Trivial Insulator Phases Research Articles

Phase- and temperature-driven chiral topological superfluids on a honeycomb lattice

The correlated spinful Haldane model exhibits rich topological phases consisting of chiral topological superfluids (TSFs) and topological spin density waves. However, most of previous studies mainly focus on the case with the fixed hopping phase or at zero temperature. In this paper, we study the attractive spinful Haldane model with arbitrary phase at finite temperature. The chiral TSFs with Chern number C = 2 and 4 emerge driven by the phase and temperature. In particular, the temperature can drive a C = 2 topological superfluid from a trivial normal insulator phase at an appropriate interaction. The bulk topology of all TSFs is uncovered by the Wilson loop method, and confirmed by the responses of edge dislocations.

Topological band engineering and tunable thermal Hall effect in trimerized Lieb lattice ferromagnets

We theoretically study the topological properties of magnons and the relevant magnon thermal Hall effect in trimerized Lieb lattice ferromagnets in the presence of next-nearest-neighbor Dzyaloshinskii-Moriya interactions. By calculating the magnon band structures and their Chern numbers with the linear spin-wave theory, we show that the system can undergo a phase transition between a magnonic topological insulator phase and a magnonic trivial insulator phase. The main results are presented in the form of topological phase diagrams, where the Chern numbers or magnon thermal Hall conductivity are shown as a function of the two lattice trimerization parameters. We find a sharp change of the thermal Hall conductivity across the critical point of phase transformations associated with topological nontrivial edge states. The behaviors reflect that the existence of trimerizations breaks the C4 rotational symmetry of the Lieb lattice. Finally, we show that our theoretical predictions could be experimentally realized in high-temperature cuprate superconductors or organic magnetic materials. Published by the American Physical Society 2024

Transitions in Xenes between excitonic, topological and trivial insulator phases: Influence of screening, band dispersion and external electric field

Using a variational approach, the binding energies E_bEb of the lowest bound excitons in Xenes under varying electric field are investigated. The internal exciton motion is described both by Dirac electron dispersion and in effective-mass approximation, while the screened electron-hole attraction is modeled by a Rytova-Keldysh potential with a 2D electronic polarizability \alpha_{2D}α2D. The most important parameters as spin-orbit-induced gap E_gEg, Fermi velocity v_FvF and \alpha_{2D}α2D are taken from ab initio density functional theory calculations. In addition, \alpha_{2D}α2D is approximated in two different ways. The relation of E_bEb and E_gEg is ruled by the screening. The existence of an excitonic insulator phase with E_b>E_gEb>Eg sensitively depends on the chosen \alpha_{2D}α2D. The values of E_gEg and \alpha_{2D}α2D are strongly modified by a vertical external electric bias UU, which defines a transition from the topological into a trivial insulator at U=E_g/2U=Eg/2, with the exception of plumbene. Within the Dirac approximation, but also within the effective mass description of the kinetic energy, the treatment of screening dominates the appearance or non-appearance of an excitonic insulator phase. Gating does not change the results: the prediction done at zero electric field is confirmed when a vertical electric field is applied. Finally, Many-Body perturbation theory approaches based on the Green’s function method, applied to stanene, confirm the absence of an excitonic insulator phase, thus validating our results obtained by ab initio modeling of \alpha_{2D}α2D.

Characterization of charge-carrier dynamics at the Bi2Se3/MgF2 interface by multiphoton pumped UV–Vis transient absorption spectroscopy

Separate relaxation dynamics of electrons and holes in experiments on optical pumping-probing of semiconductors is rarely observed due to their overlap. Here we report the separate relaxation dynamics of long-lived (∼200 μs) holes observed at room temperature in a 10 nm thick film of the 3D topological insulator (TI) Bi2Se3 coated with a 10 nm thick MgF2 layer using transient absorption spectroscopy in the UV–Vis region. The ultraslow hole dynamics was observed by applying resonant pumping of massless Dirac fermions and bound valence electrons in Bi2Se3 at a certain wavelength sufficient for their multiphoton photoemission and subsequent trapping at the Bi2Se3/MgF2 interface. The emerging deficit of electrons in the film makes it impossible for the remaining holes to recombine, thus causing their ultraslow dynamics measured at a specific probing wavelength. We also found an extremely long rise time (∼600 ps) for this ultraslow optical response, which is due to the large spin–orbit coupling splitting at the valence band maximum and the resulting intervalley scattering between the splitting components. The observed dynamics of long-lived holes is gradually suppressed with decreasing Bi2Se3 film thickness for the 2D TI Bi2Se3 (film thickness below 6 nm) due to the loss of resonance conditions for multiphoton photoemission caused by the gap opening at the Dirac surface state nodes. This behavior indicates that the dynamics of massive Dirac fermions predominantly determines the relaxation of photoexcited carriers for both the 2D topologically nontrivial and 2D topologically trivial insulator phases.

