Topological Phase Diagram Research Articles

Proximity-induced zero-energy states indistinguishable from topological edge states

When normal metals (NMs) are attached to topological insulators or topological superconductors, it is conceivable that the quantum states in these finite adjacent materials can intermix. In this case---and because the NM usually does not possess the same symmetry as the topological material---it is pertinent to ask whether zero-energy edge states in the topological layer are affected by the presence of the NM. To address this issue, we consider three prototype systems simulated by tight-binding models, namely a Su-Schrieffer-Heeger/NM, a Kitaev/NM, and a Chern insulator/NM. For all junctions investigated, we find that there exist trivial ``fine-tuned'' zero-energy states in the NM layer that can percolate into the topological region, thus mimicking a topological state. These zero-energy states are created by fine-tuning the NM chemical potential such that some of the NM states cross zero energy; they can occur even when the topological material is in the topologically trivial phase, and exist over a large region of the topological phase diagram. Interestingly, the true Majorana end modes of the Kitaev/NM model cannot be crossed by any NM state, as the NM metal layer in this case does not break particle-hole symmetry. On the other hand, when the chiral symmetry of the Su-Schrieffer-Heeger chain is broken by the attached NM, crossings are allowed. In addition, even in Chern insulators that do not preserve nonspatial symmetries, but the topological edge state self-generates a symmetry eigenvalue, such a fine-tuned zero-energy state can still occur. Our results indicate that when a topological material is attached to a metallic layer, one has to be cautious as to identify true topological edge states merely from their energy spectra and wave function profiles near the interface.

Quantized fields induced topological features in Harper-Hofstadter model

Classical magnetic fields might change the properties of topological insulators such as the time reversal symmetry protected topological edge states. This poses a question that whether quantized fields would change differently the feature of topological materials with respect to the classical one. In this paper, we propose a model to describe topological insulators (ultracold atoms in square optical lattices with magnetic field) coupled to a tunable single-mode quantized field, and discuss the topological features of the system. We find that the quantized field can induce topological quantum phase transitions in a different way. To be specific, for fixed gauge magnetic flux ratio, we calculate the energy bands for different coupling constants between the systems and the fields in both open and periodic boundary conditions. We find that the Hofstadter butterfly graph is divided into a pair for continuous gauge magnetic flux ratio, which is different from the one without single-mode quantized field. In addition, we plot topological phase diagrams characterized by Chern number as a function of the momentum of the single-mode quantized field and obtain a quantized structure with non-zero filling factor.

Strain-tunable magnetism and topological states in layered VBi2Te4.

Similar to the magnetic topological insulator of MnBi2Te4, recent studies have demonstrated that VBi2Te4 is also an ideal candidate to explore many intriguing quantum states. Different from the strong interlayer antiferromagnetic (AFM) coupling in layered MnBi2Te4, based on first-principles calculations, we find that the energy difference between AFM and ferromagnetic (FM) orders in layered VBi2Te4 is much smaller than that of MnBi2Te4. Specifically, it is found that the interlayer FM coupling can be readily achieved by applying strain. Further electronic band structures reveal that the VBi2Te4 bilayer is a time-reversal symmetry broken quantum spin Hall insulator with a spin Chern number of CS = 1, which is essentially different from the QAH state with a Chern number of C = 1 in the MnBi2Te4 bilayer. Most strikingly, the topological states of the magnetic VBi2Te4 bilayer can be well tuned by strain, whose topological phase diagram is mapped out as a function of strain by employing continuum model analyses. All of these results indicate that the layered VBi2Te4 not only enriches the family of magnetic topological materials, but also provides a promising platform to explore more exotic quantum phenomena.

Electronic Spectrum Features under the Transition from Axion Insulator Phase to Quantum Anomalous Hall Effect Phase in an Intrinsic Antiferromagnetic Topological Insulator Thin Film

In this paper, we investigate the electron topological states in a thin film of intrinsic antiferromagnetic topological insulator, focusing on their relationship with the magnetic texture. We consider a model for the film with an even number of septuple-layer blocks, which is subject to transition from the phase of an axion insulator to the phase of quantized Hall conductivity under an external magnetic field. In the continuum approach, we model an effective two-dimensional Hamiltonian of the thin film of a topological insulator with non-collinear magnetization, on the basis of which we obtain the energy spectrum and the Berry curvature. The analysis of topological indices makes it possible to construct a topological phase diagram depending on the parameters of the system and the degree of non-collinearity. For topologically different regions of the diagram, we describe the edge electronic states on the side face of the film. In addition, we investigate the spectrum of one-dimensional states on the domain wall separating domains with the opposite canting angle. We also discuss the results obtained and the experimental situation in thin films of the MnBi2Te4 compound.

