Topological Phase Diagram Research Articles

Fundamental laws of chiral band crossings: Local constraints, global constraints, and topological phase diagrams

Fundamental laws of chiral band crossings: Local constraints, global constraints, and topological phase diagrams

Quantized thermal Hall conductance and the topological phase diagram of a superconducting bismuth bilayer

Quantized thermal Hall conductance and the topological phase diagram of a superconducting bismuth bilayer

Reversible Phase Transition between Vortex Lattice and Hexagonal Polar Skyrmion Crystals.

Polar skyrmions in oxide heterostructures have recently attracted extensive interest due to their unique physical properties and potential applications. Here, we report the formation of the vortex lattice and the nanoscale polar skyrmion crystals with two-dimensional hexagonal symmetry in PbTiO3/SrTrO3 (PTO/STO) superlattices. Under an increasing external field, the system transitions from a vortex lattice phase to hexagonal polar skyrmion crystals (PSkC). The formation and annihilation process of the polar skyrmion crystals resemble the structural phase transition observed in atomic crystals. A temperature-electric field topological phase diagram is constructed, demonstrating stabilization of the vortex lattice and polar skyrmion crystals in a wide temperature and electric-field range. This study demonstrates the potential of manipulating the topological phase transition and its long-range order through an external field.

Topological Phase Transitions of the Non-Hermitian Electromagnetic Media with Magneto-electric Effect

The non-Hermitian topological properties of electromagnetic media have attracted much attention. In the present work, we reveal the properties of the topology of non-Hermitian electromagnetic media with a magneto-electric effect. By renormalizing the permittivity, we acquire the electromagnetic media topological phase diagram under the influence of magneto-electric effects. We find that the topological phase transition in the system is driven by the renormalization of the permittivity and permeability. This work provides an alternative way to explore the various topological phases of the electromagnetic media.

Phase diagrams of semi-infinite systems by renormalization group theory and Monte Carlo simulation

In this work, we used the Migdal–Kadanoff renormalization group method to investigate two three-dimensional semi-infinite Ising systems. In the first one, the surface and bulk sites are occupied by spin-3/2 and spin-1/2 respectively, whereas those of the second one are occupied by spin-1/2 on the surface and spin-3/2 in the bulk. Based on the ratio of bulk and surface exchange interactions, we explored different topologies of phase diagrams showing various second order phase transitions, namely ordinary, extraordinary, surface and special transitions. We also found that both systems exhibited first order phase transitions, multicritical points and critical end-points. The existence of a first order phase transition at low temperatures was confirmed by plotting the derivative of the free energy. The Monte Carlo simulation was also used to verify and compare the results obtained by the renormalization group for the two semi-infinite systems.

Merged Potts-clock model: Algebraic and conventional multistructured multicritical orderings in two and three dimensions.

A spin system is studied with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalization-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: Conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first- and second-order phase transitions, themselves delimited by multicritical points: Inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.

Emergence of topological and spin valley hallmarks in buckled Xene bilayers

A subclass of two-dimensional materials with honeycomb structure, namely buckled Xene monolayers, are efficient for topological applications due to varying degrees of buckling in their lattice structure and have received a significant revival of interest in the last few years. However, to-date, less attention, as compared to, planer Xene bilayers has been assigned to the buckled Xene bilayers. The buckled Xene bilayers can offer a unique platform to study transport properties in bilayer systems. In this study, we explore the unknown topological behaviour of buckled Xene bilayers by exploiting the space inversion and time-reversal (TR) symmetries in these solids. In order to exploit the underline symmetries, we use light irradiation, layered antiferromagnetic exchange magnetization and vertical electric field as an external means. By mixing these three ingredients in a proper way, we achieve various topological phases in bilayers of buckled Xene solids, including TR-broken quantum spin Hall insulator, photo-induced quantum Hall insulator, photo-induced spin-polarized quantum Hall insulator, and quantum spin-valley Hall insulator. Furthermore, we establish a topological phase diagram and identify a topological domain wall in buckled Xene bilayers when subjected to circularly polarized light and gated voltage, which opens up possibilities for the propagation of perfectly valley-polarized channels.

