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Dynamical quantum phase transitions (DQPTs) can occur following quenches in quantum systems when the rate function, a dynamical analogue of the free energy, becomes non-analytic at critical times. Here we exhaustively investigate in an exemplary model how the dynamically evolving state responds to a second quench. We demonstrate that for quenches where the initial and final Hamiltonian belong to different phases always result in DQPTs, irrespective of the intermediate quench and dynamics or the time of the second quench. However, if the initial and final Hamiltonian belong to the same equilibrium phase then the intermediate Hamiltonian must belong to a different phase. In this case, the second quench time in relation to the critical times of the first quench becomes crucial to the existence of DQPTs.

Wepropose a scheme realizing topological insulators and quantized pumps for magnon excitations, based on strongly-interacting two-component ultracold atoms trapped in optical superlattices. Specifically, we show how to engineer the Su–Schrieffer–Heeger model for magnons using state-independent superlattices, and the Rice-Mele model using state-dependent superlattices. We describe realistic experimental protocols to detect the topological signatures of magnon excitations in these two models. In particular, we show that the non-equilibrium dynamics of a single magnon can be exploited to directly detect topological winding numbers and phase transitions. We also describe how topological (quantized) pumps can be realized with magnons, and study how this phenomenon depends on the initial magnon state preparation. Our study opens a new avenue for exploring magnonic topological phases of matter and their potential applications in the context of topological magnon transport.

We present a complete quantization of Lorentzian gravity with cosmological constant, coupled to a set of topological matter fields. The approach of loop quantum gravity is used thanks to a partial gauge fixing leaving a residual gauge invariance under a compact semi-simple gauge group, namely Spin(4) = SU(2) × SU(2). A pair of quantum observables is constructed, which are non-trivial despite being gauge-equivalent to zero at the classical level. A semi-classical approximation based on appropriately defined coherent states shows non-vanishing expectation values for them, thus not reproducing their classical behaviour. [ABSTRACT FROM AUTHOR]

Guiding energy deliberately is one of the central elements in engineering and information processing. It is often achieved by designing specific transport channels in a suitable material. Topological metamaterials offer a way to construct stable and efficient channels of unprecedented versatility. However, due to their stability it can be tricky to terminate them or to temporarily shut them off without changing the material properties massively. While a lot of effort was put into realizing mechanical topological metamaterials, almost no works deal with manipulating their edge channels in sight of applications. Here, we take a step in this direction, by taking advantage of local symmetry breaking potentials to build a switchable topological phonon channel.

Topological matter in three dimensions (3D) is characterized by the presence of a topological BF term in its long-distance effective action. We show that, in 3D, there is another marginal term that must be added to the action in order to fully determine the physical content of the model. The quantum phase structure is governed by three parameters that drive the condensation of topological defects: the BF coupling, the electric permittivity and the magnetic permeability of the material. For intermediate levels of electric permittivity and magnetic permeability, the material is a topological insulator. We predict, however, new states of matter when these parameters cross critical values: a topological superconductor when the electric permittivity is increased and the magnetic permeability is lowered and a charge confinement phase in the opposite case of low electric permittivity and high magnetic permeability. Synthetic topological matter may be fabricated as 3D arrays of Josephson junctions. [ABSTRACT FROM AUTHOR]

We study two-dimensional topological gauge theories with gauge group equal to the symmetric group Sn and their string theory duals. The simplest such theory is the topological quantum field theory of principal Sn fiber bundles. Its correlators are equal to Hurwitz numbers. The operator products in the gauge theory for each finite value of n are coded in one partial permutation algebra. We propose a generalization of the partial permutation algebra to the symmetric orbifold topological quantum field theory of any seed theory and show that the theory factorizes into marked partial permutation combinatorics and seed Frobenius algebra properties. Moreover, we exploit the established correspondence between Hurwitz theory and the stationary sector of Gromov–Witten theory on the sphere to prove an exact gauge/string duality. The relevant field theory is a grand canonical version of Hurwitz theory and its two-point functions are obtained by summing over all values of the instanton degree of the maps covering the sphere. We stress that one must look for a multiplicative basis on the boundary to match the bulk operator algebra of single string insertions. The relevant boundary observables are completed cycles. [ABSTRACT FROM AUTHOR]