Engineering Floquet topological phases using elliptically polarized light

We study a two-dimensional topological system driven out of equilibrium by the application of elliptically polarized light. In particular, we analyze the Bernevig-Hughes-Zhang model when it is perturbed using an elliptically polarized light of frequency $\mathrm{\ensuremath{\Omega}}$ described in general by a vector potential $\mathbf{A}(t)=({A}_{0x}cos(\mathrm{\ensuremath{\Omega}}t),{A}_{0y}cos(\mathrm{\ensuremath{\Omega}}t+{\ensuremath{\phi}}_{0}))$. Even for a fixed value of ${\ensuremath{\phi}}_{0}$, we can change the topological character of the system by changing the $x$ and $y$ amplitudes of the drive. We therefore find a rich topological phase diagram as a function of ${A}_{0x}$, ${A}_{0y}$, and ${\ensuremath{\phi}}_{0}$. In each of these phases, the topological invariant given by the Chern number is consistent with the number of spin-polarized states present at the edges of a nanoribbon.

Creating and controlling Dirac fermions, Weyl fermions, and nodal lines in the magnetic antiperovskite Eu3PbO

The band topology of magnetic semimetals is of interest both from the fundamental science point of view and with respect to potential spintronics and memory applications. Unfortunately, only a handful of suitable topological semimetals with magnetic order have been discovered so far. One such family that hosts these characteristics is the antiperovskites, ${A}_{3}B\mathrm{O}$, a family of 3D Dirac semimetals. The $A={\mathrm{Eu}}^{2+}$ compounds magnetically order with multiple phases as a function of the applied magnetic field. Here, by combining band structure calculations with neutron diffraction and magnetic measurements, we establish the antiperovskite ${\mathrm{Eu}}_{3}\mathrm{Pb}\mathrm{O}$ as a new topological magnetic semimetal. This topological material exhibits a multitude of different topological phases with ordered Eu moments which can be easily controlled by an external magnetic field. The topological phase diagram of ${\mathrm{Eu}}_{3}\mathrm{Pb}\mathrm{O}$ includes an antiferromagnetic Dirac phase, as well as ferro- and ferrimagnetic phases with both Weyl points and nodal lines. For each of these phases, we determine the bulk band dispersions, the surface states, and the topological invariants by means of ab initio and tight-binding calculations. Our discovery of these topological phases introduces ${\mathrm{Eu}}_{3}\mathrm{Pb}\mathrm{O}$ as a new platform to study and manipulate the interplay of band topology, magnetism, and transport.

Topological phases in interacting spin-1 systems

Different topological phases of quantum systems has become areas of increased focus in recent decades. In particular, the question of how to realize and manipulate systems with non-trivial first Chern number is pursued both experimentally and theoretically. Here we go beyond typical spin 1/2 systems and consider both single and coupled spin 1 systems as a means of realizing higher first Chern numbers and studying the emergence of different topological phases. We show that rich topological phase diagrams can be realized by coupling two spin 1 systems using both numerical and analytical methods. Furthermore, we consider a concrete realization of spin 1 systems using a superconducting circuit. This realization includes non-standard spin-spin interaction terms that may endanger the topological properties. We argue however that the realistic circuit Hamiltonian including all terms should be expected to show the rich phase structure as well. This puts our theoretical predictions within reach of state-of-the-art experimental setups.

Controlling topological phases of matter with quantum light

Controlling the topological properties of quantum matter is a major goal of condensed matter physics. A major effort in this direction has been devoted to using classical light in the form of Floquet drives to manipulate and induce states with non-trivial topology. A different route can be achieved with cavity photons. Here we consider a prototypical model for topological phase transition, the one-dimensional Su-Schrieffer-Heeger model, coupled to a single mode cavity. We show that quantum light can affect the topological properties of the system, including the finite-length energy spectrum hosting edge modes and the topological phase diagram. In particular we show that depending on the lattice geometry and the strength of light-matter coupling one can either turn a trivial phase into a topological one or viceversa using quantum cavity fields. Furthermore, we compute the polariton spectrum of the coupled electron-photon system, and we note that the lower polariton branch disappears at the topological transition point. This phenomenon can be used to probe the phase transition in the Su-Schrieffer-Heeger model.

Reentrance transition in two lane bidirectional transport system with bottlenecks

Inspired from the vehicular traffic scenarios, including the companionship of two consecutive speed bumps placed within a sufficient distance on the road, we investigate a bidirectional two-lane symmetrically coupled totally asymmetric simple exclusion process with two bottlenecks in the presence of Langmuir kinetics. The steady-state system dynamics in terms of density profiles, phase diagrams, phase transitions, and shock dynamics are investigated thoroughly, exploiting hybrid mean-field theory with various strengths of the bottleneck and lane changing rates which match well with Monte Carlo simulation outcomes. It has been detected that the qualitative and quantitative topology of phase diagrams crucially depend on bottleneck and lane switching rate, emanating in monotonic as well as non-monotonic alterations in the number of steady-state phases. We observe that the effect of the bottlenecks is weakened for the increasing values of the lane changing rate. The proposed study provides many novel mixed phases resulting in bulk-induced phase transitions. The interplay between bottlenecks, lane switching, bidirectional movement, and Langmuir kinetics produces unique phenomena, including reentrance transition and phase division of mixed shock region for comparatively lower lane switching rate.