On the identity of the phase behavior in the simplest model of a binary gas mixture for square, honeycomb, and one-dimensional lattices

A complete analysis of the phase diagram of the adsorption lattice gas model of a binary gas mixture on one-dimensional and honeycomb lattices in the ground state with nearest neighbor interactions between particles was carried out. We found that in the parameter space of the lateral interactions for one-dimensional and honeycomb lattices, their division into regions with different topologies of phase diagrams is the same as for a square lattice.

Electronic structure and topological phase transition in multi-orbital triangular lattice with rotation and mirror symmetry breaking

Triangular lattice is one of the most generic structures in the two-dimensional (2D) limit with numerous exotic properties, such as magnetic frustration and quantum spin liquid. Here, we investigate the electronic properties of a multi-orbital (p x , p y , p z ) triangular lattice while focusing on the role of rotation and mirror symmetry breaking in regulating the topological phase diagram. The tight-binding modeling reveals that rotation symmetry () breaking splits the Dirac point and preserves the nodal loop. A further inclusion of broken horizontal mirror symmetry () destroys the nodal loop. Consequently, with spin–orbit coupling (SOC), the (p x , p y , p z )-orbital triangular lattice is topologically non-trivial with only or symmetry breaking. With both symmetries breaking, it becomes trivial, except when the SOC is large enough to initiate band inversion. For real materials, we propose that the recently grown AgSe/AgTe monolayer in a binary honeycomb structure is an ideal system to realize the multi-orbital triangular lattice. The first-principles calculations demonstrate that free-standing AgSe and AgTe are Z 2 non-trivial. On the Ag(111) substrate, AgSe becomes trivial because of the breaking of both and symmetries, whereas AgTe remains non-trivial because of the strong SOC of Te. Our work not only provides physical insights into the experimentally synthesized 2D binary honeycomb structures but also highlights the manipulation of electronic and topological properties through symmetry/orbital physics, which are valuable for designing new quantum materials and devices.

Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains

Many-body interactions give rise to the appearance of exotic phases in Hermitian physics. Despite their importance, many-body effects remain an open problem in non-Hermitian physics due to the complexity of treating many-body interactions. Here, we present a family of exact and numerical phase diagrams for non-Hermitian interacting Kitaev chains. In particular, we establish the exact phase boundaries for the dimerized Kitaev-Hubbard chain with complex-valued Hubbard interactions. Our results reveal that some of the Hermitian phases disappear as non-Hermiticty is enhanced. Based on our analytical findings, we explore the regime of the model that goes beyond the solvable regime, revealing regimes where non-Hermitian topological degeneracy remains. The combination of our exact and numerical phase diagrams provides an extensive description of a family of non-Hermitian interacting models. Our results provide a stepping stone toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.

Topological two-body bands in a multiband Hubbard model

In a multiband Hubbard model the self-consistency relations for the two-body bound-state bands are in the form of a nonlinear eigenvalue problem. Assuming that the resultant eigenvectors form an orthonormal set, e.g., in the strong-binding regime, here we reformulate their Berry curvatures and the associated Chern numbers. As an illustration we solve the two-body problem in a Haldane-Hubbard model with attractive on-site interactions and analyze its topological phase diagrams from weak to strong couplings, i.e., by keeping track of the gap closings in between the low-lying two-body bands. The resultant Chern numbers are consistent with the lobe structure of the phase diagrams in the strong-coupling regime.

Engineering topological phases of any winding and Chern numbers in extended Su–Schrieffer–Heeger models

Simple route of engineering topological phases for any desired value of winding and Chern numbers is found in the Su–Schrieffer–Heeger (SSH) model by adding a further neighbor hopping term of varying distances. It is known that the standard SSH model yields a single topological phase with winding number, ν = 1. In this study it is shown that how one can generate topological phases with any values of winding numbers, for examples, in the presence of a single further neighbor term which preserves inversion, particle-hole and chiral symmetries. Quench dynamics of the topological and trivial phases are studied in the presence of a specific nonlinear term. Another version of SSH model with additional modulating nearest neighbor and next-nearest-neighbor hopping parameters was introduced before which exhibit a single topological phase characterized by Chern number, . Standard form of inversion, particle-hole and chiral symmetries are broken in this model. Here this model has been studied in the presence of several types of parametrization among which, for a special case the system is found to yield a series of phases with Chern numbers, In another parametrization, multiple crossings within the edge states energy lines are found in both trivial and topological phases. Topological phase diagrams are drawn for every case. Emergence of spurious topological phases is also reported.

