Effective Model for Fractional Topological Corner Modes in Quasicrystals

Chirality-Induced Majorana Zero Modes and Majorana Polarization

Realizing Majorana Fermions has always been regarded as a crucial and formidable task in topological superconductors. In this work, we report a physical mechanism and a material platform for realizing Majorana zero modes (MZMs). This material platform consists of open circular helix molecule (CHM) proximity coupled with an s-wave superconductor (under an external magnetic field) or interconnected-CHM chain coupled with a phase-bias s-wave superconducting heterostructure (without any external magnetic field). MZMs generated here are tightly associated with the structural chirality in CHMs. Notably, the left- and right-handedness results in completely opposite Majorana polarization (MP), leading us to refer to this phenomenon as chirality-induced MP (CIMP). Importantly, the local CIMP is closely linked to chirality-induced spin polarization, providing us with an effective way to regulate MZMs through the chirality-induced spin selectivity (CISS) effect. Furthermore, MZMs can be detected by the spin-polarized current measurements related to the CISS in chiral materials.

Robust second-order topological insulator in 2D van der Waals magnet CrI3

CrI3 offers an intriguing platform for exploring fundamental physics and the innovative design of spintronics devices in two-dimensional (2D) magnets, and moreover has been instrumental in the study of topological physics. However, the 2D CrI3 monolayer and bilayers have long been thought to be topologically trivial. Here we uncover a hidden facet of the band topology of 2D CrI3 by showing that both the CrI3 monolayer and bilayers are second-order topological insulators (SOTIs) with a nonzero second Stiefel-Whitney number w2 = 1. Furthermore, the topologically nontrivial nature can be explicitly confirmed via the emergence of floating edge states and in-gap corner states. Remarkably, in contrast to most known magnetic topological states, we put forward that the SOTIs in 2D CrI3 monolayer and bilayers are highly robust against magnetic transitions, which remain intact under both ferromagnetic and antiferromagnetic configurations. These interesting predictions not only provide a comprehensive understanding of the band topology of 2D CrI3 but also offer a favorable platform to realize magnetic SOTIs for spintronics applications.

Nematic Superconductivity and Its Critical Vestigial Phases in the Quasicrystal

We propose a general mechanism to realize nematic superconductivity (SC) and reveal its exotic vestigial phases in the quasicrystal (QC). Starting from a Penrose-Hubbard model, our microscopic studies suggest that the Kohn-Luttinger mechanism driven SC in the QC is usually gapless due to violation of Anderson's theorem, rendering that both chiral and nematic SCs are common. The nematic SC in the QC can support novel vestigial phases driven by pairing phase fluctuations above its T_{c}. Our combined renormalization group and Monte Carlo studies provide a phase diagram in which, besides the conventional charge-4e SC, two critical vestigial phases emerge, i.e., the quasinematic (QN) SC and QN metal. In the two QN phases, discrete lattice rotation symmetry is counterintuitively "quasibroken" with power-law decaying orientation correlation. They separate the phase diagram into various phases connected via Berezinskii-Kosterlitz-Thouless (BKT) transitions. These remarkable critical vestigial phases, which resemble the intermediate BKT phase in the q state (q≥5) clock model, are a consequence of the fivefold (or higher) anisotropy field brought about by the unique QC symmetry, which are absent in conventional crystalline materials.

Dispersion-Selective Band Engineering in an Artificial Kagome Superlattice

The relentless pursuit of band structure engineering continues to be a fundamental aspect in solid-state research. Here, we meticulously construct an artificial kagome potential to generate and control multiple Dirac bands of graphene. This unique high-order potential harbors natural multiperiodic components, enabling the reconstruction of band structures through different potential contributions. As a result, the band components, each characterized by distinct dispersions, shift in energy at different velocities in response to the variation of artificial potential. Thereby, we observe a significant spectral weight redistribution of the multiple Dirac peaks. Furthermore, the magnetic field can effectively weaken the superlattice effect and reactivate the intrinsic Dirac band. Overall, we achieve actively dispersion-selective band engineering, a functionality that would substantially increase the freedom in band design.

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Topological Nodal-Point Superconductivity in Two-Dimensional Ferroelectric Hybrid Perovskites

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) with enhanced stability, high tunability, and strong spin-orbit coupling have shown great potential in vast applications. Here, we extend the already rich functionality of 2D HOIPs to a new territory, realizing topological superconductivity and Majorana modes for fault-tolerant quantum computation. Especially, we predict that room-temperature ferroelectric BA2PbCl4 (BA for benzylammonium) exhibits topological nodal-point superconductivity (NSC) and gapless Majorana modes on selected edges and ferroelectric domain walls when proximity-coupled to an s-wave superconductor and an in-plane Zeeman field, attractive for experimental verification and application. Since NSC is protected by spatial symmetry of 2D HOIPs, we envision more exotic topological superconducting states to be found in this class of materials due to their diverse noncentrosymmetric space groups, which may open a new avenue in the fields of HOIPs and topological superconductivity.

Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including sixfold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette (ϕ) is half of the flux quantum, zero modes are found localized around the reflected "anti-hats"; and (v) its Hofstadter spectrum is periodic in ϕ, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.

Pseudospin Polarized Dual-Higher-Order Topology in Hydrogen-Substituted Graphdiyne

Although the topological band theory is applicable to both Fermionic and bosonic systems, the same electronic and phononic topological phases are seldom reported in one natural material. In this work, we show the presence of a dual-higher-order topology in hydrogen-substituted graphdiyne (H-GDY) by first-principles calculations. The intriguing enantiomorphic flat-bands are realized in both electronic and phononic bands of H-GDY, which is confirmed to be an organic 2D second-order topological insulator (SOTI). Most importantly, we found that the topological corner states are pseudospin polarized in H-GDY, exhibiting a clockwise or counterclockwise texture perpendicular to the radial direction. Our results not only identify the existence of the dual-higher-order topology in covalent organic frameworks but also uncover a unique pseudospin polarization-coordinate locking relation, further extending the well-known spin-momentum locking relation in conventional topological insulators.