Brillouin Zone Research Articles

Scaling theory for non-Hermitian topological transitions.

Understanding the critical properties is essential for determining the physical behavior of topological systems. In this context, scaling theories based on the curvature function in momentum space, the renormalization group (RG) method, and the universality of critical exponents have proven effective. In this work, we develop a scaling theory for non-Hermitian topological states of matter. We utilize the curvature function renormalization group (CRG) method, incorporating biorthonormal vectors for a 2 × 2 non-Hermitian Dirac model. This approach allows us to analyze the Wannier state correlation function (WCF) and determine the corresponding localization critical exponent. The CRG method successfully identifies topological phase transitions and locates stable and unstable fixed points. To account for non-Hermitian effects, we construct the curvature function in the generalized Brillouin zone using non-Bloch wave functions, enabling a comprehensive WCF and CRG analysis.

Lattice-mismatched and twisted multi-layered materials for efficient solar cells.

We argue that alternating-layer structures of lattice mismatched or misaligned (twisted) atomically-thin layers should be expected to be more efficient absorbers of the broad-spectrum of solar radiation than the bulk material of each individual layer. In such mismatched layer-structures the conduction and valence bands of the bulk material, split into multiple minibands separated by minigaps confined to a small-size emerging Brillouin zone due to band-folding. We extended the Shockley-Queisser approach to calculate the photovoltaic efficiency for a band split into minibands of bandwidth $\Delta E$ and mini-gaps $\delta G$ to model the case when such structures are used as solar cells. We find a significant efficiency enhancement due to impact ionization processes, especially in the limit of small but non-zero $\delta G$, and a dramatic increase when fully concentrated sun-light is used.&#xD.

Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: Application to electronic structure and optical responses

Brillouin zone folding method for quasiperiodic superconductivity in multilayer systems: Application to electronic structure and optical responses

Dispersive nodal fermions along grain boundaries in Floquet topological crystals

Driven quantum materials often feature emergent topology, otherwise absent in static crystals. Dynamic bulk-boundary correspondence, encoded by nondissipative gapless modes residing near the Floquet zone center and/or boundaries, is its most prominent example. Here we show that topologically robust gapless dispersive modes appear along the grain boundaries, embedded in the interior of Floquet topological crystals, when the Floquet-Bloch band inversion occurring at a finite momentum (KinvFlq) and the Burgers vector (b) of the constituting array of dislocations satisfy KinvFlq·b=π (modulo 2π). Such nondissipative gapless states can be found near the center and/or edges of the Floquet Brillouin zone, irrespective of the drive protocol. We showcase these general outcomes for two-dimensional driven time-reversal symmetry breaking insulators. Promising experimental platforms hosting such dynamic topological dispersive bands in real materials are discussed.

Anomalous pumping in the non-Hermitian Rice-Mele model.

We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static one-dimensional (1D) RM model, we find two independent tuning knobs that can drive the topological transition, namely, non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we use a finite-size generalized Brillouin zone (GBZ) scheme to show that the edge modes can be distinguished from the non-hermiticity induced skin modes. Moreover, this scheme can capture the state pumping of topological edge modes as a function of $\gamma$ in the static 1D RM model and it further provides insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Furthermore, we show that the standard topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, we observe that it depends upon the driving protocols and strength of the non-Hermiticity ($\gamma$). With increasing $\gamma$, the adiabatic pumping for non-trivial protocols is destroyed first and then re-emerges as an anomalous pumping which does not have any Hermitian counterpart. Additionally, we observe that even a trivial adiabatic protocol can give rise to pumping as opposed to the Hermitian system. This is attributed to the inherent point gap physics of non-Hermitian system which we explain by reformulating a non-Bloch topological invariant for the 1+1D RM model. This invariant explains the number of pumped charges (in each period) for all the driving protocols.

Berry curvature and shift vector effects at high-order wave mixing in biased bilayer graphene

In this paper, we present a microscopic quantum theory that elucidates the nonlinear and nonperturbative optical response of biased bilayer graphene subjected to bichromatic strong laser fields. This response is analyzed using a four-band Hamiltonian derived from calculations. For the laser-stimulated dynamics, we employ structure gauge-invariant evolutionary equations to accurately describe the evolution of the single-particle density matrix across the entire Brillouin zone. The resonant generation of electron-hole pairs by the high-frequency component of the field, combined with the induction of high-order harmonic generation and high-order wave mixing by the strong low-frequency field component, leads to significant alterations in the resulting spectra. These changes are driven by the effects of Berry curvature and the shift vector, which modify the relative contributions of interband and intraband channels, thereby fundamentally reshaping the radiation spectra at high-order frequency multiplication. The numerical results are further supported by approximate analytical calculations, demonstrating that high-order wave mixing can be modeled using the classical trajectory analysis of electron-hole pairs, with Berry curvature and the shift vector significantly influencing the saddle-point equations. Published by the American Physical Society 2025

