Haldane Model Research Articles

Thermal Hall response: Violation of gravitational analogs and Einstein relations

The response of solids to temperature gradients is often described in terms of a gravitational analogue: the effect of a space-dependent temperature is modeled using a space dependent metric. We investigate the validity of this approach in describing the bulk response of quantum Hall states and other gapped chiral topological states. To this end, we consider the prototypical Haldane model in two different cases of (i) a space-dependent electrostatic potential and gravitational potential and (ii) a space-dependent temperature and chemical potential imprinted by a weak coupling to non-interacting electron baths and phonons. We find that the thermal analogue is \textit{invalid}; while a space dependent gravitational potential induces transverse energy currents proportional to the third derivative of the gravitational potential, the response to an analogous temperature profile vanishes in limit of weak coupling to the thermal bath. Similarly, the Einstein relation, the analogy between the electrostatic potential and the internal chemical potential, is not valid in such a setup.

Half-topological state in magnetic topological insulators

We predict a novel topological state, half-topological state, in magnetic topological insulators. The topological state is characterized by different topologies of electrons with different spin orientations, i.e., electrons with one spin orientation occupy a nontrivial topological insulating state, while electrons with opposite orientation occupy another insulating state with trivial topology. We demonstrate the occurrence of the half-topological state in magnetic topological insulators by employing a minimal model. The minimal model is a combination of the spinful Haldane and the double-exchange models. The double-exchange processes maintain a spontaneous magnetic ordering, while the next-nearest-neighbor hopping in the Haldane model gives rise to a nontrivial topological insulator. The minimal model is studied by applying the dynamical mean field theory. It is found that the long-range antiferromagnetic ordering drives the system from either topological or topologically trivial antiferromagnetic insulator to the half-topological state, and finally to topologically trivial antiferromagnetic insulator. The equations for the topological phase transitions are also explicitly derived.

Phase driven topological states in correlated Haldane model on a honeycomb lattice

Using mean field method and random phase approximation, we studied the phase driven topological exotic states in correlated Haldane model on a honeycomb lattice. It is found that topological spin density waves emerge with the phase change of next-nearest-neighbor hopping. We also investigated the topological properties of these spin density waves, including Chern number, edge state and Hall conductivity. Our work provides a new insight for topological phase transitions in correlated quantum anomalous Hall insulators.

Kinetic modelling of high concentration 4-Nitrophenol biodegradation by an isolated bacterial consortium and post-treatment ecotoxicity analysis

The present study documents the kinetics of aerobic batch growth and biodegradation of 4-Nitrophenol (4-NP) by an isolated bacterial consortium capable of utilizing 700 mg l−1 of 4-NP as the sole source of carbon and energy, the highest reported concentration to be biodegraded till date. The results of the batch biodegradation studies suggested that the consortium exhibited substrate inhibition kinetics and the Haldane model fitted the experimental data well. The estimated biokinetic parameters applied to biomass growth were maximum specific growth rate, μmax = 0.1532 h−1, half saturation coefficient, Ks = 4.717 mg l−1, and inhibition coefficient, Ki = 77.34 mg l−1. The specific degradation rate, q, was fitted to the model, and the kinetic parameters obtained were: qmax = 0.1700 g g−1 h−1, K's = 5.871 mg l−1, and K'i = 171.9 mg l−1. The yield coefficient (YX/S) varied in the range of 0.93–0.23 g g−1 for 12–700 mg l−1 4-NP concentration. The maintenance coefficient (m) and true yield (YG) were calculated to be 0.04491 h−1 and 0.9496 g g−1, respectively, based on the Pirt's equation. Furthermore, cytotoxicity and phytotoxicity assessment involving the animal cell line HEK293 and different seed variants, respectively, confirmed the detoxification of the biodegraded product, emphasizing the biocatalytic efficiency of the consortium in the bioremediation of 4-NP contaminated wastewater and suitability of its environmental discharge.

