall liquids to charge impurities, and is consistent with the composite Fermi liquid picture close to the half-filling. Our technique also paves the way to map moir\'e potentials, probe Wigner crystals, and investigate fractional charges in quantum Hall and Chern insulators.

Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours - such as spin or valley - that the electrons can undergo and the excitation spectrum of the broken symmetry states that they form. These properties cannot be probed directly with electrical transport measurements. The zeroth Landau level of monolayer graphene with four-fold spin-valley degeneracy is a model system for such investigations, but the nature of its broken symmetry states - particularly at partial fillings - is still not understood. Here we demonstrate a non-invasive spectroscopic technique with a scanning tunneling microscope and use it to perform measurements of the valley polarization of the electronic wavefunctions and their excitation spectrum in the partially filled zeroth Landau level of graphene. We can extract information such as the strength of Haldane pseudopotentials that characterize the repulsive interactions underlying the fractional quantum states. Our experiments also demonstrate that fractional quantum Hall phases are built upon broken symmetry states that persist at partial filling. Our experimental approach quantifies the valley phase diagram of the partially filled Landau level as a model flat band platform which is applicable to other graphene-based electronic systems.

The emergence of superconductivity with doping from correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors, as described by the Bardeen-Cooper-Schrieffer (BCS) theory. While there is now ample evidence for strong electronic correlations in MATBG, recent studies have claimed that unlike correlated insulators, superconductivity persists even when these interactions are partially screened. This suggests that the pairing in MATBG might be conventional in nature, a consequence of the large density of states of its nearly flat bands, perhaps phonon-mediated as in BCS superconductors. Here we combine tunneling and Andreev reflection spectroscopy with the scanning tunneling microscope (STM) to observe several key experimental signatures for unconventional superconductivity in MATBG. We show that the tunneling spectra below the transition temperature $T_c$ are inconsistent with that of a conventional s-wave superconductor, but rather resemble that of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunneling energy gap $\Delta_T$, which far exceeds the mean-field BCS ratio (with $2\Delta_T/k_BT_c \sim 25$) and the energy gap $\Delta_{AR}$ extracted from Andreev reflection spectroscopy ($2\Delta_{AR}/k_BT_c \sim 6$). The tunneling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase, with a suppressed density of states at the Fermi level. Moreover, the pseudogap state and superconductivity are both absent when MATBG is aligned with the hexagonal boron nitride (hBN) underneath. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic phases (QHFM), with broken spin or valley symmetry. Visualizing atomic scale electronic wavefunctions with scanning tunneling spectroscopy (STS), we resolve microscopic signatures of valley ordering in QHFM and fractional quantum Hall phases of graphene. At charge neutrality, we observe a field-tuned continuous quantum phase transition from a valley polarized state to an intervalley coherent state, with a Kekule distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekule phase, we visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley ordered phases and their topological excitations in a wide range of materials., Comment: 19 pages, 4 figures and supplementary materials

In fermionic systems, superconductivity and superfluidity are enabled through the condensation of fermion pairs. The nature of this condensate can be tuned by varying the pairing strength, with weak coupling yielding a BCS-like condensate and strong coupling resulting in a BEC-like process. However, demonstration of this cross-over has remained elusive in electronic systems. Here we study graphene double-layers separated by an atomically thin insulator. Under applied magnetic field, electrons and holes couple across the barrier to form bound magneto-excitons whose pairing strength can be continuously tuned by varying the effective layer separation. Using temperature-dependent Coulomb drag and counter-flow current measurements, we demonstrate the capability to tune the magneto-exciton condensate through the entire weak-coupling to strong-coupling phase diagram. Our results establish magneto-exciton condensates in graphene as a model platform to study the crossover between two Bosonic quantum condensate phases in a solid state system., Comment: 7 pages, 3 figures and supplementary materials

The interplay between topology and correlations can generate a variety of quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe2 as a promising material for doing so in a highly tunable fashion. The ground state of this two-dimensional (2D) crystal can be electrostatically tuned from a quantum spin Hall insulator (QSHI) to a superconductor. However, much remains unknown about the gap-opening mechanism of the insulating state. Here we report evidence that the QSHI is also an excitonic insulator (EI), arising from the spontaneous formation of electron-hole bound states (excitons). We reveal the presence of an intrinsic insulating state at the charge neutrality point (CNP) in clean samples and confirm the correlated nature of this charge-neutral insulator by tunneling spectroscopy. We provide evidence against alternative scenarios of a band insulator or a localized insulator and support the existence of an EI phase in the clean limit. These observations lay the foundation for understanding a new class of correlated insulators with nontrivial topology and identify monolayer WTe2 as a promising candidate for exploring quantum phases of ground-state excitons., Comment: 39 pages; Nat. Phys. (2021)

Two-dimensional (2D) layered semiconductors with both ultrawide bandgap and strong second harmonic generation (SHG) are essential for expanding the nonlinear optical (NLO) applications to deep-ultraviolet (DUV) region in nanoscale. Unfortunately, these materials are rare in nature and have not been discovered until now. In this Letter, we predict the B2S2O9 (BSO), an existing layered oxide, can exhibit both DUV bandgap and strong SHG effects, comparable to the best known DUV NLO bulks. The strong SHG intensities in BSO, originated from the ordered arrangement of polar SO4 and BO4 tetrahedra forming planar structure, are linearly tunable by the layer thickness. Surprisingly, the spontaneous rotations of rigid tetrahedra under strains can induce the (nearly) zero Poisson's ratios in BSO, which simultaneously result in the robust SHG effects against large strains, fundamentally differing from other known 2D NLO semiconductors. The discovery of BSO may provide an unprecedented opportunity to explore DUV NLO physics and applications in 2D limit.

Moir\'e superlattices created by the twisted stacking of two-dimensional crystalline monolayers can host electronic bands with flat energy dispersion in which interaction among electrons is strongly enhanced. These superlattices can also create non-trivial electronic band topologies making them a platform for study of many-body topological quantum states. Among the moir\'e systems realized to date, there are those predicted to have band structures and properties which can be controlled with a perpendicular electric field. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a tunable moir\'e system, for which partial filling of its flat band, transport studies have found correlated insulating states. Here we use gate-tuned scanning tunneling spectroscopy (GT-STS) to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of both electronic correlations and topology for its flat band. Our spectroscopic experiments show excellent agreement with a continuum model of TDBG band structure and reveal signatures of a correlated insulator gap at partial filling of its isolated flat band. The topological properties of this flat band are probed with the application of a magnetic field, which leads to valley polarization and the splitting of Chern bands that respond strongly to the field with a large effective g-factor. Our experiments advance our understanding of the properties of TDBG and set the stage for further investigations of correlation and topology in such tunable moir\'e systems., Comment: 13 pages, 5 figures and supplementary information