Topology of far-field signals for photonic crystal slabs

The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high-order corner states. However, this work investigated the polarization distribution of radiated fields for photonic crystal slabs to get their far-field properties of band topology. We introduced a topological invariant—the winding number of far-field polarization around the Brillouin zone boundary and confirmed a robust correspondence between it and the Chern number of energy bands from the perspective of symmetry, which can be used to analyze the process of topological phase transition. It is found that changes in the winding number and Chern number, associated with the exchange of far-field polarization singularities, especially for bound states in the continuum, will emerge during phase transition. These findings offer insights for further understanding the intriguing properties of topological materials.

Anomalous pumping in the non-Hermitian Rice-Mele model.

We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static one-dimensional (1D) RM model, we find two independent tuning knobs that can drive the topological transition, namely, non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we use a finite-size generalized Brillouin zone (GBZ) scheme to show that the edge modes can be distinguished from the non-hermiticity induced skin modes. Moreover, this scheme can capture the state pumping of topological edge modes as a function of $\gamma$ in the static 1D RM model and it further provides insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Furthermore, we show that the standard topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, we observe that it depends upon the driving protocols and strength of the non-Hermiticity ($\gamma$). With increasing $\gamma$, the adiabatic pumping for non-trivial protocols is destroyed first and then re-emerges as an anomalous pumping which does not have any Hermitian counterpart. Additionally, we observe that even a trivial adiabatic protocol can give rise to pumping as opposed to the Hermitian system. This is attributed to the inherent point gap physics of non-Hermitian system which we explain by reformulating a non-Bloch topological invariant for the 1+1D RM model. This invariant explains the number of pumped charges (in each period) for all the driving protocols.

Enhanced third-harmonic generation and degenerate four-wave mixing in an all-dielectric metasurface via Brillouin zone folding induced bound states in the continuum

Enhanced third-harmonic generation and degenerate four-wave mixing in an all-dielectric metasurface via Brillouin zone folding induced bound states in the continuum

Correspondence between Euler charges and nodal-line topology in Euler semimetals.

Real multi-bandgap systems have non-abelian topological charges, with Euler semimetals being a prominent example characterized by real triple degeneracies (RTDs) in momentum space. These RTDs serve as "Weyl points" for real topological phases. Despite theoretical interest, experimental observations of RTDs have been lacking, and studies mainly focus on individual RTDs. Here, we experimentally demonstrate physical systems with multiple RTDs in crystals, analyzing the distribution of Euler charges and their global connectivity. Through Euler curvature fields, we reveal that type I RTDs have quantized point Euler charges, while type II RTDs show continuously distributed Euler charges along nodal lines. We discover a correspondence between the Euler number of RTDs and the abelian/non-abelian topological charges of nodal lines, extending the Poincaré-Hopf index theorem to Bloch fiber bundles and ensuring nodal line connectivity. In addition, we propose a "no-go" theorem for RTD systems, mandating the balance of positive and negative Euler charges within the Brillouin zone.

Intrinsic strong self-hybrid coupling empowered by Brillouin zone folding-induced high-Q quasibound modes in van der Waals metasurfaces

Intrinsic strong self-hybrid coupling empowered by Brillouin zone folding-induced high-Q quasibound modes in van der Waals metasurfaces

Numerical study of tunable terahertz radiation from differential frequency generation in high-<i>Q</i> geometrically perturbed grating waveguide structures

Nonlinear difference frequency generation (DFG) is a key mechanism for realizing terahertz (THz) sources. Utilization of DFG within micro- and nano-structures can circumvent the phase-matching limitations while supporting device miniaturization and integrability, thus the DFG is made a significant area of research. Enhancing the local electric fields through resonant modes in micro- and nano-structures has become a promising approach to achieving efficient and tunable THz sources across a broad wavelength range. In this work, the mechanism of DFG in high-Q-factor grating-waveguide structures for efficientlytuning THz radiation over a wide spectral range is investigated by using numerical simulations based on the finite element method (COMSOL Multiphysics). Theoretical analysis reveals that modulating the positional perturbation of one of the adjacent gratings effectively doubles the grating period, causing Brillouin zone to fold. This folding shifts the dispersion curve of the guided mode (GM) within the waveguide layer above the light cone, forming a guided mode resonance (GMR) with an ultra-high Q-factor, thereby significantly enhancing THz generation in a broad spectral range. Taking a cadmium sulfide (CdS) grating-waveguide structure for example, numerical simulations demonstrate that the THz conversion efficiency reaches an order of 10<sup>–8</sup>W<sup>–1</sup> when both fundamental frequency beams have an intensity of 100 kW/cm<sup>2</sup>, which is 10<sup>9</sup> times higher than the conversion efficiency of a CdS film of the same thickness. Moreover, the fundamental frequency resonance wavelength can be widely tuned by adjusting the incident angle. High-Q-factor resonance modes enable various fundamental frequency combinations by changing the incident angles of the two fundamental frequency beams, facilitating the generation of THz waves with arbitrary frequencies. This approach ultimately enables a highly efficient and tunable THz source in a wide spectral range, providing valuable insights for generating THz sources on micro- and nanophotonic platforms.