Plant Growth-Promoting Rhizobium Nepotum Phenol Utilization: Characterization and Kinetics

Phenol is a severe pollutant that harms the environment and, potentially, human health. This study aimed to investigate the biodegradability of phenol by the plant growth-promoting bacterium R. nepotum. That included studying the growth kinetics and the effects of growth conditions such as incubation temperature, pH, and the use of different substrate concentrations. As the primary substrate, six different starting concentrations of phenol were utilized. The ability of these cells to biodegrade phenol was greatly influenced by the culture conditions. After 36 and 96 hours of incubation at pH 7 and a temperature of 28 C, this organism grew the fastest and had the highest phenol biodegradation. The biodegradation rate is much higher at 700 mg/L, the highest of the six concentrations tried. In less than 96 hours of incubation, more than 90% of the phenol (700 mg/L) had been eliminated. The Haldane model has been the most accurate for determining the relationship between the initial concentration of phenol and growth rate. In contrast, the refined Gompertz model provided the most accurate depiction of phenol biodegradation over time. As predicted by the Haldane equation, the highest specific growth rate, half-saturation coefficient, and Haldane's growth kinetics inhibition coefficient are 0.7161 h1, 15.8 parts per million (ppm), and 292 parts per million (ppm), respectively. The equation of Haldane successfully fitted the experimental data by reducing the SSR (sum of squared errors) to 3.8x10 3. According to the results of the analysis by GC-MS for the bacterial culture sample, the hydroxylase enzyme was the first to convert the phenol molecule into catechol. The catechol was subsequently broken down into 2-hydroxymucconic semialdehyde by the 2,3-dioxygenase enzyme, which occurred through the meta-pathway. It is the first study showing that R. nepotum, a plant growth promoter, has high efficiency of phenol. In phenol-stressed conditions, this could help with rhizoremediation and crop yield preservation.

Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions

Starting with general semiclassical equations of motion for electrons in the presence of electric and magnetic fields, we extend the Chambers formula to include in addition to a magnetic field, time-dependent electric fields and bands with Berry curvature. We thereby compute the conductivity tensor ${\sigma}_{{\alpha}{\beta}}(B,{\omega})$ in the presence of magnetic field for bands in two (2D) and three (3D) dimensions with Berry curvature. We focus then on several applications to magnetotransport for metals with Fermi surface topological transitions in 2D. In particular, we consider a rectangular lattice and a model related to overdoped graphene, to investigate the signatures of different types of Fermi surface topological transitions in metals in the Hall coefficient, Hall conductivity ${\sigma}_{xy}$ and longitudinal conductivity ${\sigma}_{xx}$. The behavior of those quantities as a function of frequency, when the electric field is time dependent, is also investigated. As an example of non-zero Berry curvature, we study the magnetotransport of the Haldane model within this context. In addition, we provide the linear and nonlinear electric current formula to order $E^2$.

Evolution of the Berry phase and topological properties in models for merging Dirac cones

In this paper we study the evolution of the Berry phase ( Φ B ) for cases that exhibit merging of the Dirac cones in models of massless Dirac fermions . The Berry phase captures the band topology and hence facilitates prediction of the topological character of the system. Motivated by such a scenario we consider three different systems, namely, (i) an artificial model for graphene with a constant parameter, tuning of which makes the two Dirac cones merge (Montambaux et al., 2009), (ii) a generic case for graphene where all the three hopping amplitudes (say, t a , t b and t c ) are different and in such systems merging of Dirac cones are demonstrated when the hopping amplitudes satisfy a triangle inequality (Hasegawa et al., 2006), and finally (iii) in a Haldane model where the merging of the cones can be engineered as a function of the band deformation. We find that Φ B discontinuously jumps from a value π to zero at the point where the Dirac cones merge in (i) and (ii), while (iii) exhibits a different scenario where Φ B changes from 2 π to π . The result is surprising, since except for the topological gap that exists in (iii), the band structures for the cases (i) and (ii) display similar features where two of the hopping amplitudes (say t b and t c ) are equal and the third one (say t a ) is continuously varied with respect to other two. Thus the Haldane flux enforces a non-relativistic character to the otherwise relativistic Dirac fermions. Hence there is an interplay between the presence of the topological gap in the Haldane model with the Berry phase. Finally we show the evolution of the topological properties of the Haldane model by computing the Berry curvature and the Chern number where the latter shows the gradual vanishing of the topological regime as long as one of the hopping amplitudes remain smaller than twice of the other two. Since a large number of two dimensional materials exhibit topological character, and quite a few of them undergo topological phase transitions, our work will enable a simple, yet robust technique to study these systems. • Topological aspects and electronic properties of graphene • Haldane model • Chern insulators.