Topological transitions in magnetized plasma and optical isolators based on leaky waveguide plasmon mode

Topological transitions open a fundamentally new route of research with interesting optical phenomena in photonic metamaterials. In this work, we comprehensively investigate the topology of equifrequency surfaces in magnetized plasma. The full topological phase diagrams are shown and the critical points in the topological transitions are given. The equifrequency surfaces evolve from the closed-form ellipsoid to the open forms type-I or type-II hyperboloid in the topological transitions. Remarkably, a type of nonreciprocal optical isolator is demonstrated utilizing the transformation from topological surface states to leaky modes in magnetized plasma. Our work may provide additional insights into topological wave physics and the novel optical isolator has potential applications in light modulation.

Topological magnons in one-dimensional ferromagnetic Su–Schrieffer–Heeger model with anisotropic interaction

Topological magnons in a one-dimensional (1D) ferromagnetic Su–Schrieffer–Heeger (SSH) model with anisotropic exchange interactions are investigated. Apart from the intercellular isotropic Heisenberg interaction, the intercellular anisotropic exchange interactions, i.e. Dzyaloshinskii–Moriya interaction and pseudo-dipolar interaction, also can induce the emergence of the non-trivial phase with two degenerate in-gap edge states separately localized at the two ends of the 1D chain, while the intracellular interactions instead unfavors the topological phase. The interplay among them has synergistic effects on the topological phase transition, very different from that in the two-dimensional (2D) ferromagnet. These results demonstrate that the 1D magnons possess rich topological phase diagrams distinctly different from the electronic version of the SSH model and even the 2D magnons. Due to the low dimensional structural characteristics of this 1D topological magnonic system, the magnonic crystals can be constructed from bottom to top, which has important potential applications in the design of novel magnonic devices.

Topological Phase Diagram of Pb1-xSnxSe1-yTey Quaternary Compound

We reproduce the mirror Chern number phase diagram for the quaternary compound Pb1-xSnxSe1-yTey combining accurate density functional theory and tight-biding model. The tight binding models are extracted from ab-initio results, adding constraints to reproduce the experimental results. By using the virtual crystalline approximation, we calculated the mirror Chern number as a function of the concentrations x and y. We report different hamiltonians depending on whether we want to focus on the experimental band gap or on the experimental topological transition. We calculate the transition line between the trivial insulating phase and topological insulating phase that results in good agreement with the experimental results. Finally, we add in the phase diagram the Weyl phase predicted in the literature providing a complete topological phase diagram for the Pb1-xSnxSe1-yTey quaternary compound.

Magnetic field constraint for Majorana zero modes in a hybrid nanowire

The hybrid semiconductor-superconductor nanowire is expected to serve as an experimental platform to support Majorana zero modes. By rederiving its effective Kitaev model with spins, we discover a topological phase diagram, which assigns a more precise constraint on the magnetic field strength for the emergence of Majorana zero modes. We find that the effective pairing strength dressed by the proximity effect exhibits a significant dependence on the magnetic field, and thus the topological phase region is refined into a closed triangle in the phase diagram with chemical potential vs Zeeman energy (which is obviously different from the open hyperbolic region known before). This prediction is confirmed again by an exact calculation of quantum transport, where the zero bias peak of $2{e}^{2}/h$ in the differential conductance spectrum, as the necessary evidence for the Majorana zero modes, disappears when the magnetic field grows too strong. Therefore, the hybrid nanowire system does not support Majorana zero modes under a too strong magnetic field. For illustrations with practical hybrid systems, in the InSb nanowire coupled to NbTiN, the accessible magnetic field range is around 0.1--1.5 T; when coupled to an aluminum shell, the accessible magnetic field range should be smaller than 0.12 T. Our predictions are essential to significantly narrow down the range of magnetic fields for further searching Majorana zero modes in experiments.

