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Abstract 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.

Abstract 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.

Abstract 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.

Abstract In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been expanded by considering additional crystalline symmetries. Nevertheless, realizing a three-dimensional (3D), time-reversal symmetric (class AII) topological insulator (TI) in the absence of reflection symmetries, with a classification beyond the $${\mathbb {Z}}_{2}$$ Z 2 paradigm remains an open problem. In this work we present a general procedure for constructing such systems within the framework of projected topological branes (PTBs). In particular, a 3D projected brane from a “parent” four-dimensional topological insulator exhibits a $${\mathbb {Z}}$$ Z topological classification, corroborated through its response to the inserted bulk monopole loop. More generally, PTBs have been demonstrated to be an effective route to performing dimensional reduction and embedding the topology of a $$(d+1)$$ ( d + 1 ) -dimensional “parent” Hamiltonian in d dimensions, yielding lower-dimensional topological phases beyond the AZ classification without additional symmetries. Our findings should be relevant for the metamaterial platforms, such as photonic and phononic crystals, topolectric circuits, and designer systems.

Abstract Flat band electronic systems exhibit a rich landscape of correlation-driven phases, both at the charge neutrality and finite electronic density, featuring exotic electromagnetic and thermodynamic responses. Motivated by these developments, in this paper, we explicitly include the effects of the chemical potential in a holographic model featuring approximately flat bands. In particular, we explore the phase diagram of this holographic flat band system as a function of the chemical potential. We find that at low temperatures and densities, the system features a nematic phase, transitioning into the Lifshitz phase as the chemical potential or temperature increases. To further characterize the ensuing phases, we investigate the optical conductivity and find that this observable shows strong anisotropies in the nematic phase.

Abstract 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.

Abstract 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.

Fractional Dirac materials (FDMs) feature a fractional energy-momentum relation E(k)∼|k|^{α}, where α(

Authors introduce a new class of topological materials, namely projected topological branes that are holographic images of higher-dimensional topological crystals, and feature either emergent crystalline or aperiodic quasicrystalline order. They manifest bulk-boundary and bulk-lattice defect correspondences of parent crystals and open a realistic route to harness four and higher-dimensional topological crystals in three-dimensional world.

Abstract Motivated by the phenomenology in the condensed-matter flat-band Dirac systems, we here construct a holographic model that imprints the symmetry breaking pattern of a rather simple Dirac fermion model at zero chemical potential. In the bulk we explicitly include the backreaction to the corresponding Lifshitz geometry and compute the dynamical critical exponent. Most importantly, we find that such a geometry is unstable towards a nematic phase, exhibiting an anomalous Hall effect and featuring a Drude-like shift of its spectral weight. Our findings should motivate further studies of the quantum phases emerging from such holographic models.

Abstract Topological phases of matter have recently attracted a rather notable attention in the community dealing with the holographic methods applied to strongly interacting condensed matter systems. In particular, holographic models for gapless Weyl and multi-Weyl semimetals, characterized on a lattice by the monopole-antimonopole defects of the Berry curvature in momentum space, were recently formulated. In this paper, motivated by the quest for finding topological holographic phases, we show that holographic model for multi-Weyl semimetals features a rather rich landscape of phases. In particular, it includes a novel phase which we dub xy nematic condensate, stable at strong coupling, as we explicitly show by the free energy and the quasi-normal mode analyses. Furthermore, we provide its characterization through the anomalous transport coefficients. We hope that our findings will motivate future works exploring the holographic realizations of the topological phases.

Study of the strongly correlated states in van der Waals heterostructures is one of the central topics in modern condensed matter physics. Among these, the rhombohedral trilayer graphene (RTG) occupies a prominent place since it hosts a variety of interaction-driven phases, with the metallic ones yielding exotic superconducting orders upon doping. Motivated by these experimental findings, we show within the framework of the low-energy Dirac theory that the optical conductivity can distinguish different candidates for a paramagnetic metallic ground state in this system. In particular, this observable shows a single peak in the fully gapped valence-bond state. On the other hand, the bond-current state features two pronounced peaks in the optical conductivity as the probing frequency increases. Finally, the rotational symmetry breaking charge-density wave exhibits a minimal conductivity with the value independent of the amplitude of the order parameter, which corresponds precisely to the splitting of the two cubic nodal points at the two valleys into two triplets of the band touching points featuring linearly dispersing quasiparticles. These features represent the smoking gun signatures of different candidate order parameters for the paramagnetic metallic ground state, which should motivate further experimental studies of the RTG.

