Nontrivial Phase Research Articles

Practical realization of chiral nonlinearity for strong topological protection

Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned with the requirements for nonlinearity. Here we explore nonlinear topological protection by determining nonlinear rules and demonstrate their relevance in real-world experiments. We take advantage of chiral symmetry and identify the condition for its continuation in general nonlinear environments. Applying it to one-dimensional topological lattices, we show possible evolution paths for zero-energy edge states that preserve topologically nontrivial phases regardless of the specifics of the chiral nonlinearities. Based on an acoustic prototype design with non-local nonlinearities, we theoretically, numerically, and experimentally implement the nonlinear topological edge states that persist in all nonlinear degrees and directions without any frequency shift. Our findings unveil a broad family of nonlinearities compatible with topological non-triviality, establishing a solid ground for future drilling in the emergent field of nonlinear topology.

Low-Frequency Resistance Noise in Near-Magic-Angle Twisted Bilayer Graphene.

The low-frequency resistance fluctuations, or noise, in electrical resistance not only set a performance benchmark in devices but also form a sensitive tool to probe nontrivial electronic phases and band structures in solids. Here, we report the measurement of such noise in the electrical resistance in twisted bilayer graphene (tBLG), where the layers are misoriented close to the magic angle (θ ∼ 1°). At high temperatures (T ≳ 60-70 K), the power spectral density (PSD) of the fluctuation inside the low-energy moiré bands is predominantly ∝1/f, where f is the frequency, being generally lowest close to the magic angle, and can be well-explained within the conventional McWhorter model of the '1/f noise' with trap-assisted density-mobility fluctuations. At low T (≲10 K), the measured noise exhibits a strong two-level random telegraphic signal (RTS), especially close to the moiré gap, which exhibits a ∝1/f2-like PSD that can be attributed to poorly screened resonances of the Fermi energy to specific bands of defects in the encapsulating boron nitride (hBN) layers. The low-T noise within the moiré band exhibits a series of minima at the integral as well as half-integral fillings, which align with the frequently observed van Hove singularities in the density-of-states driven by strong Coulomb interaction. Apart from providing a comprehensive account of the origin and the magnitude of noise in tBLG, our experiment also reveals noise to be significantly more sensitive to the underlying interaction effects in tBLG than the conventional time-averaged transport.

Coexistence of Kondo effect and non trivial Berry phase in Gd doped Bi2Se3: an ARPES and magneto-transport study

Abstract The presence of magnetic impurities in Topological Insulators (TI) can disrupt their Time Reversal Symmetry (TRS) and lead to the emergence of an energy gap. This study delves into the energy band structure and the Kondo effect through the introduction of Gadolinium(Gd) magnetic perturbations (at levels of x = 0.1, 0.16) into a pure Bi2Se3 single crystal. In the case of the Bi1.9Gd0.1Se3 (5%) single crystal, the Kondo effect becomes observable at temperatures below 50K. However, the unaltered parent and Bi1.84Gd0.16Se3 (8%) exhibit typical metallic behavior. The pure sample displays the highest magnetoresistance (MR) of around 225% and demonstrates quantum oscillations driven by a nontrivial berry phase. The sample doped with 5% Gd undergoes a transition from negative magnetoresistance (NMR) to positive magnetoresistance (PMR) due to a presence of mixed magnetic state resulting from the opening of a gap at the Dirac point. This gap opening is confirmed through Angle-Resolved Photoemission Spectroscopy (ARPES) measurements. Thermoelectric properties are assessed across all prepared samples. The undoped sample displays the highest Seebeck coefficient and power factor (PF) values of -398.02 µV/K and 6.83 mW/mK2, respectively, at room temperature. These values are notably high for thermoelectric applications at room temperature.

Anomalous Polarization in One-Dimensional Aperiodic Insulators

Multilevel charge pumping is a feature that was recently observed in quasiperiodic systems. In this work, we show that it is more generic and appears in different aperiodic systems. Additionally, we show that for aperiodic systems admitting arbitrarily long palindromic factors, the charge pumping protocol connects two topologically distinct insulating phases. This confirms the existence of topological phases in aperiodic systems whenever their finite-size realizations admit inversion symmetry. These phases are characterized by an anomalous edge response resulting from the bulk–boundary correspondence. We show that these signatures are all present in various chains, each representing a different class of structural aperiodicity: the Fibonacci quasicrystal, the Tribonacci quasicrystal, and the Thue–Morse chain. More specifically, we calculate three quantities: the Berry phase of the periodic approximation of the finite-size systems, the polarization response to an infinitesimal static and constant electric field in systems with open boundary conditions, and the degeneracy of the entanglement spectrum. We find that all of them provide signatures of a topologically nontrivial phase.

