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Two Dirac nodes change their relative non-Abelian topological charges from (+i, –i) to (+i, +i) through momentum-space braiding.
Non-Abelian charge conversion in bilayer binary honeycomb lattice systems
Phys. Rev. B (Letter) 113, L081101 (2026)
In two-dimensional systems with space-time inversion symmetry, Dirac nodes (DNs) carry non-Abelian topological charges that give rise to intriguing momentum-space braiding phenomena. Although the original idea was proposed in a condensed matter setting, experimental verification of non-Abelian charge conversion has so far been limited to artificial metamaterials, owing to the difficulty of identifying suitable materials in which controlled tuning of DN positions is possible. In this work, we propose for the first time that bilayer binary honeycomb lattices (BBHLs) provide a new material platform to study the non-Abelian charge conversion phenomenon, where DN positions in momentum space can be effectively manipulated. Furthermore, we generalize our proposal of momentum-space braiding from layered materials—interacting graphene—to proximitized magneto–spin–orbit graphene.
Effective theory for the Quantum Valley Hall effect with zero Berry curvature
Quantum Valley Hall effect without Berry curvature
Phys. Rev. Lett. 133, 196603 (2024)
It was widely believed in the condensed matter community that the quantum valley Hall effect requires a finite Berry curvature, which demands inversion symmetry breaking. We go beyond this notion and impose a stronger symmetry constraint—space-time inversion—that forces the Berry curvature to vanish identically across the Brillouin zone. Remarkably, we show that a quantum valley Hall effect can still exist, now governed by a new topological quantity, the Euler curvature. This discovery pushes the field beyond conventional understanding and opens fresh directions for topological classification.
Moiré patterns in large-angle twisted bilayer graphene and electronic domain walls arising from the quantum sub-valley Hall effect.
Quantum valley and subvalley Hall effect in large-angle twisted bilayer
graphene
Phys. Rev. B (Letter) 108, L121405 (2023)
Twisted bilayer graphene has emerged as a fascinating platform for novel quantum phenomena, but so far the focus has been on small twist angles where superconductivity, magnetism, and exotic Hall effects appear. Large twist angles, untill recently, on the other hand, were believed to yield only two decoupled Dirac cones with no new physics. We uncover a new effect—the sub-valley Hall effect—along with its electronic domain wall signatures at very large angles (e.g., near 21.78°). Our proposal not only reveals unexpected physics in the large-angle regime but also opens a fresh dimension for exploring twisted materials.
Unremovable linkednodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture
Phys. Rev. B (Letter) 106, L121118 (2022)
Proposal for Unremovable Linked Nodal Structures with Multiple ℤ and ℤ₂ Topological Charges over 0D, 1D, and 2D manifold
Linking structure is a new concept characterizing topological semimetals, which indicates the interweaving of gap-closing nodes at the Fermi energy (𝐸𝐹) with other nodes below 𝐸𝐹. As the number of linked nodes can be changed only via pair creation or pair annihilation, a linked node is more stable and robust than ordinary nodes without linking. Here we propose a type of linked nodal structure between a nodal line (nodal surface) at 𝐸𝐹 with another nodal line (nodal surface) below 𝐸𝐹 in two-dimensional (three-dimensional) spinless fermion systems with PT symmetry where P and T indicate inversion and time-reversal symmetries, respectively. Because of additional chiral and rotational symmetries, in our system, a double band inversion creates a pair of linked nodes carrying the same topological charges, and thus the pair is unremovable via a Lifshiftz transition, which is clearly distinct from the cases of the linked nodes reported previously. A realistic tight-binding model and effective theory are developed for such a linking structure. Also, using density-functional-theory calculations, we propose a class of materials, composed of stacked bilayer graphene with Kekulé texture, as a candidate system hosting the linked nodal structure.
Topological Surface and Rashba bulk states of trivial and non-trivial insulators
Intertwined nontrivial band topology and giant Rashba spin splitting
Phys. Rev. B 104, 085113 (2021)
Topological nontriviality and Rashba spin physics are two different quantum phenomena but can be intertwined within a CQC platform. In this paper, we present a general symmetry-based mechanism, supported by ab initio calculations, to achieve intertwined giant Rashba splitting and topological nontrivial states simultaneously in a single crystalline system.
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