本研究通过重整化群计算证明，弱无序（化学势型或磁性型）能诱导三维金属节结相发生相变，产生不同结拓扑，并可通过结 Wilson loop 积分等拓扑不变量定量表征，为无序调控节结拓扑开辟了新途径。
摘要：
在特定对称性下，三维金属中的简并点形成一维节线。这些节线有时会展现出复杂的打结结构，并已在各种背景下被研究。作为最常见的物理扰动之一，无序效应通常会引发新颖的量子相变。对于节结相而言，无序能否驱动结相变仍是一个悬而未决且引人入胜的问题。采用重整化群计算，我们证明了在弱无序存在时节结相变会涌现。具体而言，化学势型无序和磁性型无序均能诱导结相变，导致不同结拓扑的涌现。该相变可以通过拓扑不变量的变化（如结 Wilson loop 积分）进行定量表征。我们的发现为通过无序效应调控节结相的拓扑开辟了新途径。
英文摘要：
Under certain symmetries, degenerate points in three-dimensional metals form one-dimensional nodal lines. These nodal lines sometimes exhibit intricate knotted structures and have been studied in various contexts. As one of the most common physical perturbations, disorder effects often trigger novel quantum phase transitions. For nodal-knot phases, whether disorder can drive knot transitions remains an open and intriguing question. Employing renormalization-group calculations, we demonstrate that nodal-knot transitions emerge in the presence of weak disorder. Specifically, both chemical-potential-type and magnetic-type disorders can induce knot transitions, resulting in the emergence of distinct knot topologies. The transition can be quantitatively characterized by changes in topological invariants such as the knot Wilson loop integrals. Our findings open up a new avenue for manipulating the topology of nodal-knot phases through disorder effects.
With its boundary tracing out a link or knot in 3D, the Seifert surface is a 2D surface of core importance to topological classification. We propose the first-ever experimentally realistic setup where Seifert surfaces emerge as the boundary states of 4D topological matter. Unlike ordinary real space knots that exist in polymers, biomolecules and everyday life, our knots and their Seifert surfaces exist as momentum space nodal structures, where topological linkages have profound effects on optical and transport phenomena. Realized with 4D circuit lattices, our nodal Seifert systems are freed fr…
Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line re…
Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological "drumhead" surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partne…
Topological nodal line semimetals host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this paper, we use the Jones polynomial as a general topological invariant to capture the global knot topology of the nodal lines. We show that every possible change in Jones polynomial is attributed to the local evolutions around every point where two nodal lines touch. As an application of our theory, we show that nodal chain semimetals with four touching points can evolve to a Hopf-link. We extend our theory to 3D non-Hermitian multi-band exceptional line…
We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the dissipative non-Hermitian realm where the knotted nodal lines are generic and thus stable towards any small perturbation. We show that these nodal structures, taking the forms of Turk's head knots, appear in both continuum- and lattice models with relatively short-ranged hopping that is within experimental reach. To determine the topology of the nodal structures, we d…
Non-Hermitian nodal knot metals (NKMs) contains intricate complex-valued energy bands gives rise to knotted exceptional loops and new topological surface states. We introduce a formalism that connects the algebraic, geometric, and topological aspects of these surface states with their parent knots, and provide an optimized constructive ansatz for tight-binding models for non-Hermitian NKMs of arbitrary knot complexity and minimal hybridization range. Specifically, various representative non-Hermitian torus knots Hamiltonians are constructed in real-space, and their nodal topologies studied via…
We show that topological nodal points can emerge in photonic crystal possessing mirror symmetry. The mechanism of generating topological nodal points is discussed in a two-dimensional photonic square lattice, in which four topological nodal points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The topological nodes can be unbuckled through breaking the mirror symmetry and a photonic Chern insulator can …
Topological semimetal phases in two-dimensional (2D) materials have gained widespread interest due to their potential applications in developing nanoscale devices. Despite the prediction of the Dirac/Weyl points in a wide variety of 2D candidates, materials featuring topological nodal lines are still in great scarcity. Herein, we predict two stable thinnest films of aluminum diboride with hyper- and hypo-stoichiometries of Al$_2$B$_2$ and AlB$_4$ as new 2D nonmagnetic Dirac nodal line semimetals (NLSMs) which promise to offer many novel features. Our elaborate electronic structure calculations…
Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the 3D Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. In this work, we investigate the semi-classical optical response of two nodal loops in linked, unlinked and touching configurations, focusing particularly on the interplay of response anisotropy and non-linearity. We provide a geometric picture that unifies these aspects and sheds light on…
Nodal lines are symmetry-protected one-dimensional band degeneracies in momentum space, which can appear in numerous topological configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian topological physics has been proposed in space-time inversion (PT) symmetric systems, and attract widespread attention. One of the most special configurations in non-Abelian system is the earring nodal link, composing of a nodal chain linking with an isolated nodal line, is signature of non-Abelian topology and cannot be elucidated using Abelian topological classifications. Howev…
The existence and topological classification of lower-dimensional Fermi surfaces is often tied to the crystal symmetries of the underlying lattice systems. Artificially engineered lattices, such as heterostructures and other superlattices, provide promising avenues to realize desired crystal symmetries that protect lower-dimensional Fermi surface, such as nodal lines. In this work, we investigate a Weyl semimetal subjected to spatially periodic onsite potential, giving rise to several phases, including a nodal-line semimetal phase. In contrast to proposals that purely focus on lattice symmetri…
A nodal link is a special form of a line degeneracy (a nodal line) between adjacent bands in the momentum space of a three-dimensional topological crystal. Unlike nodal chains or knots, a nodal link consists of two or more mutually-linked rings that do not touch each other. Recent studies on non-Abelian band topology revealed that the topological charges of the nodal links can have the properties of quaternions. However, a photonic crystal that has a nodal link with non-Abelian charges has not been reported. Here, we propose dielectric photonic crystals in forms of double diamond structures wh…
In periodic systems, nodal lines are loops in the three-dimensional momentum space where two bands are degenerate with each other. Nodal lines exhibit rich topological features as they can take various configurations such as rings, links, chains and knots. These line nodes are usually protected by mirror or PT symmetry. Here we propose and demonstrate a novel type of photonic straight nodal lines in a D2d meta-crystal which are protected by roto-inversion time (roto-PT) symmetry. The nodal lines are located at the central axis and hinges of the Brillouin zone. They appear as quadrupole sources…
A family of topological semimetallic phases where twofold degenerate gapless points form linked rings is introduced. We refer to this phase as Weyl-link semimetals. A concrete two-band model with two linked nodal lines is constructed. We demonstrate that the Chern-Simons 3-form depends on the linking number of rings in a generic two-band model. In addition, we show the emergence of zero-energy modes in the Landau level spectrum can reveal the location of nodal lines, providing a method of probing their linking number.