Prediction of the Topologically Nontrivial Phase in Three-Dimensional ABX Zintl Compounds.

Zintl compounds have garnered research interest due to their diverse technological applications. Utilizing first-principles calculations, we performed a systematic study of ABX (A = Li, Na, K, Rb, or Cs; B = Si, Ge, Sn, or Pb; and X = P, As, Sb, or Bi) Zintl materials with the P63 mc KSnSb-type structure. Notably, six ABX Zintl compounds (RbSiBi, CsSiBi, LiGeBi, KGeBi, RbGeBi, and CsGeBi) were found to have topologically nontrivial phases, as demonstrated by the Z 2 invariant computed using the hybrid functional HSE06. Among them, RbGeBi and CsGeBi were identified as topological insulators with nontrivial bandgaps of 28 and 116 meV, respectively. The topological phase transition arises as a result of spin-orbit coupling, as demonstrated in the representative material, CsGeBi. Additionally, the existence of gapless surface states further confirmed the topologically nontrivial phases of the six materials. Moreover, phonon spectra and formation energy calculations verified that all identified nontrivial materials under the hybrid functional are dynamically and structurally stable, except LiGeBi which exhibited imaginary phonon frequencies. Finally, the thermodynamic stability of the representative material CsGeBi was verified through elastic constants and ab initio molecular dynamics simulations. These results provide foundational insights that could drive further experimental research and synthesis, potentially enabling the application of ABX Zintl compounds in electronic technologies such as quantum computing or spintronics.

Topology and PT symmetry in a non-Hermitian Su–Schrieffer–Heeger chain with periodic hopping modulation

We study the effect of periodic hopping modulation in a Su-Schrieffer-Heeger (SSH) chain with an additional onsite staggered imaginary potential (of strengthγ). Such dissipative, non-Hermitian (NH) extension amply modifies the features of the topological trivial phase (TTP) and the topological nontrivial phase (TNP) of the SSH chain, more so with the periodic hopping distribution. Generally a weak NH potential can respect the parity-time (PT) symmetry keeping the energy eigenvalues real, while a strong potential breaksPTconservation leading to imaginary edge state and complex bulk state energies in the system. We find that the non-zero energy in-gap states, that appear due to periodic hopping modulations even in theγ = 0 limit, take purely real or purely imaginary eigenvalues depending on the strength of bothγand Δ (dimerization parameter). The localization of topological edge states (in-gap states) at the boundaries are investigated that reveals extended nature not only near topological transitions (further away from|Δ/t|=1) but also near the unmodulated limit ofΔ=0. Moreover, localization of the bulk states is observed at the maximally dimerized limit of|Δ/t|=1, which increases further withγ. These dissipative features can offer additional tunability in modulating the gain-loss contrast in optical systems or in designing various quantum information processing and storage devices.

Spontaneous CP breaking in a QCD-like theory

We examine the phase structure of a QCD-like theory at θ¯ = π obtained from supersymmetric SU(N) QCD perturbed by a small amount of supersymmetry breaking via anomaly mediation (AMSB QCD). The spectrum of this theory matches that of QCD at the massless level, though the superpartners are not decoupled. In this theory it is possible to nail down the phase structure at θ¯ = π as a function of the quark masses and the number of flavors F. For one flavor we find that there is a critical quark mass, below which CP is unbroken, while above the critical mass CP is spontaneously broken. At the critical mass there is a second-order phase transition along with a massless η′. We are able to analytically solve for the minima and the critical mass for N = 2, 3 as well as for the large N limit, while for other N one can find numerical results. For two flavors, we find that CP is always broken as long as the quark masses are equal and non-zero, however there is a non-trivial phase boundary for unequal quark masses, which we find numerically. For F ≥ 3 we obtain an intricate phase boundary which reproduces the various quark mass limits. All our results are in agreement with the predictions of refs. [1–5] for ordinary QCD that were based on anomaly matching arguments for generalized symmetries and the effective chiral Lagrangian. We also briefly comment on the domain wall solutions first discussed by Draper [6], and are able to present analytic results for the simplest case of SU(2) with one flavor.