Topological phase diagram and materials realization in triangular lattice with multiple orbitals

Triangular lattice, with each site coordinating with six neighbors, is one most common network in two-dimensional (2D) limit. Manifestations of peculiar properties in the lattice, including magnetic frustration and quantum spin liquid, have been restricted to single-orbital tight-binding (TB) model so far, while the orbital degree of freedom is largely overlooked. Here, by combining TB modeling with first-principles calculations, we demonstrate the rich electronic structures of triangular lattice with multiple (p_{x}, p_{y}, p_{z}) orbitals. Type I/II Dirac point, quadratic nodal point and nodal-loops are observed, and the topological phase diagram is mapped out by manipulating the horizontal mirror symmetry, spin-orbit coupling and energy position of relevant orbitals. Remarkably, we show that large-gap quantum spin Hall phase (∼0.2 eV) can be realized in experimentally achievable systems by growing indium monolayer on a series of semiconducting substrates, such as C/Si/Ge(111) and SiC(0001) surfaces, and the proposed materials capture the TB parameter space well. Our work not only provides physical insights into the orbital physics in 2D lattices, but also sheds light on the integration of novel quantum states with conventional semiconductor technology for potential applications, such as dissipationless interconnects for electronic circuits.

Topological Floquet bands in a circularly shaken dice lattice

The hoppings of noninteracting particles in the optical dice lattice result in the gapless dispersions in the band structure formed by the three lowest minibands. In our research, we find that once a periodic driving force is applied to this optical dice lattice, the original spectral characteristics could be changed, forming three gapped quasienergy bands in the quasienergy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasienergy band shows that when the hopping strengths of the nearest-neighbor hoppings are isotropic, the system persists in the topologically nontrivial phases with Chern number $C=2$ within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighbor hopping strengths, a topological phase transition occurs, making the Chern number change from $C=2$ to $C=1$. This transition is further verified by our analytical method. Our theoretical work implies that it is feasible to realize the nontrivially topological characteristics of optical dice lattices by applying periodic shaking and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.

Kitaev chain with a fractional twist

The topological non-triviality of insulating phases of matter is by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudo-metallic component to the topological phase diagram within which the winding number is valued in $\mathbb Q$. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a non-integral winding number. We remark that this is in correspondence with Ref.[J. Differential Geom. 74(2):265-292] demonstrating that projective Dirac operators defined in the absence of spin$^\mathbb C$ structure have rational indices.

More on topological hydrodynamic modes

Based on previous work that topologically nontrivial gapless modes in relativistic hydrodynamics could be found by weakly breaking the energy momentum conservation, in this paper, we study the holographic system which produces the same hydrodynamic modes. In the hydrodynamic system, one possibility to obtain the energy momentum non-conservation is to couple the system to external gravitational fields, i.e. to observe the system in a special non-inertial frame. Similar to what happens in the hydrodynamic system, a non-inertial frame version of holography indeed produces the same topologically nontrivial gapless hydrodynamic modes. We also generalize the study of topological modes in relativistic hydrodynamics to the case with one extra U(1) current and find that more complicated topological phase diagrams could exist when we consider more possibilities of the mass terms. We also discuss the possible underlying mechanism for this topological change in the spectrum when being observed in a non-inertial reference frame.

Revealing the topological phase diagram of ZrTe5 using the complex strain fields of microbubbles

Topological materials host robust properties, unaffected by microscopic perturbations, owing to the global topological properties of the bulk electron system. Materials in which the topological invariant can be changed by easily tuning external parameters are especially sought after. Zirconium pentatelluride (ZrTe5) is one of a few experimentally available materials that reside close to the boundary of a topological phase transition, allowing the switching of its invariant by mechanical strain. Here, we unambiguously identify a topological insulator–metal transition as a function of strain, by a combination of ab initio calculations and direct measurements of the local charge density. Our model quantitatively describes the response to complex strain patterns found in bubbles of few layer ZrTe5 without fitting parameters, reproducing the mechanical deformation-dependent closing of the band gap observed using scanning tunneling microscopy. We calculate the topological phase diagram of ZrTe5 and identify the phase at equilibrium, enabling the design of device architectures, which exploit the topological switching characteristics of the system.

Non-Hermitian topology in monitored quantum circuits

We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model. We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked. The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits. For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system. Importantly, our monitored circuit realization allows direct access to steady state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model. We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.

On the dimorphism of prednisolone: The topological pressure-temperature phase diagram involving forms I and II

The dimorphism of the corticosteroid anti-inflammatory drug prednisolone has been investigated by the construction of a topological pressure–temperature phase diagram, using crystallographic and calorimetric data. The system is enantiotropic, because the temperature of the I-II equilibrium under atmospheric conditions (400–463 K) is lower than that of the two melting equilibria (518.7 K for form II and 526.3 K for form I). The slope of the I-II equilibrium in the pressure–temperature phase diagram is negative and relatively steep; therefore, form II, which is the stable form at room temperature, will not easily encounter conditions where form I will become stable even under industrial processing conditions. On the other hand, extreme small amounts of form I have been observed to spontaneously transform into form II in a time interval of about six years at room temperature and it can be concluded that although form I is very persistent under ambient conditions, it does slowly convert into form II. Moreover, the system does not obey the density rule.