Topological States Of Matter Research Articles

Axionlike quasiparticles and topological states of matter: Finite density corrections of the chiral anomaly vertex

We investigate the general structure of the chiral anomaly AVV/AAA and (LLL,RRR) vertices, in the presence of chemical potentials in perturbation theory. The study finds application in anomalous transport, whenever chirally unbalanced matter is present, with propagating external currents that are classically conserved. Examples are topological materials and the chiral magnetic effect in the plasma state of matter of the early universe. We classify the minimal number of form factors of the AVV parametrization, by a complete analysis of the Schouten identities in the presence of a heat bath. We show that the longitudinal (anomaly) sector in the axial-vector channel, for on-shell and off-shell photons, is protected against corrections coming from the insertion of a chemical potential in the fermion loop. When the photons are on-shell, we prove that the transverse sector, in the same channel, is also μ-independent and vanishes. The related effective action is shown to be always described by the exchange of a massless anomaly pole, as in the case of vanishing chemical potentials. The pole is interpreted as an interpolating axionlike quasiparticle generated by the anomaly. In each axial-vector channel, it is predicted to be a correlated fermion/antifermion pseudoscalar (axionlike) quasiparticle appearing in the response function, once the material is subjected to an external chiral perturbation. The cancellation of the μ dependence extends to any chiral current within the Standard Model, including examples such as B (baryon), L (lepton), and B−L. This holds true irrespective of whether these currents exhibit anomalies. Published by the American Physical Society 2024

Fabrication-induced even-odd discrepancy of magnetotransport in few-layer MnBi2Te4

The van der Waals antiferromagnetic topological insulator MnBi2Te4 represents a promising platform for exploring the layer-dependent magnetism and topological states of matter. Recently observed discrepancies between magnetic and transport properties have aroused controversies concerning the topological nature of MnBi2Te4 in the ground state. In this article, we demonstrate that fabrication can induce mismatched even-odd layer dependent magnetotransport in few-layer MnBi2Te4. We perform a comprehensive study of the magnetotransport properties in 6- and 7-septuple-layer MnBi2Te4, and reveal that both even- and odd-number-layer device can show zero Hall plateau phenomena in zero magnetic field. Importantly, a statistical survey of the optical contrast in more than 200 MnBi2Te4 flakes reveals that the zero Hall plateau in odd-number-layer devices arises from the reduction of the effective thickness during the fabrication, a factor that was rarely noticed in previous studies of 2D materials. Our finding not only provides an explanation to the controversies regarding the discrepancy of the even-odd layer dependent magnetotransport in MnBi2Te4, but also highlights the critical issues concerning the fabrication and characterization of 2D material devices.

3D Carbon Allotropes: Topological Quantum Materials with Obstructed Atomic Insulating Phases, Multiple Bulk‐Boundary Correspondences, and Real Topology

AbstractThe study of topological phases with unconventional bulk‐boundary correspondences and nontrivial real Chern number has garnered significant attention in the topological states of matter. Using the first‐principle calculations and theoretical analysis, a high‐throughput material screening of the 3D obstructed atomic insulators (OAIs) and 3D real Chern insulators (RCIs) based on the Samara Carbon Allotrope Database (SACADA) are performed. Results show that 422 out of 703 3D carbon allotropes are 3D OAIs with multiple bulk‐boundary correspondences, including 2D obstructed surface states (OSSs) and 1D hinge states, which are in 1D and 2Ds lower than the 3D bulk, respectively. The 2D OSSs in these OAIs can be modified when subjected to appropriate boundaries, which benefits the investigation of surface engineering and the development of efficient topological catalysts. These 422 OAIs, which have 2D and 1D boundary states, are excellent platforms for multi‐dimensional topological boundaries research. Remarkably, 138 of 422 OAIs are also 3D RCIs, which show a nontrivial real topology in the protection of spacetime inversion symmetry. This work not only provides a comprehensive list of 3D carbon‐based OAIs and RCIs, but also guides their application in various aspects based on multiple bulk‐boundary correspondences and real topological phases.