Exploring interacting topological insulator in the extended Su-Schrieffer-Heeger model

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.

Observation of type-III corner states induced by long-range interactions

Long-range interactions (LRIs) are ubiquitous in nature. Higher-order topological (HOT) insulator represents a new phase of matter. A critical issue is how LRI dictates the HOT phases. In this work, we discover four topologically distinct phases, i.e., HOT phase, the bound state in the continuum, Dirac semimetal (DSM) phase, and trivial insulator phase in a breathing kagome circuit with tunable LRIs. We find an emerging type-III corner state in the HOT phase, which splits from the edge state continuum and originates from the strong couplings between nodes at different edges. We experimentally detect this novel state by impedance and voltage measurements. In the DSM phase, the Dirac cone exhibits an itinerant feature with a tunable position that depends on the LRI strength. Our findings provide a deeper understanding of the LRI effect on exotic topological states and pave the way for regulating interactions in topolectrical circuits.

Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields

We investigate an unconventional topological phase transition that occurs in quantum spin Hall (QSH) systems when applying an external in-plane magnetic field. We show that this transition between QSH and trivial insulator phases is separated by a stable topological gapless phase, which is protected by the combination of particle-hole and reflection symmetries, and thus, we dub it as crystalline Weyl semimetal. We explore the stability of this new phase when particle-hole symmetry breaking terms are present. Especially, we predict a robust unconventional topological phase transition to be visible for materials described by the Kane and Mele model even if particle-hole symmetry is significantly broken.

Coherent surface-to-bulk vibrational coupling in the 2D topologically trivial insulator Bi2Se3 monitored by ultrafast transient absorption spectroscopy

Ultrafast carrier relaxation in the 2D topological insulator (TI) Bi2Se3 [gapped Dirac surface states (SS)] and how it inherits ultrafast relaxation in the 3D TI Bi2Se3 (gapless Dirac SS) remains a challenge for developing new optoelectronic devices based on these materials. Here ultrashort (~ 100 fs) pumping pulses of ~ 340 nm wavelength (~ 3.65 eV photon energy) were applied to study ultrafast electron relaxation in the 2D TI Bi2Se3 films with a thickness of 2 and 5 quintuple layers (~ 2 and ~ 5 nm, respectively) using transient absorption (TA) spectroscopy in the ultraviolet–visible spectral region (1.65–3.9 eV). The negative and positive contributions of TA spectra were attributed to absorption bleaching that mostly occurs in the bulk states and to the inverse bremsstrahlung type free carrier absorption in the gapped Dirac SS, respectively. Owing to this direct and selective access to the bulk and surface carrier dynamics, we were able to monitor coherent longitudinal optical (LO) phonon oscillations, which were successively launched in the bulk and surface states by the front of the relaxing electron population within the LO-phonon cascade emission. We have also recognized the coherent surface-to-bulk vibrational coupling that appears through the phase-dependent amplitude variations of coherent LO-phonon oscillations. This unique behavior manifests itself predominantly for the topologically trivial insulator phase of the 2D TI Bi2Se3 (2 nm thick film) in the photon energy range (~ 2.0–2.25 eV) where efficient energy exchange between the bulk and surface states occurs. We also found that the coherent surface-to-bulk vibrational coupling significantly weakens with increasing both the Bi2Se3 film thickness and pumping power.

Symmetry-allowed nonlinear orbital response across the topological phase transition in centrosymmetric materials

Nonlinear optical responses are commonly used as a probe for studying the electronic properties of materials. For topological materials, studies thus far focused on photogalvanic electric currents, which are forbidden in centrosymmetric materials because they require broken inversion symmetry. In this Letter, we propose a class of symmetry-allowed responses for inversion-symmetric topological insulators with two doubly degenerate bands. We consider a specific example of such a response, the orbital current, and show that the sign of the response reflects the ${\mathbb{Z}}_{2}$ topological index, i.e., the orbital current changes sign at the transition between trivial and topological insulator phases. This is illustrated in two models of topological insulators: the Bernevig-Hughes-Zhang model and the $1{T}^{\ensuremath{'}}$ phase of transition metal dichalcogenides.

