Topology under a 'twist'

Since the discovery of superconductivity and correlated insulating phases in magic-angle twisted bilayer graphene (MATBG) in 2018, twistronics - the use of angular twist between two atomically thin layers to create novel electronic properties - has become one of the major topics in condensed matter physics over recent years. The scheme of a small 'twist', while not so difficult to visualize in terms of its geometric construction, creates the so-called moiré patterns which not only modifies the electronic properties of quantum materials in a dramatic way, but also gives rise to a rich variety of new phases of matter that can boggle the brightest minds. It is particularly intriguing to ask what are the new topological phases that can be borne out of these twisted double-layer composites, particularly when electron interactions come into play.

Non-Abelian topological superconductivity in maximally twisted STVS superconductors

Motivated by recent advances in small-angle-twisted bilayer graphene and transition-metal dichalcogenides, Marcel and collaborators proposed in 2021 [Nat. Phys. 17, 519–524 (2021)] that twisting two layers of monolayer high Tc cuprates with d-wave pairing symmetry, such as Bi2Sr2CaCu2O8+δ, by a large angle of θ ≃ 45∘ , the double-layer system becomes a chiral d-wave superconductor which is known to be a chiral topological phase with Chern number C = ±2, which supports protected chiral edge modes up to the native Tc of 90K in each monolayer. While this appealing proposal provides possible realization of a long-sought high-Tc topological superconductor (TSC), a chiral d-wave TSC supports only Abelian excitations due to the spin-singlet nature of its Cooper pairs, thus not directly useful for topological quantum computation. 

Latest developments in the study of superconductivity in 2D materials, on the other hand, have pointed to unconventional spin-triplet superconductivity in rhombohedral graphene [Nature 598, 434–438 (2021)] and zerconium nitrides [Proc. Natl. Acad. Sci. 119 (13) e2117735119 (2022)] - the exotic spin-triplet SC phase is formed by spin-triplet valley-singlet (STVS) Cooper pairs which have essentially the f-wave symmetry but a full excitation gap due to isolated Fermi surfaces surrounding the opposite K-valleys (see figure on the left). In this recent article featured as Editor's highlights in Communications Physics, we propose that a similar scheme of maximal angular twist on the STVS superconductors turns the twisted double-layer into a chiral f+if'-wave superconductor with Chern number C = ±3 - an intrinsic non-Abelian TSC which hosts an unpaired Majorana mode at its superconducting vortex core. The composite system may serve directly as a platform for fault-tolerant Majorana qubits.

Intriguingly, despite similarities in construction to magic-angle graphene and twisted cuprates, the emergence of non-Abelian chiral f-wave phase in maximally twisted STVS superconductors relies on a new type of large-angle moiré physics that is absent in twisted cuprates and fundamentally different from the valley-preserving small-angle moiré physics in twisted graphene and TMD materials - the violation of valley conservation Uv(1) at maximal twist plays a crucial role for the emergence of unpaired Majorana modes.

(See also Invited symposium at APS March Meeting 2023)

Moiré flat Chern bands & correlated QAH state generated by SOCs

The formation of large-period moiré patterns in real space upon small angular twist leads to reconstructed energy bands - called moiré bands - which can be thought of as the result of downfolding the energy bands of each isolated layer into the largely reduced mini-Brillouin zone in momentum-space. These moiré bands in twisted homobilayer graphene and TMD materials, which are typically flat with bandwidths of a few to tens of milli-electron-volts due to strong electron localization, are also characterized in general by nontrivial band topology. The nontrivial band topology puts up an obstruction against forming a usual Mott insulator at special fillings under electron interactions - the interplay between interaction and topology would instead result in correlated topological phases. 

In this Letter, we propose a new mechanism for topologically nontrivial moiré flat bands - the combination of local mirror symmetry breaking and angular twist leads to nontrivial skyrmionic spin textures in the conduction band states of a twisted bilayer MoS2, which endows the moiré bands from opposite K-valleys with an unusual Chern number of C = ±2. At 1/2-filling, the Coulomb interaction drives the system into a valley-polarized quantum anomalous Hall state with potential uses for atomically thin magnetic memory devices.