Asymmetric coupling induces two-directional reentrance transition in three-lane exclusion process.

Inspired by vehicular traffic phenomena, we study a three-lane open totally asymmetric simple exclusion process with both-sided lane switching in the companionship of Langmuir kinetics. We calculate the phase diagrams, density profiles, and phase transitions through mean-field theory and successfully validate these findings with Monte Carlo simulation results. It has been found that both the qualitative and quantitative topology of phase diagrams crucially rely on the ratio of lane-switching rates called coupling strength. The proposed model has various unique mixed phases, including a double shock resulting in bulk-induced phase transitions. The interplay between both-sided coupling, third lane, and Langmuir kinetics produces unusual features, including a back-and-forth phase transition, also called a reentrance transition, in two directions for relatively nominal values of coupling strength. The presence of reentrance transition and peculiar phase boundaries leads to a rare type of phase division in which one phase lies entirely within another region. Moreover, we scrutinize the shock dynamics by analyzing four different types of shock and finite-size effects.

Singular flat bands in the modified Haldane-Dice model

Flat bands can be divided into singular and non-singular ones according to the behavior of their Bloch wave function around band-crossing points in momentum space. We analyze the flat band in the Dice model, which can be tuned by a uniaxial strain in the zigzag direction and a Haldane-type next-nearest neighbor interaction, and derive the topological phase diagram of the modified Haldane-Dice model to obtain all band-gap closings with the central band. When the central band is flat, we determine its compact localized state and classify its behavior at all band-touching points by means of the Hilbert–Schmidt quantum distance. We find that the flat band remains singular for all band-touching points (topological phase transitions) with a maximal quantum distance and give expressions for the resulting non-contractible loop states on the real-space torus.

Topological phase transition in the commensurate multifrequency Floquet Su-Schrieffer-Heeger model

Recently, Floquet systems have attracted a great deal of interest as they offer the unprecedented ability to engineer topological states through the tuning of an external time-periodic drive. Consequentially, seeking new driving protocols that allow for more exotic topological phases and transitions becomes imperative for the Floquet engineer. In this paper, we study the Su-Schrieffer-Heeger model driven by two time-dependent periodic sources with commensurate frequencies and an amplitude modulation. Imposing more than one driving frequency allows us to realize even more exotic topological phases resulting from new couplings appearing in the Fourier space representation. Moreover, we find an experimentally practical method for sweeping the system through a topological phase transition by varying the amplitude mixture of the commensurate sources. We employ the local Chern marker, a real-space representation of the Chern number, to simulate topological phase diagrams of the two-drive Floquet Hamiltonian in a variety of driving cases.

Electronic properties of twisted bilayer graphene suspended and encapsulated with hexagonal boron nitride

The recent observed anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned to hexagonal boron nitride (hBN) and unconventional ferroelectricity in Bernal bilayer graphene sandwiched by hBN present a new platform to tune the correlated properties in graphene systems. In these graphene-based moir\'e superlattices, the aligned hBN substrate plays an important role. In this paper, we analyze the effects of hBN substrate on the band structure of the TBG. By means of an atomistic tight-binding model we calculate the electronic properties of TBG suspended and encapsulated with hBN. Interestingly, we found that the physical properties of TBG are extremely sensitive to the presence of hBN and they may be completely different if TBG is suspended or encapsulated. We quantify these differences by analysing their electronic properties, optical conductivity and band topology. We found that the narrow bandwidth, band gap, local density of states and optical conductivity are significantly modified by the aligned hBN substrates. Interestingly, these electronic properties can be used as a signature of the alignment in experiment. Moreover, the TBG/hBN superlattices in the presence or absence of the two-fold rotation symmetry response differently to the external electric field. For the TBG suspended in the hBN, application of an electric field results in the charge unevenly distributed between graphene layers, which can be used to tune the strength of the valley Hall effect or the anomalous Hall effect. Such rich topological phase diagram in these systems may be useful for experiments.