Three-dimensional network model for strong topological insulator transitions

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological insulator phase already accommodated by the network model framework in the pre-existing literature, it hosts strong topological insulator phases as well. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a non-local transformation that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this transformation. We show that upon adding sufficiently strong disorder the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semi-classical percolation picture of topological phase transitions in 2D can be generalized to 3D and opens up a new venue for studying 3D topological phase transitions.

Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 ( A =K, Rb, Cs)

We investigate how the real and imaginary charge density waves interplay at the Van Hove singularity on the hexagonal lattices. A phenomenological analysis indicates the formation of $3Q$ complex orders at all three nesting momenta. Under a total phase condition, unequal phases at the three momenta break the rotation symmetry generally. The $3Q$ complex orders constitute a rich Haldane-model phase diagram. When effective time-reversal symmetries arise under 1-site translations, the Dirac semimetals are protected. The breakdown of these symmetries gaps the Dirac points and leads to the trivial and Chern insulator phases. These phases are deformations of purely real and imaginary orders, which exhibit trivial site and/or bond density and chiral flux orders, respectively. The exotic single-Dirac-point semimetals also appear along the gapless phase boundary. We further show that the theoretical model offers transparent interpretations of experimental observations in the kagome metals $\text{AV}_3\text{Sb}_5$ with $\text{A}=\text{K},\text{Rb},\text{Cs}$. The topological charge density waves may be identified with the complex orders in the Chern insulator phase. Meanwhile, the lower-temperature symmetry-breaking phenomena may be interpreted as the secondary orders from the complex order ground states. Our work sheds light on the nature of the topological charge density waves in the kagome metals $\text{AV}_3\text{Sb}_5$ and may offer useful indications to the experimentally observed charge orders in the future experiments.

Equilibrium current in a Weyl semimetal–superconductor heterostructure

A heterostructure consisting of a magnetic Weyl semimetal and a conventional superconductor exhibits an equilibrium current parallel to the superconductor interface and perpendicular to the magnetization. Analyzing a minimal model, which as a function of parameters may be in a trivial magnetic insulator phase, a Weyl semimetal phase, or a three-dimensional weak Chern insulator phase, we find that the equilibrium current is sensitive to the presence of surface states, such as the topological Fermi-arc states of the Weyl semimetal or the chiral surface states of the weak Chern insulator. While there is a nonzero equilibrium current in all three phases, the appearance of the surface states in the topological regime leads to a reversal of the direction of the current, compared to the current direction for the trivial magnetic insulator phase. We discuss the interpretation of the surface-state contribution to the equilibrium current as a real-space realization of the superconductivity-enabled equilibrium chiral magnetic effect of a single chirality, predicted to occur in bulk Weyl superconductors.

Understanding Topological Insulators in Real Space.

A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indices—such as IPR—enabling to differentiate between trivial and topological insulator phases. The approach is based on analyzing the electron delocalization between second neighbors, thus highlighting the relevance of the sublattices induced by chiral symmetry. Moreover, the second neighbor delocalization index, , also enables to identify the presence of chirality and when it is broken by doping or by eliminating atom pairs (as in the case of odd number of atoms chains). Hints to identify bulk behavior thanks to are also provided. Overall, we present a very simple, orbital invariant visualization tool that should help the analysis of chirality (independently of the crystallinity of the system) as well as spreading the concepts of topological behavior thanks to its relationship with well-known chemical concepts.

Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model

A non-Hermitian generalization of the Su-Schrieffer-Heeger model driven by a periodic external potential is investigated, and its topological features are explored. We find that the bi-orthonormal geometric phase acts as a topological index, well capturing the presence/absence of the zero modes. The model is observed to display trivial and non-trivial insulator phases and a topologically non-trivial M${\"o}$bius metallic phase. The driving field amplitude is shown to be a control parameter causing topological phase transitions in this model. While the system displays zero modes in the metallic phase apart from the non-trivial insulator phase, the metallic zero modes are not robust, as the ones found in the insulating phase. We further find that zero modes' energy converges slowly to zero as a function of the number of dimers in the M${\"o}$bius metallic phase compared to the non-trivial insulating phase.

