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.

The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the symmetries at hand. While isolated examples of TCI have been identified and studied, the same variety demands a unified theoretical framework. In this work, we show how the surfaces of TCIs can be analyzed within a general surface theory with multiple flavors of Dirac fermions, whose mass terms transform in specific ways under crystalline symmetries. We identify global obstructions to achieving a fully gapped surface, which typically lead to gapless domain walls on suitably chosen surface geometries. We perform this analysis for all 32 point groups, and subsequently for all 230 space groups, for spin-orbit-coupled electrons. We recover all previously discussed TCIs in this symmetry class, including those with "hinge" surface states. Finally, we make connections to the bulk band topology as diagnosed through symmetry-based indicators. We show that spin-orbit-coupled band insulators with nontrivial symmetry indicators are always accompanied by surface states that must be gapless somewhere on suitably chosen surfaces. We provide an explicit mapping between symmetry indicators, which can be readily calculated, and the characteristic surface states of the resulting TCIs. arXiv:1711.11589v3 [cond-mat.str-el]

No abstract

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We provide a complete classification of inversion-protected higher-order topological insulators and superconductors in any spatial dimension for the ten symmetry classes by means of a layer construction. We discuss possible physical realizations of such states starting with a time-reversal invariant topological insulator (class AII) in three dimensions or a time-reversal invariant topological superconductor (class DIII) in two or three dimensions. The former exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter hosts Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field. arXiv:1801.10050v4 [cond-mat.mes-hall]