In magic angle twisted bilayer graphene (TBG), electron-electron interactions play a central role, resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question, and it is potentially linked to the relatively high-temperature superconductivity observed in the same devices. Here, we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation, which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state, which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC order exhibits a pattern of alternating circulating currents that triples the graphene unit cell, leading to an "orbital magnetization density wave." Although translation and time-reversal symmetry are broken, a combined "Kramers" timereversal symmetry is preserved. Our analytic arguments are built on first identifying an approximate Uð4Þ × Uð4Þ symmetry, resulting from the remarkable properties of the TBG band structure, which helps select a low-energy manifold of states that are further split to favor the K-IVC state. This low-energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry-lowering perturbations can stabilize other insulators and the semimetallic state, and we discuss the ground state at half-filling and give a comparison with experiments.

We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an inter-valley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.Moiré graphene systems are a class of simple van der Waals heterostructures [1] hosting interaction driven lowenergy physics, making them an exciting platform to advance our understanding of strongly correlated quantum matter. In twisted bilayer graphene (TBG) with a small twist angle between adjacent layers, interaction effects are enhanced by van Hove singularities coming from 8 bands around charge neutrality in the Moiré-or mini-Brillouin zone (mBZ) with a very small bandwidth [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. A confirmation of the important role played by interactions in these mBZ flat bands was provided in Ref. [22] and Refs. [23][24][25][26][27], where interaction-dominated gaps were observed when 2 or 6 (filling ν = −2, 2) of the 8 flat bands in TBG are filled. Also in ABC stacked trilayer graphene Moiré systems Mott insulating behavior has been reported [28]. Interestingly, at densities near some of these Mott insulators the system becomes superconducting [25,29].Recent experiments indicate that certain magic angle graphene devices have large resistance peaks at ν = 0, 3, with the latter featuring an anomalous Hall (AH) effect detected via hysteresis in the Hall conductance as a function of the out-of-plane magnetic field [30]. The Hall conductance is of order e 2 /h but not yet quantized. Some have detected an meV-scale gap at charge neutrality, and a hysteretic behaviour of the Hall conductance with applied field at ν = −1 [31]. In this work we discuss how the breaking of the 180-degree rotational symmetry (C 2z ) by a partially aligned hexagonal boron-nitride (h-BN) substrate could explain these observations. A variety of works [32][33][34][35][36][37][38] have found that h-BN opens up a band gap at the Dirac points of monolayer graphene whose magnitude depends on the graphene / h-BN alignment angle, reaching ∆ AB ∼ 17meV [38] to ∼ 30meV [36, 37] at perfect alignment. Notably, even in seemingly unaligned devices with little or no observable h-BN induced Moiré potential, band gaps of several meV are still observed [37,38]. In TBG, the substrate can likewise gap-out the flat band Dirac points at the K ± points of the mBZ, splitting the bands as 8 = 4 + 4 to create a gap at charge * N.B. and S.C. contributed equally to this w...

One of the distinctive features of hole-doped cuprate superconductors is the onset of a "pseudogap" below a temperature T Ã . Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the twodimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is holelike and that, for a broad range of parameters, its opening is concomitant with a Fermi-surface topology change from electronlike to holelike. We identify a common link between these observations: The polelike feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi-surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this polelike feature and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

Pressure alters the physical, chemical, and electronic properties of matter. The diamond anvil cell enables tabletop experiments to investigate a diverse landscape of high-pressure phenomena. Here, we introduce and use a nanoscale sensing platform that integrates nitrogen-vacancy (NV) color centers directly into the culet of diamond anvils. We demonstrate the versatility of this platform by performing diffraction-limited imaging of both stress fields and magnetism as a function of pressure and temperature. We quantify all normal and shear stress components and demonstrate vector magnetic field imaging, enabling measurement of the pressure-driven a ↔ D phase transition in iron and the complex pressure-temperature phase diagram of gadolinium. A complementary NV-sensing modality using noise spectroscopy enables the characterization of phase transitions even in the absence of static magnetic signatures.3 of 6 Fig. 2. Full tensorial reconstruction of the stresses in a (111)-cut diamond anvil. (A) Spatially resolved maps of the loading stress (left) and mean lateral stress (right), s ⊥ ¼ 1 2 ðs XX þ s YY Þ, across the culet surface.In the inner region, where the culet surface contacts the pressure-transmitting medium (16:3:1 methanol/ ethanol/water), the loading stress is spatially uniform, whereas the lateral stress is concentrated toward the center; this qualitative difference is highlighted by a linecut (taken along the white-dashed line) of the two stresses (below), and reconstructed by finite-element analysis (orange and purple dashed lines). The black pixels indicate where the NV spectrum was obfuscated by the ruby microsphere. (B) Comparison of all stress tensor components in the fluid-contact region at P ¼ 4:9 GPa and P ¼ 13:6 GPa. At P ¼ 13:6 GPa, the pressure-transmitting medium has entered its glassy phase, and we observe a spatial gradient in the loading stress s ZZ (inset).

We present the electronic band structures of states with the same symmetry as the threesublattice planar antiferromagnetic order of the triangular lattice. Such states can also be defined on the honeycomb lattice provided the spin density waves lie on the bonds. We identify cases which are consistent with observations on twisted bilayer graphene: a correlated insulator with an energy gap, yielding a single doubly-degenerate Fermi surface upon hole doping. We also discuss extensions to metallic states which preserve spin rotation invariance, with fluctuating spin density waves and bulk Z 2 topological order.

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the "antinodal" region of the square lattice Brillouin zone and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin-density wave mean field theory of the square lattice Hubbard model, and in a CP^{1} theory of spinons. This theory leads to metals with an antinodal gap and topological order which intertwines with the observed broken symmetries.

Topological solitons, a class of stable nonlinear excitations, appear in diverse domains as in the Skyrme model of nuclear forces. Here, we argue that similar excitations play an important role in a remarkable material obtained on stacking and twisting two sheets of graphene. Close to a magic twist angle, insulating behavior is observed, which gives way to superconductivity on doping. Here, we propose a unifying description of both observations. A symmetry breaking condensate leads to the ordered insulator, while topological solitons in the condensate—skyrmions—are shown to be charge 2e bosons. Condensation of skyrmions leads to a superconductor, whose physical properties we calculate. More generally, we show how topological textures can mitigate Coulomb repulsion and provide a previously unexplored route to superconductivity. Our mechanism not only clarifies why several other moiré materials do not show superconductivity but also points to unexplored platforms where robust superconductivity is anticipated.