Dynamical multiferroicity features entangled dynamic orders: fluctuating electric dipoles induce magnetization. Hence, the material with paraelectric fluctuations can develop magnetic signatures if dynamically driven. We identify the paraelectric KTaO_{3} (KTO) as a prime candidate for the observation of the dynamical multiferroicity. We show that when a KTO sample is exposed to a circularly polarized laser pulse, the dynamically induced ionic magnetic moments are of the order of 5% of the nuclear magneton per unit cell. We determine the phonon spectrum using ab initio methods, and we identify T_{1u} as relevant phonon modes that couple to the external field and induce magnetic polarization. We also predict a corresponding electron effect for the dynamically induced magnetic moment, which is enhanced by several orders of magnitude due to the significant mass difference between electron and ionic nucleus.

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_{x^{2}−y^{2}} 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.

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk. Higher-order topological (HOT) states extend this usual bulk-boundary correspondence, so they host the modes localized at lower-dimensional boundaries, such as corners and hinges. Here we theoretically demonstrate that dislocations, ubiquitous defects in crystalline materials, can probe higher-order topology, recently realized in various platforms. We uncover that HOT insulators respond to dislocations through symmetry protected finite-energy in-gap electronic modes, localized at the defect core, which originate from an interplay between the orientation of the HOT mass domain wall and the Burgers vector of the dislocation. As such, these modes become gapless only when the Burgers vector points toward lower-dimensional gapless boundaries. Our findings are consequential for the systematic probing of the extended bulk-boundary correspondence in a broad range of HOT crystals and photonic and phononic or mechanical metamaterials through the bulk topological lattice defects.

We highlight a general theory to engineer arbitrary Hermitian tight-binding lattice models in electrical LC circuits, where the lattice sites are replaced by the electrical nodes, connected to its neighbors and to the ground by capacitors and inductors. In particular, by supplementing each node with n subnodes, where the phases of the current and voltage are the n distinct roots of unity, one can in principle realize arbitrary hopping amplitude between the sites or nodes via the shift capacitor coupling between them. This general principle is then implemented to construct a plethora of topological models in electrical circuits, topolectric circuits, where the robust zero-energy topological boundary modes manifest through a large boundary impedance, when the circuit is tuned to the resonance frequency. The simplicity of our circuit constructions is based on the fact that the existence of the boundary modes relies only on the Clifford algebra of the corresponding Hermitian matrices entering the Hamiltonian and not on their particular representation. This in turn enables us to implement a wide class of topological models through rather simple topolectric circuits with nodes consisting of only two subnodes. We anchor these outcomes from the numerical computation of the on-resonance impedance in circuit realizations of first-order (m=1), such as Chern and quantum spin Hall insulators, and second- (m=2) and third- (m=3) order topological insulators in different dimensions, featuring sharp localization on boundaries of codimensionality d_{c}=m. Finally, we subscribe to the stacked topolectric circuit construction to engineer three-dimensional Weyl, nodal-loop, quadrupolar Dirac, and Weyl semimetals, respectively, displaying surface- and hinge-localized impedance.

We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two- and three-dimensional crystalline HOT insulators, accommodating topological corner states, we gradually enhance structural randomness in the system. Within a parameter regime, as long as amorphousness is confined by an outer crystalline boundary, the system continues to host corner states, yielding amorphous HOT insulators. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator when amorphousness plagues the entire system. These outcomes are further substantiated by computing the quadrupolar (octupolar) moment in two (three) dimensions. Therefore, HOT phases can be realized in amorphous solids, when wrapped by a thin (lithographically grown, for example) crystalline layer. Our findings suggest that crystalline topological phases can be realized even in the absence of local crystalline symmetry.

