Whispering gallery resonators offer a versatile platform for manipulating the photonic transmission. Here, we study such a system, including periodically distributed pointlike impurities along the resonator with ring geometry. Based on an exact expression for the transmission probability we obtain here, we demonstrate that the bound states in the continuum (BICs) form from the whispering gallery modes at the high-symmetry momenta in the ring’s Brillouin zone. Furthermore, the presence of the inversion symmetry allows for a selective decoupling of resonant states, favoring the BIC generation and, therefore, allowing extra tunability in the optical transmission of the system.

We here introduce the concept of fragile dislocation modes, which are localized only in a fraction of a topological phase while otherwise leaking into the bulk continuum. As we demonstrate here, such dislocation modes are hosted in an obstructed atomic topological phase in the two-dimensional Su-Schrieffer-Heeger model but only in a finite region with an indirect gap at high energy. They are realized as chiral pairs at finite energies with protection stemming from a combination of the chiral (unitary particle -hole) and the point group ( C- 4 v ) symmetries, but only when the indirect gap is open. In this regime, we corroborate the stability of the defect modes by following their localization and also by explicitly adding a weak chemical potential disorder. Our findings should, therefore, be consequential for the experimental observation of such modes in designer topological crystals and classical metamaterials.

The Josephson effect is a hallmark signature of the superconducting state, which, however, has been sparsely explored in non-crystalline superconducting materials. Motivated by this, we consider a Josephson junction consisting of two superconductors with a fractal metallic interlayer, which is patterned as a Sierpi & nacute;ski carpet by removing atomic sites in a self-similar and scale-invariant manner. We here show that the fractal geometry has direct observable consequences on the Josephson effect. In particular, we demonstrate that the form of the supercurrent-magnetic field relation as the fractal generation number increases can be directly related to the self-similar fractal geometry of the normal metallic layer. Furthermore, the maxima of the corresponding diffraction pattern directly encode the self-repeating fractal structure in the course of fractal generation, implying that the corresponding magnetic length directly probes the shortest length scale in the given fractal generation. Our results should motivate future experimental efforts to verify these predictions in designer quantum materials and motivate future pursuits regarding fractal-based SQUID devices.

Lorentz symmetry appears as a quite robust feature of the strongly interacting Dirac materials even though the lattice interactions break such a symmetry. We here demonstrate that the Lorentz symmetry is restored at the quantum-critical point (QCP) separating the tilted Dirac semimetal, breaking this symmetry already at the noninteracting level, from a gapped s-wave superconducting instability. To this end, we employ a one-loop ϵ = (3 − D)-expansion close to the D = 3 upper critical dimension of the corresponding Gross-Neveu-Yukawa field theory. In particular, we show that the tilt parameter is irrelevant and ultimately vanishes at the QCP separating the two phases. In fact, as we argue here, such a Lorentz symmetry restoration may be generic for the strongly interacting tilted Dirac semimetals, irrespective of whether they feature mirror-symmetric or mirror-asymmetric tilting, and is also insensitive to whether the instability represents an insulator or a gapped superconductor. The proposed scenario can be tested in the quantum Monte Carlo simulations of the interacting tilted Dirac fermion lattice models.

Lorentz space–time symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum materials coupled to an environment thus far remained unexplored. We here introduce a general framework of constructing symmetry-protected Lorentz-invariant non-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslike anti-Hermitian Dirac operators to its Hermitian counterpart. Such NH DSMs feature purely real or imaginary isotropic linear band dispersion, yielding a vanishing density of states. Dynamic mass orderings in NH DSMs thus take place for strong Hubbard-like local interactions through a quantum phase transition, hosting a non-Fermi liquid, beyond which the system becomes an insulator. We show that depending on the internal Clifford algebra between the NH Dirac operator and candidate mass order-parameter, the resulting quantum-critical fluid either remains coupled with the environment or recovers full Hermiticity by decoupling from the bath, while always enjoying an emergent Yukawa-Lorentz symmetry in terms of a unique terminal velocity. We showcase the competition between such mass orderings, their hallmarks on quasi-particle spectra in the ordered phases, and the relevance of our findings for correlated designer NH Dirac materials.