The long fascination that antiferromagnetic materials has exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena, including various classes of anomalous spin and charge Hall effects and unconventional magnonic transport, and also homochiral magnetic entities such as skyrmions. With these breakthroughs, antiferromagnets stand out as a rich playground for the investigation of novel topological behavior, and as promising candidate materials for disruptive low-power microelectronic applications. Remarkably, the newly discovered phenomena are all related to the topology of the magnetic, electronic or magnonic ground state of the antiferromagnets. This review exposes how non-trivial topology emerges at different levels in antiferromagnets and explores the novel mechanisms that have been discovered recently. We also discuss how novel classes of quantum magnets could enrich the currently expanding field of antiferromagnetic spintronics and how spin transport can in turn favor a better understanding of exotic quantum excitations. [ABSTRACT FROM AUTHOR]

We consider the system of two parallel sheets of graphene which are moving with relative parallel velocity v ⃗ and calculate the Casimir energy by using the scattering approach. We analyze in detail the normal (perpendicular to the planes) Casimir force for two systems—graphene/graphene and ideal metal/graphene. In the non-relativistic case v ≪ v F, the relative correction to the Casimir energy (E v − E 0) / E 0 is proportional to the (v / c)2 (the maximum value is 0.0033 for the gapeless case and v = v F) for the first system, and it is zero up to the Fermi velocity v = v F for system ideal metal/graphene. [ABSTRACT FROM AUTHOR]

A Dirac operator on the plane with constant (positive) mass is a Chern insulator, sitting in class D of the Kitaev table. Despite its simplicity, this system is topologically ill-behaved: the non-compact Brillouin zone prevents definition of a bulk invariant, and naively placing the model on a manifold with boundary results in violations of the bulk-edge correspondence (BEC). We overcome both issues by letting the mass spatially vary in the vertical direction, interpolating between the original model and its negative-mass counterpart. Proper bulk and edge indices can now be defined. They are shown to coincide, thereby embodying BEC. The shallow-water model exhibits the same illnesses as the 2D massive Dirac. Identical problems suggest identical solutions, and indeed extending the approach above to this setting yields proper indices and another instance of BEC. [ABSTRACT FROM AUTHOR]

Non-Hermitian Hamiltonians effectively describing the physics of open systems have become an important tool in various physical platforms, such as photonics, mechanical systems, and electric circuits. The study of non-Hermitian states in electric circuits is developing rapidly recently and forming the field of topoelectrical circuits. Here, we report on the theoretical realization of a higher-order exceptional points (EPs) topological circuit induced by gain and loss. It is shown that, by tuning the value of the positive and negative resistors in the circuit, EPs can collide and merge leading to higher-order singularities. We observe the different energy-difference conserving dynamics near the EPs and the enhanced sensitivity at higher-order EPs. Our results show a way to get higher sensitivity in a non-Hermitian electrical circuit. [ABSTRACT FROM AUTHOR]

In this paper, we consider the quantization of the 2D BF model coupled to topological matter. Guided by the rigid supersymmetry, this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of loop quantum gravity methods. [ABSTRACT FROM AUTHOR]

Unmovable nodal points (UNPs) and lines (UNLs) are band crossings whose positions in the Brillouin zone are unaltered by symmetry preserving perturbations. Not only positions but also the band structure in their vicinity are determined by the little group of wave vectors and its irreducible (co)representations. In this paper, we give the full set of electronic dispersions near all UNPs and UNLs in non-magnetic quasi two-dimensional (2D) materials, both with and without spin–orbit coupling (SOC). Analysis of all layer gray single and double groups gives nineteen different quasiparticles, the great majority of which are unavoidable for a 2D material that belongs to a certain layer group. This includes Weyl and Dirac nodal lines, dispersions with quadratic or cubic splitting, anisotropic Weyl and Dirac cones, whose orientation can be varied by e.g. strain etc. We indicated quasiparticles that are robust to SOC. For convenience, our results are concisely presented graphically—as a map, not in a tabular, encyclopedia form. They may be of use as checkpoints and/or for fitting experimentally (via e.g. ARPES) and numerically obtained electronic band structures data, as well as for deeper theoretical investigations. [ABSTRACT FROM AUTHOR]

We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip, using boundary conditions to investigate the influence of finite-size effects on the Hall conductivity. By exploiting the translation symmetry along the strip, we determine both the general spectral properties of the system for a large class of boundary conditions respecting such symmetry, and the full spectrum for (fibered) Robin boundary conditions. In particular, we find that the latter introduce a new kind of states with no classical analogues, and add a finer structure to the quantization pattern of the Hall conductivity. Moreover, our model also predicts the breakdown of the quantum Hall effect at high values of the applied electric field. [ABSTRACT FROM AUTHOR]