Global and local topological quantized responses from geometry, light, and time

To describe a spin-$\frac{1}{2}$ particle on the Bloch sphere with a radial magnetic field and topological states of matter from the reciprocal space, we introduce $C$ square (${C}^{2}$) as a local formulation of the global topological invariant. For the Haldane model on the honeycomb lattice, this ${C}^{2}$ can be measured from the Dirac points through circularly polarized light related to the high-symmetry $M$ point(s). For the quantum spin Hall effect and the Kane-Mele model, the ${\mathbb{Z}}_{2}$ topological number robust to interactions can be measured locally from a correspondence between the Pfaffian and light. We address a relation with a spin pump and the quantum spin Hall conductance. The analogy between light and magnetic nuclear resonance may be applied for imaging, among other applications.

Dynamics of the Entanglement Zero Modes in the Haldane Model under a Quantum Quench

We investigate evolution of entanglement spectra of the Haldane model for Chern insulators upon a sudden quench within the same topological phase. In particular, we focus on the location of the entanglement spectrum crossing, which signifies the bulk topology. It is shown that the coplanarity condition for the pseudomagnetic field of the model, which can be used to determine the crossing in the equilibrium case, needs to be relaxed. We analytically derive the non-equilibrium condition with the help of an edge-state wave function ansatz and a dynamically induced length-scale cutoff. With spectral analyses, it is realized that the oscillatory behavior of the crossing is dominated by the interband excitations at the van Hove singularities.

Thermal currents obtained and mutually switched by a modified Haldane model in graphene

By using the transfer matrix method, we discover three types of current, such as the 100% spin-valley polarized current, pure spin-valley current and pure charge current, in a two-terminal graphene system. These types of current can be obtained and mutually switched by modulating the parameters of the modified Haldane model (MHM). In our work, these types of current are driven by the thermal bias. Compared with this method of increasing the one-lead temperature (with a fixed temperature difference), the thermal currents can be more effectively strengthened by increasing the temperature difference (with a fixed one-lead temperature). In order to rapidly turn off these currents, we choose to enhance the intensity of the off-resonant circularly polarized light instead of canceling the temperature difference. These results indicate that the graphene system with the MHM has promising applications in the spin and valley caloritronics.

Reconfigurable Light Imaging in Photonic Higher-Order Topological Insulators

Topological phases of matter with robust edge states have revolutionized the fundamental intuitions for wave control. The recent development of higher-order topological insulators (HOTIs) realizes even lower dimensional topological states that enable versatile wave manipulations (e.g., light imaging). However, in conventional HOTIs, the topological states are usually protected by certain crystalline symmetries and therefore bounded at specific locations, hindering their applications in modern digital ears, which often prefer tunability and reconfigurability. Here, we report the reconfigurable light imaging based on topological corner states and anti-chiral edge states in a two-dimensional (2D) photonic HOTI with a honeycomb lattice of yttrium iron garnet (YIG, a ferrite material) rods. Sublattices A and B are applied with magnetic fields in opposite directions, which realize the so-called modified Haldane model that hosts anti-chiral edge modes. By further breaking the lattice’s inversion symmetry via adjusting the radii of A and B rods, topological edge states with valley degrees of freedom emerge, which not only exhibit valley-dependence but also surprisingly show anti-chiral behaviors. In the valley edge gap, which is of nontrivial higher-order topology, corner states appear. With different combinations of corner states and anti-chiral edge states, versatile reconfigurable light imaging can be realized. As examples, a multiplexing waveguide-resonator device, a pine tree imaging that can be lit up or put out at will and selective imaging for partial objects in a two-heart pattern are demonstrated. The proposed HOTI shows high potential in future intelligent devices with exciting tunable and reconfigurable functions, which may inspire a wide range of applications such as topological switching, imaging processing, and nonreciprocal integrated photonics.

Topological study of a Bogoliubov–de Gennes system of pseudo-spin- 1/2 bosons with conserved magnetization in a honeycomb lattice