In nodal-line semimetals, the gaps close along loops in ${\bf k}$ space, which are not at high-symmetry points. Typical mechanisms for the emergence of nodal lines involve mirror symmetry and the $π$ Berry phase. Here, we show via ab initio calculations that fcc calcium (Ca), strontium (Sr) and ytterbium (Yb) have topological nodal lines with the $π$ Berry phase near the Fermi level, when spin-orbit interaction is neglected. In particular, Ca becomes a nodal-line semimetal at high pressure. Owing to nodal lines, the Zak phase becomes either $π$ or 0 depending on the wavavector ${\bf k}$, and t…
Three-dimensional (3D) Weyl and Dirac semimetals garner considerable attention in condensed matter physics due to the exploration of entirely new topological phases and related unconventional surface states. Nodal line and ring semimetals on the other hand can facilitate 3D band crossings characterized by nontrivial links such as coupled chains and knots that are protected by the underlying crystal symmetry. Experimental complexities, detrimental effects of the spin-orbit interaction, along with the merging of the underlying surface states into the bulk pose great challenges for growing advanc…
Weyl semimetals and nodal line semimetals are characterized by linear band touching at zero-dimensional points and one-dimensional lines, respectively. We predict that a circularly polarized light drives nodal line semimetals into Weyl semimetals. The Floquet Weyl points thus obtained are tunable by the incident light, which enables investigations of them in a highly controllable manner. The transition from nodal line semimetals to Weyl semimetals is accompanied by the emergence of a large and tunable anomalous Hall conductivity. Our predictions are experimentally testable by transport measure…
It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that, in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell's equation…
We show theoretically that a heterostructure of monolayer FeTe$_{1-x}$Se$_x$ - a superconducting quantum spin Hall material - with a monolayer of FeTe - a bicollinear antiferromagnet - realizes a higher order topological superconductor phase characterized by emergent Majorana zero modes pinned to the sample corners. We provide a minimal effective model for this system, analyze the origin of higher order topology, and fully characterize the topological phase diagram. Despite the conventional s-wave pairing, we find rather surprising emergence of a novel topological nodal superconductor in the p…
Confinement-induced Majorana modes in a nodal topological superconductor
Università degli studi di Genova（热那亚大学）；SPIN-CNR, Consiglio Nazionale delle Ricerca（意大利国家研究委员会自旋物理中心）；University of Würzburg（维尔茨堡大学）；Technische Universität Braunschweig（布伦瑞克工业大学）
We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with $d_Q>0$. As a demonstrative example, we relate a two dimensional anisotropic semimetal with $d_L=d_Q=1$, describing the topological transition between a Dirac semimetal and a normal insulator, and its three dimensional counterparts with $d_L=1$, $d_Q=2$. We address the quant…
Persistent nonlinear Hall effect driven by parallel field across a topological phase transition and intraband sign-reversing integer quantum Hall effect
Discovery of an Antiferromagnetic Topological Nodal-line Kondo Semimetal
Beijing Normal University（北京师范大学）；Zhejiang University（浙江大学）；Donostia International Physics Center (DIPC)（多诺斯蒂亚国际物理中心）；University of Oxford（牛津大学）；Diamond Light Source（钻石光源）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Nanjing University（南京大学）；ShanghaiTech University（上海科技大学）；Tsinghua University（清华大学）；MAX IV Laboratory, Lund University（隆德大学MAX IV实验室）；Stanford Synchrotron Radiation Light Source, SLAC National Accelerator Laboratory（斯坦福同步辐射光源，SLAC国家加速器实验室）；Swiss Light Source, Paul Scherrer Institute（瑞士光源，保罗谢尔研究所）；Tokyo Institute of Technology（东京工业大学）；Princeton University（普林斯顿大学）
Electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing 'forbidden' symmetries via quasiperiodic ordering with low-dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional chalcogenide quasicrystal and approximant, and investigate associated electronic and topological properties. Ultra-thin two-dimensional layers of the materials with a composition close to Ta1.6Te, derived from a layered transition metal dichalcogenide, are iso…
Quasiparticle excitations of free electrons in condensed-matter physics, characterized by the dimensionality of the band crossing, can find their elementary-particle analogs in high-energy physics, such as Majorana, Weyl, and Dirac fermions. While crystalline symmetry allows more quasiparticle excitations and exotic fermions to emerge. Using symmetry analysis and {\it ab-initio} calculations, we propose that the 3D honeycomb crystal NaCu$_3$Te$_2$ hosts triply degenerate nodal points (TDNPs) which are perfectly separated from the bulk states. We find a tunable phase transition between TDNPs an…
