Nontrivial Topological Phase Research Articles

Majorana Bound States Hallmarks in a Quantum Topological Interferometer Ring

AbstractIn this work, the conductance and current correlations properties of a quantum topological interferometer consisting of a quantum dot coupled to two Majorana bound states (MBSs) confined at both ends of a 1D topological superconductor ring nanowire is investigated. The ring in its topological nontrivial and trivial phases is analyzed to show that the tunneling conductance, shot noise, and Fano factor present unique characteristics to distinguish the hallmark of MBSs. The findings are reinforced by taking advantage of the full correspondence between the quantum topological interferometer and a quantum‐dot effectively coupled to a single Majorana state in a straight topological superconductor wire configuration. It is shown that besides the characteristic zero‐bias conductance and the already known shot noise features, the Fano factor provides significant information to distinguish the MBSs presence.

Experimental demonstration of a reconfigurable acoustic second-order topological insulator using condensed soda cans array

Traditional topological insulators support the topologically protected boundary states that are one dimension lower than the system itself. Recently, higher-order topological insulators have received increasing attention in the field of acoustic wave manipulation due to their unique bulk-boundary correspondence principle, hosting both gapped edge states and in-gap corner states simultaneously. However, for most of the topological acoustic systems, the lack of reconfigurability and the inevitable outer trivial regions with considerable thickness restrict the potential applications of acoustic topological insulators. Here, we experimentally demonstrate a reconfigurable condensed acoustic second-order topological insulator in free space by using subwavelength soda cans whose side length is significantly reduced to 1.89 times of the corresponding wavelength. The topological nontrivial phase is introduced through tunably modulating the interval between cans. Without the typically required outer trivial regions, we observe the topological corner states at the corner of the finite structures in both simulations and experiments. Furthermore, the robustness against the defects induced by dislocations and deformations is discussed. We foresee that the proposal may facilitate the application potentials of topological acoustics in low-frequency sound manipulations.

Crossdimensional universality classes in static and periodically driven Kitaev models

The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts crossdimensional universality classes: although the static Kitaev model is defined on a two-dimensional (2D) honeycomb lattice, its criticality falls into the universality class of one-dimensional (1D) linear Dirac models. For the periodically driven Kitaev model, in addition to the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.

Anomalous viscosity of a chiral two-orbital superconductor in tight-binding model

We study the linear response of the deformation potential of a chiral two-orbital superconductor Sr $$_2$$ RuO $$_4$$ to the applied strain. This response rises due to the strain-induced modified interatomic distances. In the linear response theory, the deformation potential–deformation potential correlation function defines the full complex frequency-dependent viscosity tensor. We calculate the anti-symmetric part of this tensor, the phonon Hall viscosity, to consider the static and dynamical Hall responses. The static phonon Hall static enables us to distinguish the different topological phases of Sr $$_2$$ RuO $$_4$$ . We focus on two regimes: (a) the phonon Hall viscosity due to the changes in the hopping energies of the tight-binding Hamiltonian and is termed the normal phonon Hall viscosity and (b) the phonon Hall viscosity due to the variation in the amplitudes of the order parameter of the superconducting state that causes an anomalous momentum transport coefficient and is analogous to the one-dimensional odd isotropic part of the viscosity tensor of an incompressible fluid in two dimension space. In both cases, the tetragonal crystal symmetry which corresponds to the isotropy in the system plays an important role. We also investigate the effect of the crystal symmetry on the stability of the nontrivial topological phase.

From trivial to topological paramagnets: The case of Z2 and Z23 symmetries in two dimensions

Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and non-trivial bosonic symmetry-protected topological phases, protected by $\mathbb{Z}_2$ and $\mathbb{Z}_2^3$ symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, $\sqrt{3}\times\sqrt{3}$ order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.