We consider a Bogolibov-de Geenes (BdG) Hamiltonian, which is a non-Hermitian Hamiltonian with pseudo-Hermiticity, for a system of (pseudo) spin-$1/2$ bosons in a honeycomb lattice under the condition that the population difference between the two spin components, i.e., magnetization, is a constant. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry, with stable bulk bands but unstable edge modes which can be populated at an exponentially fast rate. We quantitatively study the topological properties of this model within the framework of the 38-fold way for non-Hermitian systems. We find, through the symmetry analysis of the Bloch Hamiltonian, that this model is classified either as two copies of symmetry class AIII+$\eta_-$ or two copies of symmetry class A+$\eta$ depending on whether the (total) system is time-reversal-symmetric, where $\eta$ is the matrix representing pseudo-Hermiticity and $\eta_-$ indicates that pseudo-Hermiticity and chiral symmetry operators anticommute. We prove, within the context of non-Hermitian physics where eigenstates obey the bi-orthonormality relation, that a stable bulk is characterized by a single topological invariant, the Chern number for the Haldane model, independent of pairing interactions. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes, which is expected to be useful for models built upon copies of the Haldane model across a broad array of disciplines. We adapt the theorem in our recent work [Phys. Rev. A 104, 013305 (2021)] to pseudo-Hermitian Hamiltonians that are less restrictive than BdG Hamiltonians and apply it to highlight that the vanishing of an unconventional commutator between number-conserving and number-nonconserving parts of the Hamiltonian indicates whether a system can be made to act as a topological amplifier.

Lattice dynamics with molecular Berry curvature: Chiral optical phonons

Under the Born-Oppenheimer approximation, the electronic ground state evolves adiabatically and can accumulate geometrical phases characterized by the molecular Berry curvature. In this work, we study the effect of the molecular Berry curvature on the lattice dynamics in a system with broken time-reversal symmetry. The molecular Berry curvature is formulated based on the single-particle electronic Bloch states. It manifests as a nonlocal effective magnetic field in the equations of motion of the ions that are beyond the widely adopted Raman spin-lattice coupling model. We employ the Bogoliubov transformation to solve the quantized equations of motion and to obtain phonon polarization vectors. We apply our formula to the Haldane model on a honeycomb lattice and find a large molecular Berry curvature around the Brillouin zone center. As a result, the degeneracy of the optical branches at this point is lifted intrinsically. The lifted optical phonons show circular polarizations, possess large phonon Berry curvature, and have a nearly quantized angular momentum that modifies the Einstein-de Haas effect.

Chitosan production by Penicillium citrinum using paper mill wastewater and rice straw hydrolysate as low-cost substrates in a continuous stirred tank reactor

ABSTRACT In this study, paper mill wastewater and hemicellulose hydrolysate were evaluated as low-cost substrates for fungal chitosan production using Penicillium citrinum. Submerged fermentation was first studied using a bioreactor operated under batch, fed-batch and continuous modes with paper mill wastewater as the substrate. Very high removal (91%) of organics as chemical oxygen demand (COD) in the wastewater with 160 mg L-1 chitosan production by P. citrinum was obtained using the bioreactor operated under fed-batch mode for 72 h. Moreover, 86% reduction of phenolics in the wastewater with 89% decolourization efficiency was achieved in the fed-batch experiments with the bioreactor. Under the continuous mode of operation with the bioreactor, maximum chitosan production of 170 mg L-1 was observed. The effect of acetic acid addition to the wastewater for enhancing chitosan production by the fungus was further studied in a batch system. Chitosan productivity of 2.33 mg L-1 h-1 was obtained with 50 mg/L acetic acid. Various models, viz. Monod, Haldane, Andrews, Webb and Yano, were fitted to the experimental data for understanding the kinetics involved in the process. Haldane model accurately fitted the experimental data on biomass specific growth rate, acetic acid consumption rate and chitosan production rate by P. citrinum with acetic acid addition to the wastewater. Fungal fermentation of another low-cost substrate, rice straw hydrolysate, was further studied using the batch-operated bioreactor; and a maximum chitosan titre of 911 mg L−1 was achieved using the detoxified rice straw hydrolysate. Highlights Low-cost substrates for chitosan production by Penicillium citrinum are reported Acetic acid addition to paper mill wastewater enhances chitosan production Biomass growth and chitosan production follow substrate inhibition kinetics Fed-batch -operated bioreactor resulted in 91% wastewater treatment efficiency Maximum chitosan titre of 911 mg L−1 was achieved with rice straw hydrolysate

High-Harmonic Generation Approaching the Quantum Critical Point of Strongly Correlated Systems.

