André Grossi Fonseca

We classify gapped phases and characteristic nodal points of non-Hermitian band structures on two-dimensional nonorientable parameter spaces. Such spaces arise in a wide range of physical systems in the presence of nonsymmorphic parameter space symmetries. For gapped phases, we find that nonorientable spaces provide a natural setting for exploring fundamental structural problems in braid group theory, such as torsion and conjugacy. Gapless systems, which host exceptional points (EPs), explicitly violate fermion doubling, even in two-band models. We demonstrate that EPs traversing the nonorientable parameter space exhibit non-Abelian charge inversion. These braided phases and their transitions leave distinct signatures in the form of bulk Fermi arc degeneracies, offering a concrete route toward experimental realization and verification.

We introduce new classes of gapped topological phases characterized by quantized crystalline-electromagnetic responses, termed multipolar Chern insulators. These systems are characterized by nonsymmorphic momentum-space symmetries and mirror symmetries, leading to quantization of momentum-weighted Berry curvature multipole moments. We construct lattice models for such phases and numerically confirm their quantized responses. These systems exhibit bound charge and momentum densities at lattice and magnetic defects, as well as currents induced by electric or time-varying strain fields. Our Letter extends the classification of topological matter by uncovering novel symmetry-protected topological phases with quantized responses.

We introduce a general mechanism for obtaining Weyl points in a stack of two-dimensional (2D) quasicrystals, which can be extended to any stack of aperiodic layers. We do so by driving a topological phase transition with the vertical crystal momentum as the tuning parameter, which leads to gap closures at the critical points sourcing Berry curvature. To illustrate, we use a simple 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. The presence of Weyl points is established via the local Chern marker, projected band structure, and density of states. Interestingly, we uncover an analog of Fermi arcs in the quasicrystalline setting, which we deem Fermi-Bragg arcs, densely distributed lines connecting the band degeneracies and indexed by the Bragg peaks. Signatures of such surface states in quantum oscillations and the prospect of a fully quasicrystalline Weyl system are also discussed. The flexibility of our proposal brings opportunities for realizing other gapless topological phases in aperiodic systems, paving the way for a significantly expanded role for topological band theory.

We introduce a general mechanism for obtaining Weyl points in a stack of 2D quasicrystals, which can be extended to any stack of aperiodic layers. We do so by driving a topological phase transition with the vertical crystal-momentum as the tuning parameter, which leads to gap closures at the critical points sourcing Berry curvature. To illustrate, we use a simple 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. The presence of Weyl points is established via the local Chern marker, projected band structure and density of states. Interestingly, we uncover an analogue of Fermi arcs in the quasicrystalline setting, which we deem Fermi-Bragg arcs, densely distributed lines connecting the band degeneracies and indexed by the Bragg peaks. Signatures of such surface states in quantum oscillations and the prospect of a fully quasicrystalline Weyl system are also discussed. The flexibility of our proposal brings new opportunities for realizing other gapless topological phases in aperiodic systems, paving the way for a significantly expanded role for topological band theory.