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We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to nonlocal interlayer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wave vectors. We find that at all nonzero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal-symmetric and spatially nonuniform order. This order, which we dub the "incommensurate Kekulé spiral"(IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries but preserves a modified translation symmetry T^′-which simultaneously shifts the spatial coordinates and rotates the U(1) angle which characterizes the spontaneous intervalley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

We consider three-dimensional superconductors in class DIII with a fourfold rotation axis and inversion symmetry. It is shown that such systems can exhibit higher-order topology with helical Majorana hinge modes. In the case of even-parity superconductors, we show that higher-order topological superconductors can be obtained by adding a small pairing with the appropriate C4 symmetry implementation to a topological insulator. We also show that a hybrid case is possible, where Majorana surface cones resulting from nontrivial strong topology coexist with helical hinge modes. We propose a bulk invariant detecting this hybrid scenario, and numerically analyze a tight binding model exhibiting both Majorana cones and hinge modes.

We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size L scales as S∼Llog[ξf(L/ξ)] in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where f(x) is a scaling function which depends on the shape of the Fermi surface and ξ is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states.

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the "cascade" physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.

We investigate the effect of uniaxial heterostrain on the interacting phase diagram of magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values (ε∼0.1%-0.2%) drive a zero-temperature phase transition between the symmetry-broken "Kramers intervalley-coherent" insulator and a nematic semimetal. The critical strain lies within the range of experimentally observed strain values, and we therefore predict that strain is at least partly responsible for the sample-dependent experimental observations.

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 2 e 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., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

Motivated by the recent observation of an anomalous Hall effect in twisted bilayer graphene, we use a lowest Landau level model to understand the origin of the underlying symmetry-broken correlated state. 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 intervalley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

We extend the concept of strange correlators, defined for symmetry-protected phases in You et al. [Phys. Rev. Lett. 112, 247202 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.247202], to topological phases of matter by taking the inner product between string-net ground states and product states. The resulting two-dimensional partition functions are shown to be either critical or symmetry broken, since the corresponding transfer matrices inherit all matrix product operator symmetries of the string-net states. For the case of critical systems, these nonlocal matrix product operator symmetries are the lattice remnants of topological conformal defects in the field theory description. Following Aasen et al. [J. Phys. A 49, 354001 (2016)JPAMB51751-811310.1088/1751-8113/49/35/354001], we argue that the different conformal boundary conditions can be obtained by applying the strange correlator concept to the different topological sectors of the string net obtained from Ocneanu's tube algebra. This is demonstrated on the lattice by calculating the conformal field theory spectra in the different topological sectors for the Fibonacci (hard-hexagon) and Ising string net. Additionally, we provide a complementary perspective on symmetry-preserving real-space renormalization by showing how known tensor network renormalization methods can be understood as the approximate truncation of an exactly coarse-grained strange correlator.

Edge theories of symmetry-protected topological phases are well known to possess global symmetry anomalies. In this Letter we focus on two-dimensional bosonic phases protected by an on-site symmetry and analyze the corresponding edge anomalies in more detail. Physical interpretations of the anomaly in terms of an obstruction to orbifolding and constructing symmetry-preserving boundaries are connected to the cohomology classification of symmetry-protected phases in two dimensions. Using the tensor network and matrix product state formalism we numerically illustrate our arguments and discuss computational detection schemes to identify symmetry-protected order in a ground state wave function.

We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws-including a topological correction-emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.