Elio. J. König

Motivated by recent experiments on rhombohedral stacked multilayer graphene and the observation of the anomalous Hall effect in a spontaneous spin-valley-polarized quarter-metal state, we calculate the anomalous Hall conductivity for this system in the presence of two types of impurities: weak and dense as well as sparse and strong. Our calculation of σ x y is based on the Kubo-Streda diagrammatic approach. In a model with Gaussian disorder applicable to weak dense impurities, this involves all noncrossing diagrams (intrinsic, side-jump and Gaussian skew-scattering contributions) and additionally, diagrams with two intersecting impurities, X and Ψ , representing diffractive skew-scattering processes. A “Mercedes star” diagram (non-Gaussian skew scattering) is furthermore included to treat in the case of strong, sparse impurities. We supplement our asymptotically exact analytical solutions for an isotropic model without warping effects by seminumerical calculations accounting perturbatively for warping, which plays a crucial role in the low-energy band structure.

Symmetry protected topological (SPT) phases are fundamental quantum many-body states of matter beyond Landau’s paradigm. Here, we introduce the concept of quantum restoration of SPT (QRSPT) phases, where the protecting symmetry appears to be spontaneously broken at the shortest spatiotemporal scales, but restored after averaging over quantum fluctuations, so that topological features re-emerge. To illustrate the concept, we study a one-dimensional fermionic Su-Schrieffer-Heeger model with fluctuating superconducting order. We solve this problem in several limiting cases using a variety of analytical methods and compare them to numerical (density matrix renormalization group) simulations, which are valid throughout the parameter regime. We thereby map out the phase diagram and identify a QRSPT phase with topological features which are reminiscent of (but not identical to) the topology of the underlying free fermion system. The paradigm of QRSPT phases thereby stimulates a new perspective for the constructive design of novel topological quantum many-body phases.

Topological band structures interfering with moiré superstructures give rise to a plethora of emergent phenomena, which are pivotal for correlated insulating and superconducting states of twisttronics materials. While quasiperiodicity was up to now a notion mostly reserved for solid-state materials and cold atoms, we here demonstrate the capacity of conventional superconducting circuits to emulate moiré physics in charge space. With two examples, we show that Hofstadter's butterfly and the magic-angle effect are directly visible in spectroscopic transport measurements. Importantly, these features survive in the presence of harmonic trapping potentials due to parasitic linear capacitances. Our proposed platform benefits from unprecedented tuning capabilities and opens the door to probe incommensurate physics in virtually any spatial dimension.

Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to the understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential understanding of their consequences. In this work, we identify a fundamental connection between gapless SPTs and recently introduced multiplicative topological phases, demonstrating that multiplicative topological phases are an intuitive and general approach to realizing concrete models for gapless SPTs. In particular, they are naturally well suited to realizing higher-dimensional, stable, and intrinsically gapless SPTs through the combination of canonical topological insulator and semimetal models with critical gapless models in symmetry-protected tensor product constructions, opening avenues to far broader and deeper investigation of topology via short-range entanglement.

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we here study an exactly integrable, local model for a fractionalized topological insulator. Using a controlled perturbation theory about this limit, we demonstrate the existence of topological bands of zeros in the exact fermionic Green’s function and show that in this model they do affect the topological invariant of the system, but not the quantized transport response. Close to (but prior to) the Higgs transition signaling the breakdown of fractionalization, the topological bands of zeros acquire a finite “lifetime.” We also discuss the appearance of edge states and edge zeros at real space domain walls separating different phases of the system. This model provides a fertile ground for controlled studies of the phenomenology of Green’s function zeros and the underlying exactly solvable lattice gauge theory illustrates the synergetic cross pollination between solid-state theory, high-energy physics, and quantum information science. Published by the American Physical Society 2024