Electronic, magnetic, and topological properties of ferromagnetic 2D perovskite-type oxides

Abstract Two-dimensional (2D) materials within the hematene-type binary oxides and perovskites family have recently gathered huge research interest for nanoelectronic devices. However, the exploration of their fascinating topological properties remains limited. Herein, through first-principles calculations, we systematically examine the electronic, magnetic, and topological properties of substitutionally doped 2D ABO3 (A=As, Sb, or Bi, and B = V, Nb, or Ta) perovskite structures at the B site of a B2O3 system. Interestingly, the atomic substitution makes the 2D ABO3 structures dynamically stable. Our detailed calculations show the ferromagnetic and antiferromagnetic phases of these materials. The calculated Chern number (C) for the ferromagnetic 2D ABO3 (A = As, Sb, or Bi, B = Nb or Ta) suggests their topologically non-trivial phases. Furthermore, the computed nontrivial Berry curvature highlights the topological properties in AsNbO3. These findings highlight opportunities in 2D-ABO3 materials, for applications in spintronics.

An unusual phase transition in a non-Hermitian Su–Schrieffer–Heeger model

This article studies a non-Hermitian Su-Schrieffer-Heeger model which has periodically staggered Hermitian and non-Hermitian dimers. The changes in topological phases of the considered chiral symmetric model with respect to the introduced non-Hermiticity are studied where we find that the system supports only complex eigenspectra for all values ofu ≠ 0 and it stabilizes only non-trivial insulating phase for higher loss-gain strength. Even if the system acts as a trivial insulator in the Hermitian limit, the increase in loss-gain strength induces phase transition to non-trivial insulating phase through a (gapless) semi-metallic phase. Interesting phenomenon is observed in the case where Hermitian system acts as a non-trivial insulator. In such a situation, the introduced non-Hermiticity neither leaves the non-trivial phase undisturbed nor induces switching to trivial phase. Rather, it shows transition from non-trivial insulating phase to the same where it is mediated by the stabilization of (non-trivial) semi-metallic phase. This unusual transition between the non-trivial insulating phases through non-trivial semi-metallic phase gives rise to a question regarding the topological states of the system under open boundary conditions. So, we analyze the possibility of stable edge states in these two non-trivial insulating phases and check the characteristic difference between them. In addition, we study the nature of topological states in the case of non-trivial gapless (semi-metallic) region.

Cyclic Evolution of Synergized Spin and Orbital Angular Momenta.

Spin angular momentum (SAM) and orbital angular momentum (OAM)are fundamental physical characteristics described by polarization and spatial degrees of freedom, respectively. Polarization is a feature of vector fields while spatial phase gradient determines the OAM ubiquitous to any scalar field. Common wisdom treats these two degrees of freedom as independent principles to manipulate wave propagations. Here, their synergy is demonstrated. This is achieved by introducing two orthogonal p-orbitals as eigenbases, whose spatial modal features are exploited to generate OAM, and the associated orbital orientations provide means to simultaneously manipulate polarizations. Through periodic modulation and directional coupling, a full cyclic evolution of synchronized and synergized SAM-OAM is realized. Remarkably, this evolution acquires a nontrivial geometric phase, leading to its representation on a Möbius strip. Experimentally, an acoustic cavity array is designed, whose dipole resonances precisely mimic the p-orbitals, with pressure fields featuring the spatial characteristics and velocity fields the vectorial orientations. Based on this synergy, a spin-orbital-Hall effect is further showcased, highlighting the intricate locking of handedness, directionality, spin density, and spatial mode profile. This study unveils a fundamental connection between SAM and OAM, promising avenues for their novel applications in trapping, coding, and communications.

Probing marginal stability in the spherical p = 2 model

Abstract In this paper, we investigate the marginally stable nature of the low-temperature trivial spin-glass phase in spherical p = 2 spin glass by perturbing the system with three different kinds of non-linear interactions. In particular, we compare the effect of three additional dense four-body interactions, namely ferromagnetic couplings, purely disordered couplings and couplings with competing disordered and ferromagnetic interactions. Our study, characterized by the effort to present in a clear and pedagogical way the derivation of all the results, shows that the marginal stability property of the spherical spin glass depends in fact on which kind of perturbation is applied to the system. In general, a certain degree of frustration is needed in the additional terms in order to induce a transition from a trivial to a non-trivial spin-glass phase. On the other hand, the addition of generic non-frustrated interactions does not destabilize the trivial spin-glass phase.