Multi-Weyl semimetals feature band crossings with the dispersion that is, in general, linear in only one direction, and as a consequence their band structure is characterized by the monopole charge n which can be greater than one. We show that a single screw dislocation defect oriented in the direction connecting the nodal points, which acts as an effective pseudomagnetic flux tube, can serve as a direct probe of the monopole charge n≥1 characterizing the bulk band structure of a multi-Weyl semimetal. To this end, as a proof of principle, we propose a rather simple mesoscopic setup in which the monopole charge leaves a direct imprint on the conductance measured in the plane perpendicular to the dislocation. In particular, the ratio of the positions of the neighboring maxima in the conductance as a function of the gate voltage can serve to deduce the monopole charge, while the value of the effective pseudomagnetic flux can be extracted from the position of a conductance maximum. We expect that these findings will prompt further studies on the role of multiple dislocations, as well as other topological lattice defects, such as grain boundaries and disclinations, in topological nodal materials.

We address the emergent quantum critical phenomena for (pseudo)spin-3/2 birefringent fermions, featuring two effective Fermi velocities, when they reside close to itinerant Mott transitions realized through spontaneous symmetry breaking and triggered by strong local or Hubbard-like repulsive interactions. Irrespective of the nature of the mass orderings that produce fully gapped quasiparticle spectra in the ordered phase, which otherwise can be grouped into three classes, the system always possesses a unique terminal velocity near the corresponding quantum critical point. The associated critical regime accommodates a relativistic non-Fermi liquid of strongly coupled collective bosonic and spin-1/2 Dirac excitations with vanishing weight of the quasiparticle pole. These conclusions are also operative near superconducting critical points. Therefore, relativistic non-Fermi liquid possibly constitutes a robust superuniversal description for the entire family of strongly correlated arbitrary half-integer spin Dirac materials.

Interaction-driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite, making its direct observation difficult in linear transport. We propose the nonlinear Hall effect as a direct probe of this transition when inversion symmetry is broken. Specifically, for a two-dimensional Dirac material with a tilted low-energy dispersion, we predict a transformation of the characteristic interband resonance peak into a non-Lorentzian form in the collisionless regime. Furthermore, we show that inversion-symmetry-breaking quantum phase transition is controlled by an exotic tilt-dependent line of critical points. As this line is approached from the ordered side, the nonlinear Hall conductivity is suppressed owing to the scattering between the strongly coupled incoherent fermionic and bosonic excitations. Our results should motivate further studies of nonlinear responses in strongly interacting Dirac materials.

Higher-order topological (HOT) states, hosting topologically protected modes on lower-dimensional boundaries, such as hinges and corners, have recently extended the realm of the static topological phases. Here we demonstrate the possibility of realizing a two-dimensional Floquet second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment Q_{xy}^{Flq}=0.5, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold (C_{4}) and time-reversal (T) symmetry breaking Dirac mass perturbation. Furthermore, we show that Q_{xy}^{Flq} becomes independent of the choice of origin as the system approaches the thermodynamic limit. We also analyze the dynamics of a corner mode after a sudden quench, when the C_{4} and T symmetry breaking perturbation is switched off, and find that the corresponding survival probability displays periodic appearances of complete, partial and no revival for long time, encoding the signature of corner modes in a QSHI. Our protocol is sufficiently general to explore the territory of dynamical HOT phases in insulators and gapless systems.

Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal (WSM)-insulator quantum-critical point. But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point. The field-theoretic predictions for the correlation length exponent ν=2 and dynamic scaling exponent z=5/4 at this multicritical point are in good agreement with the ones extracted numerically, yielding ν=1.98±0.10 and z=1.26±0.05, from the scaling of the average density of states (DOS). Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT. We here demonstrate that in the presence of generic but strong disorder, the WSM-metal QPT is ultimately always characterized by the exponents ν=1 and z=3/2 (to one-loop order), originating from intranode or chiral-symmetric (e.g., regular and axial potential) disorder. We here anchor such emergent chiral superuniversality through complementary renormalization-group calculations, controlled via ε expansions, and numerical analysis of average DOS across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy. The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Grüneisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid, are discussed.