Quantum spin Hall and quantum anomalous Hall states in magnetic Ti2Te2O single layer

Magnetic topological insulators, such as MnBi2Te4 have attracted great attention recently due to their application to the quantum anomalous Hall (QAH) effect. However, the magnetic quantum spin Hall (QSH) effect in two-dimensional (2D) materials has not yet been reported. Here based on first-principle calculations we find that Ti2Te2O, a van der Waals layered compound, can cherish both the QAH and QSH states, depending on the magnetic order in its single layer. If the single layer was in a chessboard antiferromagnetic (FM) state, it is a QSH insulator which carries two counterpropagating helical edge states. The spin–orbit-couplings induced bulk band gap can approach as large as 0.31 eV. On the other hand, if the monolayer becomes FM, exchange interactions would push one pair of bands away from the Fermi energy and leave only one chiral edge state remaining, which turns the compound into a Chern insulator (precisely, it is semimetallic with a topologically direct band gap). Both magnetic orders explicitly break the time reversal symmetry and split the energy bands of different spin orientations. To our knowledge, Ti2Te2O is the first compound that predicted to possess both intrinsic QSH and QAH effects. Our works provide new possibilities to reach a controllable phase transition between two topological nontrivial phases through magnetism tailoring.

Topological Properties in a Λ/V-Type Dice Model

We studied a non-interacting Λ/V-type dice model composed of three triangular sublattices. By considering the isotropic nearest-neighbor hoppings and the next-nearest-neighbor hoppings with the phase, as well as the quasi-staggered on-site potential, we acquired the full phase diagrams under the different fillings of the energy bands. There are abundant topological non-trivial phases with different Chern numbers C=±1, as well as higher ones ±2,±3 and a metal phase in several regimes. In addition, we also checked the bulk–edge correspondence of the system by analyzing the edge-state energy spectrum.

Topological Edge States of a Majorana BBH Model

We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

Strong Coupling, Hyperbolic Metamaterials and Optical Tamm States in Layered Dielectric-Plasmonic Media

Thin films of noble metals with thickness smaller than the wavelength of light constitute one of the most investigated structures in plasmonics. The fact that surface plasmon modes can be excited in these films by different ways and the simplicity of fabrication offer ideal conditions for applications in nanophotonics. The generation of optical modes in coupled Fabry-Pérot planar cavities and their migration to hyperbolic metamaterials is investigated. Coupled Fabry-Pérot cavities behave as simple coupled resonators. When the intra-cavity media have different refractive indices in two or more coupled cavities resonance anti-crossings arise. The application of this kind of strong coupling in sensing is foreseen. Beyond the cavity modes excited by propagating waves, also long range plasmonic guided modes can be excited using emitters or evanescent waves. A periodic structure made by multiple plasmonic films and dielectrica supports bulk plasmons, of large propagation constant and increasing field amplitude. The optical response of these structures approaches that of the hyperbolic metamaterial predicted by the effective medium theory. Light can propagate with full transmission in a structure made of a photonic crystal based on quarter wavelength layers and a second photonic crystal with an overlapping forbidden band, but presenting a non-trivial topological phase achieved by band inversion. This is due to excitation of optical Tamm states at the boundary between both crystals. The extension to multiple optical Tamm states using dielectric and plasmonic materials and the symmetries of the edge states is investigated.

Anderson disorder-induced nontrivial topological phase transitions in two-dimensional topological superconductors

We numerically investigate the quantum phase transitions induced by Anderson disorder in a topological superconductor (TSC), which is composed of a quantum anomalous Hall insulator (QAHI) and a proximity coupled $s$-wave superconductor (SC). From the transport phenomena presented, we deduce that with the increase of Anderson disorder strength, the topological quantum phase changes from Chern number $\mathcal{N}=0$ to $\mathcal{N}=1$ and finally to $\mathcal{N}=2$. Then we use the effective-medium theory to verify our numerical results and conclude that the phase transitions should ascribe to the negative correction of topological mass.

A generic Slater-Koster description of the electronic structure of centrosymmetric halide perovskites.

The halide perovskites have truly emerged as efficient optoelectronic materials and show the promise of exhibiting nontrivial topological phases. Since the bandgap is the deterministic factor for these quantum phases, here, we present a comprehensive electronic structure study using first-principle methods by considering nine inorganic halide perovskites CsBX3 (B = Ge, Sn, Pb; X = Cl, Br, I) in their three structural polymorphs (cubic, tetragonal, and orthorhombic). A series of exchange-correlation (XC) functionals are examined toward accurate estimation of the bandgap. Furthermore, while 13 orbitals are active in constructing the valence and conduction band spectra, here, we establish that a 4 orbital based minimal basis set is sufficient to build the Slater-Koster tight-binding (SK-TB) model, which is capable of reproducing the bulk and surface electronic structures in the vicinity of the Fermi level. Therefore, like the Wannier based TB model, the presented SK-TB model can also be considered an efficient tool to examine the bulk and surface electronic structures of the halide family of compounds. As estimated by comparing the model study and DFT band structure, the dominant electron coupling strengths are found to be nearly independent of XC functionals, which further establishes the utility of the SK-TB model.

Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators

The observation of abundant topological properties in optical platforms has attracted people's attention due to their great advantages in fundamental topological research and practical applications. Here, we use a double Su-Schrieffer-Heeger (SSH) chain structure composed of split ring resonators (SRRs) to mimic a Kitaev model. By properly tuning the orientation angles of the slits of the SRRs, we can ingeniously design the complex coupling distribution. We experimentally measure the topological phase transition of the double SSH model by adjusting the distance between the two chains and observe the topological bound states in the topological nontrivial phase. Importantly, inserting a trivial structure into the topological chain, we show the coupling of two topological bound states. By increasing the length of the inserted trivial chain, we observe that two topological bound states gradually approach each other and degenerate in the critical state. In addition, we theoretically study the controllable topological bound states and exceptional point physics formed by topological bound states. Our findings not only clearly show the establishing process of the photonic bound states in a double SSH chain, but also may facilitate some applications such as sensors, energy transfer, and switch with topological protection.5 MoreReceived 2 September 2020Revised 20 January 2021Accepted 25 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013122Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMetamaterialsTopological effects in photonic systemsTopological phases of matterAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Quantum spin Hall effect in antiferromagnetic topological heterobilayers

The quantum spin Hall (QSH) insulator, ensured by the time-reversal ($\mathcal{T}$) symmetry, has been a conceptual milestone of complex topological phases and well known to realize the quantum anomalous Hall effect when $\mathcal{T}$ symmetry is broken by introducing ferromagnetism. Here, based on first-principles calculations and a tight-binding model, we show that, unlike previous $\mathcal{T}$-symmetry breaking, the QSH phase can survive under the antiferromagnetic long-range order in a RbCuSe/CsMnP heterobilayer consisting of a nonmagnetic QSH insulator RbCuSe and an antiferromagnetic insulator CsMnP. The calculated spin Chern number, ${\mathcal{Z}}_{2}$ invariant, and gapless edge state confirm the topological nontrivial phase clearly. Moreover, the role of effective and Rashba spin-orbit coupling and the magnitude of antiferromagnetism are discussed to reveal the underlying physical mechanism. Our results may lead to further scientific and technological advances in topological magnetism and antiferromagnetic spintronics.

Interface State in One-dimensional Acoustic Resonator System with Inversion Symmetry Breaking

Topological sonic crystals are artificial periodic structures that support robust edge or interface state. Most previous studies on interface state in one-dimensional system heavily rely on Su-Schrieffer-Heeger (SSH) model, which modulates inter and intra hopping strength to yield a nontrivial topological phase. Whether it is possible to achieve interface states by connecting two trivial phases remains a question. To this point, in this paper, we propose a novel method of breaking the inversion symmetry of diatomic and elaborate the underlying mechanism using a spring-mass model. Instead of modulating spring stiffness corresponding to hopping strength which is intrinsically requested in the SSH model, we perturb the masses to break inversion symmetry while springs remain unchanged. Although breaking inversion symmetry in diatomic does not lead to a nontrivial phase, it is found that the interface state would still emerge within the chain formed by connecting two different configurations. Subsequently, this mechanism is applied to a one-dimensional acoustic resonator system connecting two different configurations to realize interface state. Simulation results reveal that acoustic wave has strongly localized at predicted interface frequency. Our study provides a novel approach of producing interface states in the one-dimensional acoustic system.

Phase diagrams of superconducting topological surface states

In this paper, we present a detailed study on the phase diagrams of superconducting topological surface states, especially, focusing on the interplay between crystalline symmetry and topology of the effective BdG Hamiltonian. We show that for the 4 x 4 kinematic Hamiltonian of the normal state, a mirror symmetry M can be defined, and for the M-odd pairings, the classification of the 8 x 8 BdG Hamiltonian is ℤ⊕ℤ, and the time-reversal symmetry is broken intrinsically. The topological non-trivial phase can support chiral Majorana edge modes, and can be realized in the thin films of iron-based superconductor such as FeSeTe.