Pseudogap in electron-doped cuprates: Strong correlation leading to band splitting

The pseudogap phenomena have been a long-standing mystery of the cuprate high-temperature superconductors. The pseudogap in the electron-doped cuprates has been attributed to band folding due to antiferromagnetic (AFM) long-range order or short-range correlation. We performed an angle-resolved photoemission spectroscopy study of the electron-doped cuprates Pr1.3-xLa0.7CexCuO4 showing spin-glass, disordered AFM behaviors, and superconductivity at low temperatures and, by measurements with fine momentum cuts, found that the gap opens on the unfolded Fermi surface rather than the AFM Brillouin zone boundary. The gap did not show a node, following the full symmetry of the Brillouin zone, and its magnitude decreased from the zone-diagonal to (π,0) directions, opposite to the hole-doped case. These observations were reproduced by cluster dynamical-mean-field-theory calculation, which took into account electron correlation precisely within a (CuO2)4 cluster. The present experimental and theoretical results are consistent with the mechanism that electron or hole doping into a Mott insulator creates an in-gap band that is separated from the upper or lower Hubbard band by the pseudogap.

All-Electron BSE@GW Method with Numeric Atom-Centered Orbitals for Extended Periodic Systems.

Green's function theory has emerged as a powerful many-body approach not only in condensed matter physics but also in quantum chemistry in recent years. We have developed a new all-electron implementation of the BSE@GW formalism using numeric atom-centered orbital basis sets (Liu, C. J. Chem. Phys. 2020, 152, 044105). We present our recent developments in implementing this formalism for extended periodic systems. We discuss its numerical implementation and various convergence tests pertaining to numerical atom-centered orbitals, auxiliary basis sets for the resolution-of-identity formalism, and Brillouin zone sampling. Several proof-of-principle examples are presented to compare with other formalisms, illustrating the new all-electron BSE@GW method for extended periodic systems.

Symmetry-protected and Brillouin zone folding driven bound states in the continuum in dielectric nanorod arrays for effcient third harmonic generation

Abstract Two types of bound states in continuum (BICs), symmetry-protected and Brillouin zone folding driven, are identified in the hollow Si nanorod arrays. By modulating the direction and distance of the air holes from the center of the nanorods, it is possible to achieve either a single quasi-BIC or three quasi-BICs. The transmission spectra exhibit ultra-narrow lines, and the quasi-BICs demonstrate ultra-high Q factors. Additionally, effcient third-harmonic generation occurs at low pump intensities. The results indicate that the proposed nanostructures of two types of BICs with a flexible modulation hold great potential applications for nonlinear photonic devices.

Quantum computing topological invariants of two-dimensional quantum matter

Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers. Published by the American Physical Society 2024

Theoretical Study of Exciton Properties of Dilute Gainasn Semiconductors

In this research, the electronic band structure, electronic properties and the exciton binding energy of dilute quaternary GaInAsN alloy semiconductors are investigated. This study was aimed to theoretically study the exciton properties of dilute GaInAsN semiconductors. The effects of Nitrogen incorporation in InGaAs alloy was studied within the band anti-crossing model (BAC). The pseudopotential inputs within the virtual crystal approximation (VCA) was employed to make modifications for the nitrogen and indium related alloy disorder effects. The Harrison’s model used to study the bandstructure. In general, the results of our computations are in agreement with recent experimental findings. It is found that the presence of nitrogen in the GaInAsN alloy reduces the fundamental bandgap energy within the band anticrossing (BAC) model in the vicinity of the first Brillouin zone boundary, to . The heavy hole and electron effective masses, reduced mass, energy band gap, high frequency dielectric constant, static dielectric constant, the refractive indices, polarity, covalency, Bohr radius and binding energy are also modified by the nitrogen and indium fractions of the alloy. For all the alloy compositions studied, it was observed that the binding energies of the excitons vary between the values for InAs and GaAs . Also, the corresponding excitons Bohr radii vary between the values for InAs and GaAs . The information derived from the present study predicts that GaInAsN tunable binding energies and electronic properties are of great technological importance for mid-infrared (MIR) optoelectronics.

