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In multilayer moir\'e heterostructures, the interference of multiple twist angles ubiquitously leads to tunable ultra-long-wavelength patterns known as supermoir\'e lattices. However, their impact on the system's many-body electronic phase diagram remains largely unexplored. We present local compressibility measurements revealing numerous incompressible states resulting from supermoir\'e-lattice-scale isospin symmetry breaking driven by strong interactions. By using the supermoir\'e lattice occupancy as a probe of isospin symmetry, we observe an unexpected doubling of the miniband filling near $\nu=-2$, possibly indicating a hidden phase transition or normal-state pairing proximal to the superconducting phase. Our work establishes supermoir\'e lattices as a tunable parameter for designing novel quantum phases and an effective tool for unraveling correlated phenomena in moir\'e materials.

In strongly interacting systems with multiple energy bands, the interplay between electrons with different effective masses and the enlarged Hilbert space drives intricate correlated phenomena that do not occur in single-band systems. Recently, magic-angle twisted trilayer graphene (MATTG) has emerged as a promising tunable platform for such investigations: the system hosts both slowly dispersing, "heavy" electrons inhabiting its flat bands as well as delocalized "light" bands that disperse as free Dirac fermions. Most remarkably, superconductivity in twisted trilayer graphene and multilayer analogues with additional dispersive bands exhibits Pauli limit violation and spans a wider range of phase space compared to that in twisted bilayer graphene, where the dispersive bands are absent. This suggests that the interactions between different bands may play a fundamental role in stabilizing correlated phases in twisted graphene multilayers. Here, we elucidate the interplay between the light and heavy electrons in MATTG as a function of doping and magnetic field by performing local compressibility measurements with a scanning single-electron-transistor microscope. We establish that commonly observed resistive features near moir\'e band fillings $\nu$=-2, 1, 2 and 3 host a finite population of light Dirac electrons at the Fermi level despite a gap opening in the flat band sector. At higher magnetic field and near charge neutrality, we discover a new type of phase transition sequence that is robust over nearly 10 micrometers but exhibits complex spatial dependence. Mean-field calculations establish that these transitions arise from the competing population of the two subsystems and that the Dirac sector can be viewed as a new flavor analogous to the spin and valley degrees of freedom.

Since the discovery of high-temperature superconductivity in the copper oxide materials, there have been sustained efforts to both understand the origins of this phase and discover new cuprate-like superconducting materials. One prime materials platform has been the rare-earth nickelates and indeed superconductivity was recently discovered in the doped compound Nd$_{0.8}$Sr$_{0.2}$NiO$_2$. Undoped NdNiO$_2$ belongs to a series of layered square-planar nickelates with chemical formula Nd$_{n+1}$Ni$_n$O$_{2n+2}$ and is known as the 'infinite-layer' ($n = \infty$) nickelate. Here, we report the synthesis of the quintuple-layer ($n = 5$) member of this series, Nd$_6$Ni$_5$O$_{12}$, in which optimal cuprate-like electron filling ($d^{8.8}$) is achieved without chemical doping. We observe a superconducting transition beginning at $\sim$13 K. Electronic structure calculations, in tandem with magnetoresistive and spectroscopic measurements, suggest that Nd$_6$Ni$_5$O$_{12}$ interpolates between cuprate-like and infinite-layer nickelate-like behavior. In engineering a distinct superconducting nickelate, we identify the square-planar nickelates as a new family of superconductors which can be tuned via both doping and dimensionality., Comment: 21 pages, 4 figures

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue toward manipulating non-abelian excitations. Early theoretical studies have predicted their existence in systems with energetically flat Chern bands and highlighted the critical role of a particular quantum band geometry. Thus far, however, FCI states have only been observed in Bernal-stacked bilayer graphene aligned with hexagonal boron nitride (BLG/hBN), in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field and limiting its potential for applications. By contrast, magic angle twisted bilayer graphene (MATBG) supports flat Chern bands at zero magnetic field, and therefore offers a promising route toward stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in MATBG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically-trivial charge density wave states. Unlike the BLG/hBN platform, we demonstrate that the principal role of the weak magnetic field here is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum band geometry favorable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in moir\'e systems with native flat Chern bands.

Symmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at filling factor $\nu=1$ that spontaneously breaks spin rotation symmetry. This ferromagnet has been shown to support spin-wave excitations known as magnons which can be generated and detected electrically. While long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations--including the magnon chemical potential and density--have thus far proven out of reach of experiments. Here, we present local measurements of the electron compressibility under the influence of magnons, which reveal a reduction of the $\nu=1$ gap by up to 20%. Combining these measurements with estimates of the temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables extraction of the free magnon density, magnon chemical potential, and average skyrmion spin. Our methods furnish a novel means of probing the thermodynamic properties of charge-neutral excitations that is applicable to other symmetry-broken electronic phases.