Impurity effects in a two-dimensional nonsymmorphic Dirac semimetal

We theoretically study the impurity-induced states in a two-dimensional nonsymmorphic Dirac semimetal based on the T-matrix method. For calculating the local density of states, we find that for a Dirac system with two symmetry-inequivalent Dirac points the impurity states are similar to those in an ordinary two-dimensional Dirac sysytem. Whereas for the situation of two symmetry-equivalent Dirac points, the impurity states exhibit many distinct features, which are attributed to the spin-sublattice correlation associated with nonsymmorphic symmetry. In particular, these features are robust for the presence of the chiral symmetry-breaking term. Furthermore the impurity states in a Weyl semimetal and topological insulator with nonsymmorphic symmetries are derived and discussed. Thus the impurity effects of a two-dimensional nonsymmorphic Dirac semimetal can be used to probe the various topological nontrivial phases.

Ground energy level transition for two-body interacting Fermionic system with spin-orbit coupling and Zeeman interaction

Experimental realization of artificial gauge field has made it possible to simulate important models with electromagnetic field or spin-orbit interaction in condensed matter physics, which opens a new avenue to engineer novel quantum states and phenomena. The spin-orbit coupled system reveals many significant phenomena in condensed matter physics, such as quantum spin Hall effect, topological insulator and topological superconductor. The combined effect of Zeeman interaction and spin-orbit coupling leads to a nontrivial topological phase. The analytic solution of few-body system provides an in-depth insight into the physical phenomena, which has been studied extensively. Through the analytic study of two-body physics, we show new quantum phenomena for various gauge field parameters. We investigate the two-body interacting fermionic gas with spin-orbit coupling and Zeeman interaction in a ring trap. Through the plane wave expansion method, two-body fermionic system is solved analytically. In the absence of Zeeman interaction, the total momentum of the ground state is zero. With the increase of Zeeman interaction, an energy level crossing occurs between the lowest energy levels for different total momentum spaces and the ground state changes from zero total momentum space to non-zero total momentum space. Considering the Zeeman interaction, the total momentum of the ground state changes from zero to finite value. The single particle analysis shows that the ground energy level transition is induced by Zeeman energy level splitting. The momentum distributions of the ground state are given to provide an intuitive physical picture. This work can be further extended to the exploration of the heteroatom system, lattice system and higher spin system.

Phonon-induced Floquet topological phases protected by space-time symmetries

The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, presumably with alterations in the commutation/anticommutation relations with respect to non-spatial symmetries. We show how a coherently excited phonon mode can be used to promote a spatial symmetry with which the static system is always trivial, to a space-time symmetry which supports non-trivial Floquet higher-order topological phase. We present two examples -- one in class D and another in class AIII where a coherently excited phonon mode promotes the reflection symmetry to a time-glide symmetry such that the commutation/anticommutation relations between spatial and non-spatial symmetries are modified. These altered relations allow the previously trivial system to host gapless modes of co-dimension two at reflection-symmetric boundaries.

Fractional values of orbital angular momentum in problems of classical physics

Classical field theory problems for which the presence of nontrivial topological Pauli phase is essential (i.e. fractional values of the orbital angular momentum are possible in two-dimensional case) are discussed within the two-dimensional Helmholtz equation. As examples, we consider the “wedge problem” — determination of the field created by a point charge placed between two conducting half-planes — and the Fresnel diffraction from knife edge.

Tunable two dimensional ferromagnetic topological half-metal CrO2 by electronic correction and spin direction

Spintronics is one of the most promising information technologies now, especially for nontrivial topological Dirac half-metal, which exhibits extraordinary electronic band and transport properties. In this work, we propose that 1T-CrO2 nanosheet is mechanical stable, large spin-gap, and room temperature ferromagnetic Dirac half metal. It also exhibits a desirable giant magneto band structure effect, and when the spin direction is switched from in-plane to out-of-plane with a spin orbital coupling effect, it will exhibit nontrivial topological phase transition. The topological tunable electronic band property makes it a very promising two-dimensional nanosheet for spintronics.