Lattice Systems Research Articles

Layer-resolved electronic behavior in a Kondo lattice system, CeAgAs2

We investigate the electronic structure of an antiferromagnetic Kondo lattice system CeAgAs2 employing hard x-ray photoemission spectroscopy. CeAgAs2, an orthorhombic variant of HfCuSi2 structure, exhibits antiferromagnetic ground state, Kondo like resistivity upturn and compensation of magnetic moments at low temperatures. The photoemission spectra obtained at different photon energies suggest termination of the cleaved surface at cis-trans-As layers. The depth-resolved data show significant surface-bulk differences in the As and Ce core level spectra. The As 2p bulk spectrum shows distinct two peaks corresponding to two different As layers. The peak at higher binding energy correspond to cis-trans-As layers and is weakly hybridized with the adjacent Ce layers. The As layers between Ce and Ag-layers possess close to trivalent configuration due to strong hybridization with the neighboring atoms and the corresponding feature appear at lower binding energy. Ce 3d core level spectra show multiple features reflecting strong Ce-As hybridization and strong correlation. Intense f 0 peak is observed in the surface spectrum while it is insignificant in the bulk. In addition, we observe a features at binding energy lower than the well-screened feature indicating the presence of additional interactions. This feature becomes more intense in the bulk spectra suggesting it to be a bulk property. Increase in temperature leads to a spectral weight transfer to higher binding energies in the core level spectra and a depletion of spectral intensity at the Fermi level as expected in a Kondo material. These results reveal interesting surface-bulk differences, complex interplay of intra- and inter-layer covalency, and electron correlation in the electronic structure of this novel Kondo lattice system.

Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators

We consider the effect of a local interatomic repulsion on synthetic heterostructures where a discrete synthetic dimension is created by Raman processes on top of SU(N)SU(N)-symmetric two-dimensional lattice systems. At a filling of one fermion per site, increasing the interaction strength, the system is driven towards a Mott state which is adiabatically connected to a band insulator. The chiral currents associated with the synthetic magnetic field increase all the way to the Mott transition, where they reach the maximum value, and they remain finite in the whole insulating state. The transition towards the Mott-band insulator is associated with the opening of a gap within the low-energy quasiparticle peak, while a mean-field picture is recovered deep in the insulating state.

Improved design and experimental demonstration of ultrahigh-Q C6-symmetric H1 hexapole photonic crystal nanocavities.

An H1 photonic crystal nanocavity (PCN) is based on a single point defect and has eigenmodes with a variety of symmetric features. Thus, it is a promising building block for photonic tight-binding lattice systems that can be used in studies on condensed matter, non-Hermitian and topological physics. However, improving its radiative quality (Q) factor has been considered challenging. Here, we report the design of a hexapole mode of an H1 PCN with a Q factor exceeding 108. We achieved such extremely high-Q conditions by varying only four structural modulation parameters thanks to the C6 symmetry of the mode, despite the need of more complicated optimizations for many other PCNs. Our fabricated silicon H1 PCNs exhibited a systematic change in their resonant wavelengths depending on the spatial shift of the air holes in units of 1 nm. Out of 26 such samples, we found eight PCNs with loaded Q factors over one million. The best sample was of a measured Q factor of 1.2 × 106, and its intrinsic Q factor was estimated to be 1.5 × 106. We examined the difference between the theoretical and experimental performances by conducting a simulation of systems with input and output waveguides and with randomly distributed radii of air holes. Automated optimization using the same design parameters further increased the theoretical Q factor by up to 4.5 × 108, which is two orders of magnitude higher than in the previous studies. We clarify that this striking improvement of the Q factor was enabled by the gradual variation in effective optical confinement potential, which was missing in our former design. Our work elevates the performance of the H1 PCN to the ultrahigh-Q level and paves the way for its large-scale arrays with unconventional functionalities.