Dynamical detection of mean-field topological phases in an interacting Chern insulator

Interactions generically have important effects on topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change a topological phase diagram, which, however, is typically hard to measure in an experiment. Here we propose a scheme based on quench dynamics to detect the mean-field topological phase diagram of an interacting Chern insulator described by the QAH-Hubbard model, with nontrivial dynamical quantum physics being uncovered. We focus on the dynamical properties of the system at a weak to intermediate Hubbard interaction, which mainly induces a ferromagnetic order under the mean-field level. Remarkably, three characteristic times---${t}_{s}, {t}_{c}$, and ${t}^{*}$---are found in the quench dynamics. The first two (${t}_{s},{t}_{c}$) capture the emergences of dynamical self-consistent particle density and the dynamical topological phase transition, respectively, while the third one (${t}^{*}$) gives a linear scaling time on the topological phase boundaries. We show generically that the characteristic times obey ${t}_{s}>{t}^{*}>{t}_{c}$ (${t}^{*}<{t}_{s}<{t}_{c}$) in the repulsive (attractive) interacting regime, when the system is quenched from an initial nearly fully polarized state to the topologically nontrivial regimes. Moreover, the Chern number of the equilibrium phase of postquench interacting Hamiltonian can be determined by any two of the three timescales, providing a dynamical way to determine the equilibrium mean-field topological phases. Experimentally, the measurement of ${t}_{s}$ is challenging, while ${t}_{c}$ and ${t}^{*}$ can be directly read out by measuring the spin polarizations of four Dirac points and the time-dependent particle density, respectively, showing the feasibility of the present dynamical scheme. Our work opens a way to detect by quench dynamics the mean-field phase diagram of Chern insulators with interactions.

Non-Trivial Band Topology Criteria for Magneto-Spin–Orbit Graphene

Band structure and topology of magneto-spin–orbit graphene is investigated using the proposed tight-binding model that incorporates both Rashba and sublattice-resolved collinear exchange couplings in a generic ferrimagnetic (FIM) setting for in-plane and out-of-plane magnetization directions. The resulting band structures were analyzed for possibilities to extract the strengths of exchange and Rashba couplings from experimental spin-resolved ARPES measurements of the valley gaps and π-state spin-splittings. It was shown that the topologically trivial in-plane FIM situation admits simple expressions for these quantities, whereas the out-of-plane FIM, which admits a nontrivial band topology, is harder to analyze. The obtained topological phase diagrams for the out-of-plane FIM case show that the anomalous Hall conductance is quite stable with respect to the antiferromagnetic (AFM) interaction, which tends to interfere with the QAHE phase; moreover, the topological phase transition has a rather smooth character with respect to the AFM coupling strength.

Entanglement entropy distinguishes PT-symmetry and topological phases in a class of non-unitary quantum walks

We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this symmetry is unbroken by its eigenstates. An asymptotic analysis at long times reveals that the quantum walk can indefinitely sustain hybrid entanglement in the unbroken symmetry phase even when gain and loss mechanisms are present. However, when the gain-loss strength is too large, the PT-symmetry of the model is spontaneously broken and entanglement vanishes. The entanglement entropy is therefore an effective and robust parameter for constructing PT-symmetry and topological phase diagrams in this non-unitary dynamical system.

Floquet topological phases on a honeycomb lattice using elliptically polarized light

We study the effect of driving a two-dimensional honeycomb system out of equilibrium using an elliptically polarized light as a time-dependent perturbation. In particular, we try to understand the topological phase diagram of this driven system when the external drive is a vector potential given by . These topological phases are characterized by the Floquet Chern number which, in each of these phases, is related to the number of robust edge modes on a nanoribbon. We show that varying the ratio A 0x /A 0y of the external drive is a possible way to take the system from a trivial to a topological phase and vice versa.