The interplay between strong electron-electron interactions and band topology can lead to novel electronic states that spontaneously break symmetries. The discovery of flat bands in magic-angle twisted bilayer graphene (MATBG) with nontrivial topology has provided a unique platform in which to search for new symmetry-broken phases. Recent scanning tunneling microscopy and transport experiments have revealed a sequence of topological insulating phases in MATBG with Chern numbers $C=\pm 3, \, \pm 2, \, \pm 1$ near moir\'e band filling factors $\nu = \pm 1, \, \pm 2, \, \pm 3$, corresponding to a simple pattern of flavor-symmetry-breaking Chern insulators. Here, we report high-resolution local compressibility measurements of MATBG with a scanning single electron transistor that reveal a new sequence of incompressible states with unexpected Chern numbers observed down to zero magnetic field. We find that the Chern numbers for eight of the observed incompressible states are incompatible with the simple picture in which the $C= \pm 1$ bands are sequentially filled. We show that the emergence of these unusual incompressible phases can be understood as a consequence of broken translation symmetry that doubles the moir\'e unit cell and splits each $C=\pm 1$ band into a $C=\pm 1$ band and a $C=0$ band. Our findings significantly expand the known phase diagram of MATBG, and shed light onto the origin of the close competition between different correlated phases in the system.

In the presence of interactions, electrons in condensed-matter systems can behave hydrodynamically, exhibiting phenomena associated with classical fluids, such as vortices and Poiseuille flow. In most conductors, electron-electron interactions are minimized by screening effects, hindering the search for hydrodynamic materials; however, recently, a class of semimetals has been reported to exhibit prominent interactions. Here we study the current flow in the layered semimetal tungsten ditelluride by imaging the local magnetic field using a nitrogen-vacancy defect in a diamond. We image the spatial current profile within three-dimensional tungsten ditelluride and find that it exhibits non-uniform current density, indicating hydrodynamic flow. Our temperature-resolve current profile measurements reveal a non-monotonic temperature dependence, with the strongest hydrodynamic effects at approximately 20 K. We also report ab initio calculations showing that electron-electron interactions are not explained by the Coulomb interaction alone, but are predominantly mediated by phonons. This provides a promising avenue in the search for hydrodynamic flow and prominent electron interactions in high-carrier-density materials., Comment: 11 pages, 4 figures + supplementary material

Quantum interferometers are powerful tools for probing the wave-nature and exchange statistics of indistinguishable particles. Of particular interest are interferometers formed by the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) that guide electrons without dissipation. Using quantum point contacts (QPCs) as beamsplitters, these 1D channels can be split and recombined, enabling interference of charged particles. Such quantum Hall interferometers (QHIs) can be used for studying exchange statistics of anyonic quasiparticles. In this study we develop a robust QHI fabrication technique in van der Waals (vdW) materials and realize a graphene-based Fabry-P\'erot (FP) QHI. By careful heterostructure design, we are able to measure pure Aharonov-Bohm (AB) interference effect in the integer QHE, a major technical challenge in finite size FP interferometers. We find that integer edge modes exhibit high visibility interference due to relatively large velocities and long phase coherence lengths. Our QHI with tunable QPCs presents a versatile platform for interferometer studies in vdW materials and enables future experiments in the fractional QHE.

At nonzero temperatures, superconductors contain excitations known as Bogoliubov quasiparticles. The mesoscopic dynamics of quasiparticles inform the design of quantum information processors, among other devices. Knowledge of these dynamics stems from experiments in which quasiparticles are injected in a controlled fashion, typically at energies comparable to the pairing energy . Here we perform tunnel spectroscopy of a mesoscopic superconductor under high electric field. We observe quasiparticle injection due to field-emitted electrons with 10^6 times the pairing energy, an unexplored regime of quasiparticle dynamics. Upon application of a gate voltage, the quasiparticle injection decreases the critical current and, at sufficiently high electric field, the field-emission current (< 0.1 nA) switches the mesoscopic superconductor into the normal state, consistent with earlier results. We expect that high-energy injection will be useful for developing quasiparticle-tolerant quantum information processors, will allow rapid control of resonator quality factors, and will enable the design of electric-field-controlled superconducting devices with new functionality., Comment: Nat. Nanotechnol. (2021)

The electron-hole plasma in charge-neutral graphene is predicted to realize a quantum critical system whose transport features a universal hydrodynamic description, even at room temperature. This quantum critical "Dirac fluid" is expected to have a shear viscosity close to a minimum bound, with an inter-particle scattering rate saturating at the Planckian time $\hbar/(k_B T)$. While electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene, a "smoking gun" of viscous behavior remains elusive. In this work, we directly image viscous Dirac fluid flow in graphene at room temperature via measurement of the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy (NV) centers in diamond. Scanning single-spin and wide-field magnetometry reveals a parabolic Poiseuille profile for electron flow in a graphene channel near the charge neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in an Ohmic conductor. Via combined imaging-transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly-ideal electron fluid in neutral graphene at room temperature. Our results pave the way to study hydrodynamic transport in quantum critical fluids relevant to strongly-correlated electrons in high-$T_c$ superconductors. This work also highlights the capability of quantum spin magnetometers to probe correlated-electronic phenomena at the nanoscale., Comment: Author list and title have been updated in published version