Fractional Dirac materials (FDMs) feature a fractional energy-momentum relation E(k)∼|k|α, where α(<1) is a real noninteger number, in contrast to that in conventional Dirac materials with α=1. Here we analyze the effects of short- and long-range Coulomb repulsions in two- and three-dimensional FDMs. Only a strong short-range interaction causes nucleation of a correlated insulator that takes place through a quantum critical point. The universality class of the associated quantum phase transition is determined by the correlation length exponent ν-1=d-α and dynamic scaling exponent z=α, set by the band curvature. On the other hand, the fractional dispersion is protected against long-range interaction due to its nonanalytic structure. Rather, a linear Dirac dispersion gets generated under coarse graining, and the associated Fermi velocity increases logarithmically in the infrared regime, thereby yielding a two-fluid system. Altogether, correlated FDMs unfold a rich landscape accommodating unconventional emergent many-body phenomena.

Topological lattice defects, such as dislocations and grain boundaries (GBs), are ubiquitously present in the bulk of quantum materials and externally tunable in metamaterials. In terms of robust modes, localized near the defect cores, they are instrumental in identifying topological crystals, featuring the hallmark band inversion at a finite momentum (translationally active type). Here we show that the GB superlattices in both two-dimensional and three-dimensional translationally active higher-order topological insulators harbor a myriad of dispersive modes that are typically placed at finite energies, but always well-separated from the bulk states. However, when the Burgers vector of the constituting edge dislocations points toward the gapless corners or hinges, both second-order and third-order topological insulators accommodate self-organized emergent topological metals near the zero energy (half-filling) in the GB mini Brillouin zone. We discuss possible material platforms where our proposed scenarios can be realized through the band-structure and defect engineering.

Majorana zero modes (MZMs) are of central importance for modern condensed matter physics and quantum information due to their non-Abelian nature, which thereby offers the possibility of realizing topological quantum bits. We here show that a grain boundary (GB) defect can host a topological superconductor (SC), with a pair of cohabitating MZMs at its end when immersed in a parent two-dimensional gapped topological SC with the Fermi surface enclosing a nonzero momentum. The essence of our proposal lies in the magnetic-field driven hybridization of the localized MZMs at the elementary blocks of the GB defect, the single lattice dislocations, due to the MZM spin being locked to the Burgers vector. Indeed, as we show through numerical and analytical calculations, the GB topological SC with two localized MZMs emerges in a finite range of both the angle and magnitude of the external magnetic field. Our work demonstrates the possibility of defect-based platforms for quantum information technology and opens up a route for their systematic search in future.

In this article, we study the formation of the bound states in the continuum (BICs) in a two-channel Fano-Anderson model. We employ the Green's function formalism, together with the equation of motion method, to analyze the relevant observables, such as the transmission coefficient and the density of states. Most importantly, our results show that the system hosts true BICs for the case of a symmetric configuration with degenerate impurity levels, and a complete transmission channel is then suppressed. Finally, we argue that the proposed mechanism could be relevant for the realization of BICs in electronic and photonic systems.

We show that corner Majorana zero modes in a two-dimensional p + id topological superconductor can be controlled by the manipulation of the parent p-wave superconducting order. Assuming that the p-wave superconducting order is in either a chiral or helical phase, we find that when a d(x2-y2) wave superconducting order is induced, the system exhibits quite different behavior depending on the nature of the parent p-wave phase. In particular, we find that while in the helical phase, a localized Majorana mode appears at each of the four corners, in the chiral phase, it is localized along only two of the four edges. We furthermore demonstrate that the Majoranas can be directly controlled by the form of the edges, as we explicitly show in the case of circular edges. We argue that the application of strain may provide additional means of fine-tuning the Majorana zero modes in the system; in particular, it can partially gap them out. Our findings may be relevant for probing the topology in two-dimensional mixed-pairing superconductors.