Topological spin textures as an emerging class of topological matter offer a medium for information storage and processing. The recently discovered topological Hall effect (THE) is considered as a fingerprint for electrically probing the Dzyaloshinskii–Moriya (DM) interaction and corresponding non-trivial spin-textures. In this paper, the THE and its electrical control are observed in ultrathin (⩽8 unit cells. u.c.) 4D ferromagnetic SrRuO3 films grown on SrTiO3(0 0 1) substrates, indicating the existence of gate-bias-tunable DM interaction in the single SrRuO3 layer without contacting 5D oxide SrIrO3 layer. High-resolution lattice structure analysis revealed that the interfacial RuO6 octahedral tilting induced by local orthorhombic-to-tetragonal structural phase transition exists across the SrRuO3/SrTiO3 interface, which naturally breaks the inversion symmetry. Our theoretical calculations demonstrate that the DM interaction arises owing to the broken inversion symmetry and strong spin–orbit interaction of 4D SrRuO3. This interfacial RuO6 octahedral tilting-induced DM interaction can stabilize the Néel-type magnetic skyrmions, which in turn accounts for the observed THE in transport. Besides the fundamental significance, the understanding of THE in oxides and its electrical manipulation presented in this work could advance the low power cost topological electronic and spintronic applications. [ABSTRACT FROM AUTHOR]

Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang–Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga–Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology. [ABSTRACT FROM AUTHOR]

It is proposed that a lattice, with constituent masses and spring constants, may be considered as a model system for topological matter. For instance, a relative variation of the inter- and intra-unit cell spring constants can be used to create, tune, and invert band structure. Such an aspect is obtained while preserving time reversal symmetry, and consequently emulates the quantum spin Hall effect. The modal displacement fields of the mass-spring lattice were superposed so to yield pseudospin fields, with positive or negative group velocity. Considering that harmonic oscillators are the basis of classical and quantum excitations over a range of physical systems, the spring-mass system yields further insight into the constituents and possible utility of topological material. [ABSTRACT FROM AUTHOR]

Quasiparticles are a powerful concept of condensed matter quantum theory. In this review, the appearence and the properties of quasiparticles are presented in a unifying perspective. The principles behind the existence of quasiparticle excitations in both quantum disordered and ordered phases of fermionic and bosonic systems are discussed. The lifetime of quasiparticles is considered in particular near a continuous classical or quantum phase transition, when the nature of quasiparticles on both sides of a transition into an ordered state changes. A new concept of critical quasiparticles near a quantum critical point is introduced, and applied to quantum phase transitions in heavy fermion metals. Fractional quasiparticles in systems of restricted dimensionality are reviewed. Dirac quasiparticles emerging in so-called Dirac materials are discussed. The more recent discoveries of topologically protected chiral quasiparticles in topological matter and Majorana quasiparticles in topological superconductors are briefly reviewed. [ABSTRACT FROM AUTHOR]

SrRuO3 (SRO)-based heterostructures have attracted much attention for potential applications such as electrodes, oxide spintronics, topological electronics and electrocatalytic function mainly due to the strong spinâ€"orbit coupling, itinerant ferromagnetism with 4 d electrons, high metallic conductivity, perpendicular magnetic anisotropy and rich oxygen octahedral distortion of SRO. Here, this work aims to offer a timely and systematic review on SRO-based heterostructures for its emerging opportunities in oxide spintronic and topological electronic applications. We first present a brief summary of the current status in SRO-based heterostructures and describe the motivations of this review. We then briefly review the surface and interface modulation in SRO-based heterostructures, including oxygen octahedral distortions (antiferrodistortive mode and ferroelectric mode) engineering and ion defect engineering. In the third part, we discuss the spin-charge interconversion phenomena in SRO-based heterostructures, covering the inverse spin Hall effect and current-induced spin-orbit torques. Particularly, in the fourth part, we discuss the emergent topological Hall effect and underlying mechanism in SRO-based heterostructures, including the two-channel anomalous Hall effect and Berry phase manipulation. The fifth part presents the magnetic Weyl fermions and its electric-field control of SRO films. We finally conclude with a discussion of challenges and prospects of SRO-based heterostructures, which provides a guidance for exploring novel physical properties and designing multifunctional devices based on SRO. [ABSTRACT FROM AUTHOR]