Half quantized Hall effect

Here we report a half-quantized Hall effect in a metal or semimetal. The Hall conductance is half quantized and the longitudinal conductance is nonzero. Consequently, the Hall resistivity is not quantized. The half quantization occurs when the parity symmetry or time reversal symmetry emerges near the Fermi surface or Fermi level while the symmetry is broken in the whole system. A recent experiment reports the observation of the half-quantized Hall conductance in a magnetically-doped topological insulator. We discover that a single gapless Dirac cone exists in the band structure and has half-quantized conductance when the Fermi level intercepts the gapless surface states in which the parity symmetry is invariant. As there are no localized chiral edge states in the gapless and metallic system, we find that the chiral edge current is carried by the gapless surface states. The current density peaks at the edge and decays in a power law rather than the exponential decay as in the conventional quantum anomalous Hall effect. The half quantized Hall conductance is a signature of parity anomaly in a single gapless Dirac cone on a lattice. We term the nontrivial quantum phase as “parity anomalous semimetal”. The work opens the door to exploring novel topological states of matter with fractional topological invariants.

Single crystal synthesis and characterization of proposed eight-fold degenerate topological material Bi2PdO4

Materials with nonsymmorphic symmetries have numerous applications and have recently come to the forefront as potentially containing novel topological states of matter, such as eight-fold fermions. In this paper, we report the single crystal growth of eight-fold degenerate topological material, Bi2PdO4 via melt-growth technique. The structural properties and chemical composition are confirmed by X-ray diffraction (XRD) and energy-dispersive x-ray analysis studies, respectively. Powder XRD shows that Bi2PdO4 crystallizes in the tetragonal P4/ncc (#130) type structure which is made up of PdO4 square planar units along the c direction. Because of the decreasing trend of magnetization with field, this sample exhibits room temperature diamagnetism. Our temperature dependent resistivity measurement suggests the semiconducting nature of the compound with an estimated band gap of ∼153 meV from Arrhenius fitting. Our Raman spectroscopy data shows peak shifting with decreasing temperature from 300 K to 100 K. Our density functional theory calculation suggests eightfold band crossing at the A point. From our DFT calculations, we determined a band gap of 176 meV in the absence of Spin-Orbit Coupling (SOC) and 180 meV with SOC. This aligns with our experimental observations. Finally, our present study provides a new direction for further transport and spectroscopic investigation in this compound.

In-Gap Edge and Domain-Wall States in Largely Perturbed Phononic Su–Schrieffer–Heeger Lattices

Topological states of matter have attracted significant attention due to their intrinsic wave-guiding and localization capabilities robust against disorders and defects in electronic, photonic, and phononic systems. Despite the above topological features that phononic crystals share with their electronic and photonic counterparts, finite-frequency topological states in phononic crystals may not always survive. In this work, we discuss the survivability of topological states in Su–Schrieffer–Heeger models with both local and non-local interactions and larger symmetry perturbation. Although such a discussion is still about ideal mass-spring models, the insights from this study set the expectations for continuum phononic crystals, which can further instruct the application of phononic crystals for practical purposes.

Doping effects of Kagome superconductor <i>A</i>V<sub>3</sub>Sb<sub>5</sub> (<i>A</i> = K, Rb, Cs)

Material with Kagome lattice provides an excellent platform for studying electronic correlation effects, topological states of matter, unconventional superconductivity, and geometric frustration. The recently discovered Kagome superconductors <i>A</i>V<sub>3</sub>Sb<sub>5</sub> (<i>A</i> = K, Rb, Cs) have attracted widespread attention in the field of condensed matter physics, and many efforts have been made to elucidate their novel physical properties, such as charge density wave, unconventional superconductivity, and band topology. Meanwhile, many groups have effectively tuned these novel properties through chemical doping, offering a good opportunity for further understanding the materials of this system. In this paper, we comprehensively review the latest research progress of the doping effect of this rapidly developed <i>A</i>V<sub>3</sub>Sb<sub>5</sub> system, with the objective of further promoting the in-depth research into Kagome superconductor. Specifically, we review the chemical doping in CsV<sub>3</sub>Sb<sub>5</sub> with elements such as Nb, Ta, Ti, and Sn, and the surface doping with elements Cs or O as well, and describe their influences on the novel quantum properties, especially superconductivity, charge density wave, and electronic band structure of the material. Furthermore, the intricate physical mechanism of doping manipulation is discussed, in order to provide a basic knowledge for further understanding and studying the rich quantum effects of the system, such as charge density waves, time reversal symmetry breaking, and superconductivity.