Topological insulating phase in nonsymmorphic bulk AX2 (A = Ca, Sr, or Ba; and X = As, Sb, or Bi) compounds

Owing to their unique topologically protected gapless boundary states, topological insulators (TIs) are attracting substantial interest in spintronics and quantum computing. Here, we discuss the structural, electronic, and topological properties of bulk alkaline earth di-pnictides AX2 (where A= Ca, Sr, or Ba and X= As, Sb, or Bi) using first-principles calculations under the hybrid functional approach. Our structural analysis based on phonon dispersion and molecular dynamics calculations establishes the thermodynamic stability of these materials and indicates their potential for synthesis. All investigated compounds are shown to host nontrivial phases upon including spin–orbit coupling. CaAs2, SrSb2, and BaSb2 are found to be strong TIs with sizable bandgaps of up to 213 meV. Nontrivial topology in the case of SrSb2 was further confirmed through surface state computations which showed the presence of gapless surface states. In addition, we demonstrate that using the hybrid functional approach can enhance the accuracy of the calculations to predict experimental findings. Finally, our study suggests that the alkaline earth di-pnictide family would provide a promising materials platform for developing applications of TIs.

Final-state rescattering mechanism of charmed baryon decays

The dynamical studies on the non-leptonic weak decays of charmed baryons are always challenging, due to the large non-perturbative contributions at the charm scale. In this work, we develop the final-state rescattering mechanism to study the two-body non-leptonic decays of charmed baryons. The final-state interaction is a physical picture of long-distance effects. Instead of using the Cutkosky rule to calculate the hadronic triangle diagrams which can only provide the imaginary part of decay amplitudes, we point out that the loop integral is more appropriate, as both the real parts and the imaginary parts of amplitudes can be calculated completely. In this way, it can be obtained for the non-trivial strong phases which are essential to calculate CP violations. With the physical picture of long-distance effects and the reasonable method of calculations, it is amazingly achieved that all the nine existing experimental data of branching fractions for the Λc+ decays into an octet light baryon and a vector meson can be explained by only one parameter of the model. Besides, the decay asymmetries and CP violations are not sensitive to the model parameter, since the dependence on the parameter is mainly cancelled in the ratios, so that the theoretical uncertainties on these observables are lowered down.

Defining Stable Phases of Open Quantum Systems

The steady states of dynamical processes can exhibit stable nontrivial phases, which can also serve as fault-tolerant classical or quantum memories. For Markovian quantum (classical) dynamics, these steady states are extremal eigenvectors of the non-Hermitian operators that generate the dynamics, i.e., quantum channels (Markov chains). However, since these operators are non-Hermitian, their spectra are an unreliable guide to dynamical relaxation timescales or to stability against perturbations. We propose an alternative dynamical criterion for a steady state to be in a stable phase, which we name uniformity: Informally, our criterion amounts to requiring that, under sufficiently small local perturbations of the dynamics, the unperturbed and perturbed steady states are related to one another by a finite-time dissipative evolution. We show that this criterion implies many of the properties one would want from any reasonable definition of a phase. We prove that uniformity is satisfied in a canonical classical cellular automaton, and we provide numerical evidence that the gap determines the relaxation rate between nearby steady states in the same phase, a situation we conjecture holds generically whenever uniformity is satisfied. We further conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability. Published by the American Physical Society 2024

Topological phase transitions via attosecond x-ray absorption spectroscopy

We present a numerical experiment that demonstrates the possibility to capture topological phase transitions via an x-ray absorption spectroscopy scheme. We consider a Chern insulator whose topological phase is tuned via a second-order hopping. We perform time-dynamics simulations of the out-of-equilibrium laser-driven electron motion that enables us to model a realistic attosecond spectroscopy scheme. In particular, we use an ultrafast scheme with a circularly polarized IR pump pulse and an attosecond x-ray probe pulse. A laser-induced dichroism-type spectrum shows a clear signature of the topological phase transition. We are able to connect these signatures with the Berry structure of the system. This work extend the applications of attosecond absorption spectroscopy to systems presenting a non-trivial topological phase.