Among ultrathin monoelemental two-dimensional (2D) materials, bismuthene, the single layer of heavier group-VÎ' element bismuth (Bi), has been predicted to have large non trivial gap. Here, we demonstrate the growth of Bi films by molecular beam epitaxy on 2D-HfTe2 template. At the initial stage of Bi deposition (1â€"2 bilayers, BL), both the pseudocubic Bi(110) and the hexagonal Bi(111) phases are formed. When reaching 3 BL Bi, a transformation to pure hexagonal Bi(111) occurs. The electronic band structure of 3 BL Bi(111) films was measured by angle-resolved photoemission spectroscopy showing very good matching with the density functional theory band structure calculations of 3 BL free standing Bi(111). The grown Bi(111) thin film was capped with a protective Al2O3 layer and its stability under ambient conditions, necessary for practical applications and device fabrication, was confirmed by x-ray photoelectron spectroscopy and Raman spectroscopy. [ABSTRACT FROM AUTHOR]

Three-dimensional topological insulator (3D TI) nanowires display remarkable magnetotransport properties that can be attributed to their spin-momentum-locked surface states such as quasiballistic transport and Aharonov–Bohm oscillations. Here, we focus on the transport properties of a 3D TI nanowire with a gated section that forms an electronic Fabry–Pérot (FP) interferometer that can be tuned to act as a surface-state filter or energy barrier. By tuning the carrier density and length of the gated section of the wire, the interference pattern can be controlled and the nanowire can become fully transparent for certain topological surface-state input modes while completely filtering out others. We also consider the interplay of FP interference with an external magnetic field, with which Klein tunneling can be induced, and transverse asymmetry of the gated section, e.g. due to a top-gated structure, which displays an interesting analogy with Rashba nanowires. Due to its rich conductance phenomenology, we propose a 3D TI nanowire with gated section as an ideal setup for a detailed transport-based characterization of 3D TI nanowire surface states near the Dirac point, which could be useful towards realizing 3D TI nanowire-based topological superconductivity and Majorana bound states. [ABSTRACT FROM AUTHOR]

Weyl semimetals are prominent examples of topologically protected quantum matter. These materials are the three-dimensional counterparts of graphene and great efforts are being devoted to achieve a thorough understanding of their fundamental physics. In this work, we aim at contributing to this end by discussing the effect of a single magnetic impurity in Weyl semimetals as a first step towards considering a larger number of point-like impurities. We find that resonances appear in the local density of states (LDOS) with a Friedel-like behaviour, oscillating as a function of distance. By studying the spin-resolved LDOS, we can observe non-trivial and anisotropic spin textures where the spin components perpendicular to the spin of the impurity wind around the latter, until the spin becomes completely parallel to the impurity right at the impurity's location. Friedel oscillations also play a relevant role in the form of the spin textures, forming an oscillatory pattern. We believe our results can pave the way to further studies which consider the presence of a large number of random magnetic impurities. [ABSTRACT FROM AUTHOR]

The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena—topological phases and dynamical quantum phase transitions (DQPTs)—in non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the critical momenta and critical time of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su–Schrieffer–Heeger model. Finally, we suggest a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond. [ABSTRACT FROM AUTHOR]

Majorana bound states (MBSs) can occur in Josephson junctions of conventional s-wave superconductors coupled via a strong topological insulator. In configurations of multiple line junctions meeting at a point, the criterion for the MBS to exist coincides with the presence of a fractional Josephson vortex with 2π phase winding. We investigate the dynamic stability of such vortices in arrays of tri- and quad-junctions. The existence of fractional vortices in arrays is demonstrated, but the dynamic stability is found to depend critically on the current-phase relation and the inductance. We propose the idea, and study the feasibility, of manipulating the location of the vortices in arrays by using current pulses, compatible with rapid single flux quantum technology. It is shown theoretically, using a modified resistively shunted junction model, that braiding operations can be achieved using current pulses injected from the edge of the array. It is necessary to use vortex sites with elevated critical current as traps. [ABSTRACT FROM AUTHOR]

We theoretically studied the corner states in photonic Kagome lattice with long-range interactions. Literature has confirmed that such model supports zero-energy corner states and finite-energy corner states known as type-II corner states. In this paper, through careful research, we found that there is another new type of finite-energy corner state in this system. By using the approximation method, we realized that the addition of long-range interactions causes coupling between topological edge states, which in turn makes these finite-energy corner states split from the edge states. Moreover, these finite-energy corner states are not located on the corners, but around the corners. And they are immune to the disorder in coupling strengths. Thus we call them topological bounded corner states. Our work reveals a way to generate bounded corner states by the long-range interactions, which offers a way for designing novel bounded devices. [ABSTRACT FROM AUTHOR]

Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory. [ABSTRACT FROM AUTHOR]