Electron Beams on the Brillouin Zone: A Cohomological Approach via Sheaves of Fourier Algebras

Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons. This is a continuous topological parameter space bearing the homotopy of a torus. Since the base localization space has the homotopy of a torus, if we vary the quasi-momentum in a direction, when the edge of the zone is reached, we obtain a closed path. Then, if we lift this loop from the base space to the sections of the sheaf-theoretic fibration induced by the localization of the energy eigenfunctions, we obtain a global topological phase factor which encodes the topological structure of the Brillouin zone. Because it is homotopically equivalent to a torus, the global phase factor turns out to be quantized, taking integer values. The experimental significance of this model stems from the recent discovery that there are observable global topological phase factors in fairly ordinary materials. In this communication, we show that it is the unitary representation theory of the discrete Heisenberg group in terms of commutative modular symplectic variables, giving rise to a joint commutative representation space endowed with an integral and Z2-invariant symplectic form that articulates the specific form of the topological conditions characterizing both the quantum Hall effect and the spin quantum Hall effect under a unified sheaf-theoretic cohomological framework.

Macroscopic Quantum Tunneling of a Topological Ferromagnet.

The recent advent of topological states of matter spawned many significant discoveries. The quantum anomalous Hall (QAH) effectis a prime example due to its potential for applications in quantum metrology, as well as its influence on fundamental research into the underlying topological and magnetic states and into axion electrodynamics. Here, electronic transport studies on a (V,Bi,Sb)2 Te3 ferromagnetic topological insulator nanostructure in the QAH regime are presented. This allows access to the dynamics of an individual ferromagnetic domain. The domain size is estimated to be in the 50-100 nm range. Telegraph noise resulting from the magnetization fluctuations of this domain is observed in the Hall signal. Careful analysis of the influence of temperature and external magnetic field on the domain switching statistics provides evidence for quantum tunneling (QT) of magnetization in a macrospin state. This ferromagnetic macrospin is not only the largest magnetic object in which QT is observed, but also the first observation of the effect in a topological state ofmatter.

Valley-Tunable Even-Denominator Fractional Quantum Hall State in the Lowest Landau Level of an Anisotropic System.

Fractional quantum Hall states (FQHSs) at even-denominator Landau level filling factors (ν) are of prime interest as they are predicted to host exotic, topological states of matter. We report here the observation of a FQHS at ν=1/2 in a two-dimensional electron system of exceptionally high quality, confined to a wide AlAs quantum well, where the electrons can occupy multiple conduction-band valleys with an anisotropic effective mass. The anisotropy and multivalley degree of freedom offer an unprecedented tunability of the ν=1/2 FQHS as we can control both the valley occupancy via the application of in-plane strain, and the ratio between the strengths of the short- and long-range Coulomb interaction by tilting the sample in the magnetic field to change the electron charge distribution. Thanks to this tunability, we observe phase transitions from a compressible Fermi liquid to an incompressible FQHS and then to an insulating phase as a function of tilt angle. We find that this evolution and the energy gap of the ν=1/2 FQHS depend strongly on valley occupancy.