Topological signatures of triply degenerate fermions in Heusler alloys: an ab initio study

Triply degenerate nodal point (TP) fermions, lacking elementary particle counterparts, have been theoretically anticipated as quasiparticle excitations near specific band crossing points constrained by distinct space-group symmetries instead of Lorentz invariance. Here, based onfirst-principlescalculations and symmetry analysis, we demonstrate the presence of TP fermions in Heusler alloys. Furthermore, we predict that these Heusler alloys are dynamically stable, exhibiting TP fermions along four distinctC3axes in the F-43m space group. We show thatα-LiCaPdSb harbours peculiar Fermi arcs and surface states on the (111) and (001) crystal facets, owing to the coexistence of threefold rotational and time reversal symmetry. More interestingly, a modest tensile strain can increase the distance of fermions along the Γ-Lhigh symmetric line by as much as 21.10%, which give rise to measurable Fermi arcs. Furthermore, we investigate non-trivial topological insulator phase inβ-LiCaPdSb, by changing the chemical environment through placing transition metal atoms at various Wyckoff positions. Theβ-LiCaPdSb harbour a semi-metallic nature, and by breaking cubic symmetry, it undergoes a transition from semi-metal to a non-trivial topological insulator. In addition, for the first time, rare-earth LaPtBi half-Heusler alloy is examined under strain to uncover multiple band inversions associated with the TP fermionic phase. The observed multiple band inversion is entirely unaffected by spin-orbit coupling. We show that the LaPtBi compound hosts TP fermions, which are linked to aZ2topological invariant. Remarkably, with clear band crossings and multiple band inversion, we point out the possibilities of the LaPtBi for displaying a rich topological phase diagram. Our work provides a prototype material platform for experimental detection through angle-resolved photoemission spectroscopy or scanning tunnelling spectroscopy and practical spintronic applications.

Topological interface and corner states of flexural waves in metamaterial plates with glide-symmetric holes

This study investigates the topological localization and propagation of flexural waves in metamaterial plates with perforated holes exhibiting glide symmetry. The dispersion relations of flexural waves in this mechanical system exhibit four-fold Dirac degeneracies at the M point of the Brillouin zone. By properly adjusting the rotation angles of the perforated holes, these degeneracies can be lifted up to create omnidirectional bandgaps, enabling nontrivial topological phases. Both numerical and experimental results demonstrate multiple topological states of flexural waves in the developed elastic metaplates, including dual-band helical interface states and anisotropic interface/corner states. The simple perforated metaplates with glide-symmetric holes provide novel, manufacturable platforms for the flexible manipulation of topological flexural waves, greatly facilitating potential applications such as energy harvesting and signal enhancement.

Pure-quartic solitons with PT-symmetric nonlinearity.

We propose a new, to the best of our knowledge, class of soliton based on the interaction of parity-time (PT) symmetric nonlinearity and quartic dispersion or diffraction. This novel kind of soliton is related to the recently discovered pure-quartic solitons (PQS), which arise from the balance of the Kerr nonlinearity and quartic dispersion, through a complex coordinate shift. We find that the PT-symmetric pure-quartic soliton presents important differences with respect to its Hermitian (Kerr) counterpart, including a nontrivial phase structure, a skewed spectral intensity, and a higher power for the same propagation constant. Further analysis reveals these solitons are linearly stable.

Anomalies of average symmetries: entanglement and open quantum systems

Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.

Strain-modulated antiferromagnetic Chern insulator in NiOsCl6 monolayer

Abstract Recently, Chern insulators in an antiferromagnetic (AFM) phase have been suggested theoretically and predicted in a few materials. However, the experimental observation of two-dimensional AFM quantum anomalous Hall effect is still a challenge to date. In this work, we propose that an AFM Chern insulator can be realized in a two-dimensional monolayer of NiOsCl$_6$ modulated by a compressive strain. Strain modulation is accessible experimentally and used widely in predicting and tuning topological nontrivial phases. With first-principles calculations, we have investigated the structural, magnetic and electronic properties of NiOsCl$_6$. Its stability has been confirmed through molecular dynamical simulations, elasticity constant and phonon spectrum. It has a collinear AFM order, with opposite magnetic moments of 1.3 $\mu_B$ on each Ni/Os atom, respectively, and the Néel temperature is estimated to be 93 $K$. In the absence of strain, it functions as an AFM insulator with a direct gap with spin-orbital coupling included. Compressive strain will induce a transition from a normal insulator to a Chern insulator characterized by a Chern number $C = 1$, with a band gap of about 30 meV. This transition is accompanied by a structural distortion. Remarkably, the Chern insulator phase persists within the 3$\%$-10$\%$ compressive strain range, offering an alternative platform for the utilization of AFM materials in spintronic devices.