By employing the exact diagonalization method, we investigate the high-harmonic generation (HHG) of the correlated systems under the strong laser irradiation. For the extended Hubbard model on a periodic chain, HHG close to the quantum critical point (QCP) is more significant compared to two neighboring gapped phases (i.e., charge-density-wave and spin-density wave states), especially in low frequencies. We confirm that the systems in the vicinity of the QCP are supersensitive to the external field and more optical-transition channels via excited states are responsible for HHG. This feature holds the potential of obtaining high-efficiency harmonics by making use of materials approaching QCP. Based on the two-dimensional Haldane model, we further propose that the even- or odd-order components of generated harmonics can be promisingly regarded as spectral signals to distinguish the topologically ordered phases from locally ordered ones. Our findings in this Letter pave the way to achieve ultrafast light source from HHG in strongly correlated materials and to study quantum phase transition by nonlinear optics in strong laser fields.

Competition of first-order and second-order topology on the honeycomb lattice

We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekul\'e-distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains twelve distinct phases. All phases can be characterized by the first Chern number or by a quantized $\mathbb{Z}_Q$ Berry phase. Highlights include phases with high Chern numbers, a novel $\mathbb{Z}_6$ topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phases at lower fillings, and find again first-order and second-order topological phases. Finally, we identify real-space structures which feature corner states not only at half but also at third and sixth fillings, in agreement with the quantized $\mathbb{Z}_Q$ Berry phases.

Influence of On-Site Potential Energy on Bands of Haldane Model and Implementation of Its Topoelectrical Circuit

Influence of On-Site Potential Energy on Bands of Haldane Model and Implementation of Its Topoelectrical Circuit

Kinetics Modelling of Pseudomonas stutzeri strain DN2 Growth Behaviour in Tributyltin Chloride

A predictive model was performed to describe Pseudomonas stutzeri strain DN2 growth behaviour in tributyltin chloride, using primary Modelling and a polynomial model as a secondary predictive model. In this investigation, data predicted using the modified Logistic (ML) was the most accurate. The Bias Factor (Bf) and Accuracy Factor (Af) values for the (ML) model were 1.39 and 1.51, indicating that the predictions were within a reliable range. The low RMSE value of 0.14, R2 and adj R2 (0.99) value closer to 1, showing that modified logistics is better than the other models at describing the growth behaviour of Pseudomonas stutzeri strain DN2 in toxic tributyltin chloride. Both the Aiba and Haldane models on the other hand, among the secondary model best fit the behaviours having low RMSE and MSE values and adjR2 value closer to 1. In this study, the primary and secondary kinetics of Pseudomonas stutzeri strain DN2 growth behaviour in tributyltin chloride was explored and it was shown in this study that the modified logistic and the Haldane models better suit the growth behavior of Pseudomonas stutzeri strain DN2 in tributyltin chloride. The parameters obtained from the modelling exercise will be very valuable in transferring the laboratory results to the field.

Frequency dependence of the light-induced Hall effect in dissipative graphene

We determine the Hall conductivity of light-driven graphene, with specific focus on its frequency dependence, and compare it to the static effective approximation, based on Floquet states. This approximation gives the Haldane model as the effective model for light-driven graphene, with a gapped spectrum and a quantized Hall conductivity of $-2e^2/h$. We simulate both the light-driven and the effective model, and explicitly include the dissipative environment in our simulations. We investigate the effect of different driving regimes and dissipation strengths on the Hall conductivity in graphene. As a central result, the Hall conductivity of the light-driven system is not well approximated by the effective model, except for a regime of intermediate driving frequencies and small dissipation where the Hall conductivity contribution of the Dirac point approximately recovers the quantized value of $-2e^2/h$, as well as in the transient dynamics for weak dissipation.

A novel process of salt tolerance partial denitrification and anammox (ST-PDA) for treating saline wastewater

In the study, the salt-tolerant partial denitrification and Anammox (ST-PDA) process was established, meanwhile, the feasibility of salinity inhibition model as the boundary control method and the subsequent operation performance were studied. Study indicated that the performance of salt-tolerant PD sludge was the optimum under the 10 g·L-1 salinity, and AnAOB also maintained high activity at the salinity. Haldane and Aiba models verified that NO3–-N (substrate) and FNA (product) would have negative consequences for performance of ST-PDA system. However, the effect of FNA would be eliminated by self-alkalization in the denitrification process. A 90% nitrogen removal rate was achieved and the average effluent total nitrogen of 17.8 mg·L-1 was maintained in the system. The high throughput sequencing revealed that the species richness decreased with the salinity increased, while Thauera played a major role in nitrogen removal in saline environment. The study provides a novel insights for salt-containing industrial wastewater.