Quantum anomalous semimetals

The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far all the topological phases such as integer quantum Hall effect and topological insulators are characterized by integer topological invariants. None is a half integer or fractional. Here we propose a type of semimetals which hosts a single cone of Wilson fermions. The Wilson fermions possess linear dispersion near the Dirac point, but break the chiral or parity symmetry such that an unpaired Dirac cone can be realized on a lattice. In order to avoid the fermion doubling problem, the chiral symmetry or parity symmetry must be broken explicitly if the hermiticity, locality and translational invariance all hold. We find that the system can be classified by the relative homotopy group, and a half-integer topological invariant. We term the nontrivial quantum phase as quantum anomalous semimetal. The work opens the door towards exploring novel states of matter with fractional topological charge.

Feasibility of Kitaev quantum spin liquids in ultracold polar molecules

Ultracold atoms and molecules trapped in optical lattices are expected to serve as simulators of strongly correlated systems and topological states of matter. A fascinating example is to realize the Kitaev quantum spin liquid by using ultracold polar molecules. However, although experimental implementation of the Kitaev-type interaction was proposed, the stability of the Kitaev quantum spin liquid has not been fully investigated thus far. Here we study a quantum spin model with long-range angle-dependent Kitaev-type interactions proposed for the polar molecules, by the pseudofermion functional renormalization group method. We reveal that the ground state is magnetically ordered in both ferromagnetic and antiferromagnetic models regardless of the spatial anisotropy of the interactions, while the isotropic case is most frustrated and closest to the realization of the Kitaev quantum spin liquid. Furthermore, by introducing a cutoff in the interaction range, we clarify how the Kitaev quantum spin liquid is destroyed by the long-range interactions. The results urge us to reconsider the feasibility of the Kitaev quantum spin liquid in ultracold polar molecules.

Uncovering the Kagome Ferromagnet within a Family of Metal-Organic Frameworks.

Kagome networks of ferromagnetically or antiferromagnetically coupled magnetic moments represent important models in the pursuit of a diverse array of novel quantum and topological states of matter. Here, we explore a family of Cu2+-containing metal–organic frameworks (MOFs) bearing kagome layers pillared by ditopic organic linkers with the general formula Cu3(CO3)2(x)3·2ClO4 (MOF-x), where x is 1,2-bis(4-pyridyl)ethane (bpe), 1,2-bis(4-pyridyl)ethylene (bpy), or 4,4′-azopyridine (azpy). Despite more than a decade of investigation, the nature of the magnetic exchange interactions in these materials remained unclear, meaning that whether the underlying magnetic model is that of an kagome ferromagnet or antiferromagnet is unknown. Using single-crystal X-ray diffraction, we have developed a chemically intuitive crystal structure for this family of materials. Then, through a combination of magnetic susceptibility, powder neutron diffraction, and muon-spin spectroscopy measurements, we show that the magnetic ground state of this family consists of ferromagnetic kagome layers that are coupled antiferromagnetically via their extended organic pillaring linkers.

Topological Corner States in Non-Unitary Coinless Discrete-Time Quantum Walks

The discrete-time quantum walk provides a versatile platform for exploring abundant topological phenomena due to its intrinsic spin-orbit coupling. In this work, we study the non-Hermitian second-order topology in a two-dimensional non-unitary coinless discrete-time quantum walk, which is realizable in the three-dimensional photonic waveguides. By adding the non-unitary gain-loss substep operators into the one-step operator of the coinless discrete-time quantum walk, we find the appearance of the four-degenerate zero-dimensional corner states at ReE = 0 when the gain-loss parameter of the system is larger than a critical value. This intriguing phenomenon originates from the nontrivial second-order topology of the system, which can be characterized by a second-order topological invariant of polarizations. Finally, we show that the exotic corner states can be observed experimentally through the probability distributions during the multistep non-unitary coinless discrete-time quantum walks. Our work potentially pave the way for exploring exotic non-Hermitian higher-order topological states of matter in coinless discrete-time quantum walks.

Quantum materials out of equilibrium

Illuminating materials with lasers can create intriguing magnetic and topological states of matter..