Structural and electronic properties of realistic two-dimensional amorphous topological insulators

We investigate the structure and electronic spectra properties of two-dimensional amorphous bismuthene structures and show that these systems are topological insulators. We employ a realistic modeling of amorphous geometries together with density functional theory for electronic structure calculations. We investigate the system topological properties throughout the amorphization process and find that the robustness of the topological phase is associated with the spin–orbit coupling strength and size of the pristine topological gap. Using recursive non-equilibrium Green’s function, we study the electronic transport properties of nanoribbons devices with lengths comparable to experimentally synthesized materials. We find a 2e 2/h conductance plateau within the topological gap and an onset of Anderson localization at the trivial insulator phase.

Excitonic insulator phase and condensate dynamics in a topological one-dimensional model

We employ mean-field approximation to investigate the interplay between the nontrivial band topology and the formation of excitonic insulator (EI) in a one-dimensional chain of atomic $s-p$ orbitals in the presence of repulsive inter-orbital Coulomb interaction. We find that our model, in a non-interacting regime, admits topological and trivial insulator phases, whereas, in strong Coulomb interaction limit, the chiral symmetry is broken and the system undergoes a topological-excitonic insulator phase transition. The latter phase transition stems from an orbital pseudomagnetization and band inversion around $k=0$. Our findings show that contrary to the topological insulator phase, electron-hole bound states do not form exciton condensate in the trivial band insulator phase due to lack of band inversion. Interestingly, the EI phase in low $s-p$ hybridization limit hosts a Bardeen-Cooper-Schrieffer (BCS)/Bose-Einstein condensation (BEC) crossover. Irradiated by a pump pulse, our findings reveal that the oscillations of exciton states strongly depend on the frequency of the laser pulse. We further explore the signatures of dynamics of the exciton condensate in optical measurements.

Mixture of scalar bosons and two-color fermions in one dimension: Superfluid-insulator transitions

Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of new non-trivial insulator phases that depend on the sign of the boson-fermion interaction. These non-trivial insulator phases satisfy the conditions $\rho_B\pm\rho_F=n$ and $\rho_B\pm \tfrac{1}{2}\rho_F=n$, with the plus (minus) sign for repulsive (attractive) interactions and $n$ an integer. Far from fermionic half-filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.

Detecting topology through dynamics in interacting fermionic wires

We describe a protocol to read out the topological invariant of interacting 1D chiral models, based on measuring the mean chiral displacement of time-evolving bulk excitations. We present analytical calculations and numerical Matrix Product State simulations of interacting Su-Schrieffer-Heeger (SSH) chains, demonstrating how the mean chiral displacement allows to distinguish between topological insulator, trivial insulator and symmetry-broken phases. Finally, we provide an experimental blueprint for realizing a model displaying these three phases and describe how to detect those.

Topological Dirac Semimetal Phase in Bismuth Based Anode Materials for Sodium-Ion Batteries

Bismuth has recently attracted interest in connection with Na-ion battery anodes due to its high volumetric capacity. It reacts with Na to form Na 3 Bi which is a prototypical Dirac semimetal with a nontrivial electronic structure. Density-functional-theory based first-principles calculations are playing a key role in understanding the fascinating electronic structure of Na 3 Bi and other topological materials. In particular, the strongly-constrained-and-appropriately-normed (SCAN) meta-generalized-gradient-approximation (meta-GGA) has shown significant improvement over the widely used generalized-gradient-approximation (GGA) scheme in capturing energetic, structural, and electronic properties of many classes of materials. Here, we discuss the electronic structure of Na 3 Bi within the SCAN framework and show that the resulting Fermi velocities and s-band shift around the Γ point are in better agreement with experiments than the corresponding GGA predictions. SCAN yields a purely spin-orbit-coupling (SOC) driven Dirac semimetal state in Na 3 Bi in contrast with the earlier GGA results. Our analysis reveals the presence of a topological phase transition from the Dirac semimetal to a trivial band insulator phase in Na 3 Bi x Sb 1 − x alloys as the strength of the SOC varies with Sb content, and gives insight into the role of the SOC in modulating conduction properties of Na 3 Bi.

Three-dimensional topological magnon systems

We propose a class of models for a magnonic analog of topological insulators in three dimensions. The models have pseudo-time-reversal symmetry which ensures the existence of bosonic Kramers pairs. We define a set of $\mathbb{Z}_2$ topological invariants that characterizes different topological phases and determines the presence or absence of surface Dirac cones. This is demonstrated by considering a bosonic counterpart of the Fu-Kane-Mele model on a diamond lattice. The model is found to exhibit three distinct phases analogous to strong topological, weak topological, and trivial insulator phases of the original fermionic model. We also discuss a possible realization of the thermal Hall effect of surface magnons in the presence of a magnetic field in proximity to a normal ferromagnet.