Artificial Intelligence (AI) In Education: Pros and Cons Among Secondary School Teachers in Malang, Indonesia

Artificial Intelligence (AI) became a concern of many scholars including Educators. Some educators believed that AI can be a very sophisticated tool to support teaching and learning processes, but others believed otherwise. Discussion on Implementation of AI in the field of education always stimulates the appearance of pros and cons. This study tries to explore secondary school teacher perspectives on the use of Artificial Intelligence in the field of education. This study explores 15 teachers of secondary school in Malang. In-depth interview was taken to get comprehensive data. The result of this study showed that there are 5 AI tools which became frequently used by teachers, those are: ChatGPT, Grammarly, Canva, Gamma, and Class point. Interestingly, 42% of the informants are using AI for professional purposes like supporting their teaching and learning process. Besides, 33% of the informants are using it for academic purposes like writing the article, news, or other tasks which are able to improve their academic competences. There were also 25% of the informants were used AI for personal purposes which is not correlated to their profession as teachers, like for having fun, trial and error, or out of curiosity. Moreover, the use of Artificial Intelligence in the field of education created two-side of perspectives: pro and con. The pro argued that AI can be fully adapted in secondary school for its numerous benefits for both teacher and student, while the con argued that AI would have many problems if it was implemented. There are four arguments behind the pros: the use of AI in education proved that teachers are adaptive towards newest technology, it is also able to improve teacher skills and competencies, it also can support teacher’s administrative tasks, and students need to be introduced to the latest technology for their future. On the other side, there are three arguments behind the cons: ethical issues, lack of learning process, and technology dependencies and loss of human interaction.

Multiple high-Q Brillouin zone folding guided mode resonances in all-dielectric metasurfaces

High quality (Q) factors guided mode resonances (GMRs) are important platform for enhancing light–matter interactions. Conventional GMRs are excited by embedding periodic nanoholes in planar thin films, where the size of the holes determines the Q-factors. These control methods are relatively limited. In this work, we study multiple high-Q band folding GMRs in the near-infrared region and explore their sensing characteristics. By constructing a nanohole dimer metasurface, five band folding ultrahigh-Q GMRs are formed and corresponding high-Q GMRs are obtained by changing the size of one nanohole to break the mirror symmetry of the structure and thus manipulate the energy radiation of the modes. These resonance modes exhibit greater stability in momentum space, and their excitation is not strictly dependent on perpendicularly incident light, which facilitates experimental testing. We fabricate a series of samples to confirm these high-Q GMRs, with experimental Q-factors reaching 5.0 × 103. Next, we investigate the sensing characteristics of these GMRs, and due to the significant differences in their field distributions, TM0 mode has the best sensing performance among the five modes. Here, by spin-coating photoresists on the surface of the devices, we examine their sensing properties. It is proved that the specificity of the eigenfield localization of TM0 mode results in an excellent performance of the sensing properties of this mode, with an experimental sensitivity and figure of merit of 124 nm/RIU and 105, respectively. This work provides a route for the realization of metasurfaces with high Q-factors, which has potential applications in nanophotonics.

Full Spectrum Electrochromic WO3 Mechanism and Optical Modulation via Ex Situ Spectroscopic Ellipsometry: Effect of Li+ Surface Permeation.

Tungsten oxide (WO3) electrochromic devices are obtaining increasing interest due to their color change and thermal regulation. However, most previous work focuses on the absorption or transmission spectra of materials, rather than the optical parameters evolution in full spectrum in the electrochromic processes. Herein, we developed a systematic protocol of ex situ methods to clarify the evolutions of subtle structure changes, Raman vibration modes, and optical parameters of WO3 thin films in electrochromic processes as stimulated by dosage-dependent Li+ insertion. We obtained the below information by ex situ spectroscopic ellipsometry. (1) Layer-by-layer Li+ embedding mechanism demonstrated by individual film thickness analysis. (2) The details of its optical leap in the Brillouin zone in the full spectral. (3) The optical constants varied with the Li+ insertion in the ultraviolet, visible, and near-infrared bands, demonstrating the potential for applications in chip fabrication, deep-sea exploration, and optical measurements. (4) Simulated angular modulation laws of WO3 films for full spectra in different Li+ insertion states. This ex situ method to study the optical properties of electrochromic devices are important for monitoring phase transition kinetics, the analysis of optical leaps, and the study of ion diffusion mechanisms and the stoichiometry-dependent changes in optical constants over the full spectral. This work shows that electrochromic films in Li+ surface permeation can be applied in the field of zoom lenses, optical phase modulators, and other precision optical components. Our work provides a new solution for the development of zoom lenses and a new application scenario for the application of electrochromic devices.