Brillouin Klein bottle from artificial gauge fields

A Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under {{mathbb{Z}}}_{2} gauge fields, i.e., hopping amplitudes with phases ±1, the fundamental domain of momentum space can assume the topology of a Klein bottle. This drastic change of the Brillouin zone theory is due to the projective symmetry algebra enforced by the gauge field. Remarkably, the non-orientability of the Brillouin Klein bottle corresponds to the topological classification by a {{mathbb{Z}}}_{2} invariant, in contrast to the Chern number valued in {mathbb{Z}} for the usual Brillouin torus. The result is a novel Klein bottle insulator featuring topological modes at two edges related by a nonlocal twist, radically distinct from all previous topological insulators. Our prediction can be readily achieved in various artificial crystals, and the discovery opens a new direction to explore topological physics by gauge-field-modified fundamental structures of physics.

Coexistence of multiple Weyl fermions and quantum anomalous Hall effect in 2D half-metallic Cr2NT2

Topological state in two-dimensional (2D) magnetic system has attracted widespread attention due to its potential application in spintronics and quantum computing fields. As a novel topological states of matter, Weyl semimetals with multiple topological phases have been studied. However, realizing multiple topological phases in 2D magnetic system and studying their entanglement still face great challenges. In this work, using first-principles calculations, we predict that 2D monolayer Cr2NT2 (T = -OH, -F, =O) has multiple Weyl fermions (WFs) and large spin-down gap. Ferromagnetic ground states of monolayer Cr2NT2meet the dynamic, thermal and mechanical stabilities. Without spin-orbit coupling (SOC), these WPs are fully spin-polarized. When considering SOC, apart from WP3 in Cr2NO2, all WPs are opened the gap, and the chiral edge states are observed in Cr2NT2. In particular, there is a quantum anomalous Hall effect in Cr2NF2. Further, a biaxial strain in the a-b plane leads to the emergence of rich topological phases without SOC. In addtion, an effective four-band tight-binding model is constructed to clarify the origin of WFs in the non-trivial band topology. Finally, we calculate the Berry curvature and abnormal Hall conductivity of Cr2NT2, and find that they are a non-zero energy points around the Fermi level, indicating that monolayer Cr2NT2 are promising candidates for spintronic applications. Therefore, it is necessary to explore 2D magnetic materials with multiple types of WFs and QAH phases.

Global and local topological quantized responses from geometry, light, and time

To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square (${C}^{2}$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this ${C}^{2}$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the ${\mathbb{Z}}_{2}$ topological number robust to interactions can be measured locally from a correspondence between the Pfaffian and light. We address a relation with a spin pump and the quantum spin Hall conductance. The analogy between light and magnetic nuclear resonance may be applied for imaging, among other applications.

Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains

Floquet spin chains have been a venue for understanding topological states of matter that are qualitatively different from their static counterparts by, for example, hosting π edge modes that show stable period-doubled dynamics. However the stability of these edge modes to interactions has traditionally required the system to be many-body localized in order to suppress heating. In contrast, here we show that even in the absence of disorder, and in the presence of bulk heating, π edge modes are long lived. Their lifetime is extracted from exact diagonalization and is found to be non-perturbative in the interaction strength. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace. In this subspace, the π edge mode manifests as the quasi-stable edge mode of an inhomogeneous Su-Schrieffer-Heeger model whose dimerization vanishes in the bulk of the Krylov chain.

Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers

Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles:~the Fubini-Study metric, which introduces a notion of distance between quantum states defined over a parameter space, and the Berry curvature associated with Berry-phase effects and topological band structures. In fact, recent studies have revealed direct relations between these two important quantities, suggesting that topological properties can, in special cases, be deduced from the quantum metric. In this work, we establish general and exact relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians. In particular, we demonstrate that topological indices (Chern numbers or winding numbers) are bounded by the quantum volume determined by the quantum metric. Our theoretical framework, which builds on the Clifford algebra of Dirac matrices, is applicable to topological insulators and semimetals of arbitrary spatial dimensions, with or without chiral symmetry. This work clarifies the role of the Fubini-Study metric in topological states of matter, suggesting unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.