Damped and driven breathers and metastability

In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrödinger equations subject to spatially localized driving and damping. They provide an alternate description of the metastable behavior in such lattice systems which agrees with previous predictions for the evolution of metastable states while providing more accurate approximations to these states. We analyze the stability of these breathers, finding a very small positive eigenvalue whose eigenvector lies almost tangent to the surface of the cylinder formed by the family of breathers. This causes solutions to slide along the cylinder without leaving its neighborhood for very long times.

Stable pair liquid phase in fermionic systems

We predict the existence of a pair-liquid phase in lattice fermion systems with finite-range attractive interactions. This exotic state competes on one side with a normal Fermi liquid of unpaired fermions and on the other side with a phase-separated state where all fermions are coupled into macroscopic clusters. We show that such a phase is absent in bosonic systems and therefore is protected by the exclusion principle. In contrast with zero-range attractive systems where clustering of more than two fermions is directly prohibited, here quantum statistics acts dynamically and in a more subtle way. Since a many-fermion wave function must have nodes, the cluster formation threshold is larger than the pair formation threshold. By directly solving a four-body Schroedinger equation on one- and two-dimensional lattices, we map the boundaries of pair stability. The pair liquid phase should be observable in cold atom systems. We also discuss implications for the preformed-pair mechanism of high-temperature superconductivity.

Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice

Non-symmorphic symmetries protect Dirac nodal lines and cones in lattice systems. Here, we investigate the spectral properties of a two-dimensional lattice belonging to a non-symmorphic group. Specifically, we look at the herringbone lattice, characterized by two sets of glide symmetries applied in two orthogonal directions. We describe the system using a nearest-neighbor tight-binding model containing horizontal and vertical hopping terms. We find two nonequivalent Dirac cones inside the first Brillouin zone along a high-symmetry path. We tune these Dirac cones’ positions by breaking the lattice symmetries using on-site potentials. These Dirac cones can merge into a semi-Dirac cone or unfold along a high-symmetry path. Finally, we perturb the system by applying a dimerization of the hopping terms. We report a flow of Dirac cones inside the first Brillouin zone describing quasi-hyperbolic curves. We present an implementation in terms of CO atoms placed on the top of a Cu(111) surface.

Abstract Number ‐ 5: Interim Results of PRE‐SEAL IT Saccular Endovascular Aneurysm Lattice System First in Human Interventional Trial

Introduction Preliminary in vivo animal intracranial aneurysm (IA) studies have demonstrated promising immediate and follow‐up aneurysm occlusion rates using the novel Saccular Endovascular Aneurysm Lattice (SEAL) system. The PRE‐SEALTM IT trial was designed to assess the feasibility, safety, and effectiveness of the SEAL system in patients with previously untreated ruptured and unruptured wide‐neck IA. Methods PRE‐SEAL IT is an on‐going, prospective, interventional, core‐lab adjudicated, single‐arm study performed in Medellin, Columbia. Key inclusion criteria included: 1. Age 20–80 years, 2. Saccular shape, bifurcation, or terminus IA, 3. Wide neck aneurysm with neck size ≥4 mm or dome‐to‐neck ratio <2, and 4. IA diameter 2mm to 25mm. Consented and enrolled patients were treated with the SEALTM device. A follow‐up DSA was performed at 24‐hours, 6 months, and 12 months and a MRA at 3 months. Final clinical follow‐up was at 24‐months. Primary efficacy outcome was achieving complete occlusion (WOS grade A or B) at 6 months angiographic follow up. Primary safety outcome was any stroke with an increase in NIHSS of 4 up to discharge. Results From December 2021 through June 2022, 15 patients have been enrolled into the PRE‐SEAL IT trial. Ten women and 5 men were treated with the SEAL device, with a mean age of 56.8±9.5 years. Of the 15 IA, 12 were anterior circulation (ICA‐T (1), MCA (7), AcomA (3), A2‐A3 (1)) and 3 posterior circulations (Basilar, VBJ‐fenestration, SCA), and 14 were unruptured (93.3%). Mean aneurysm width was 6.1±2.5mm. Immediate post‐procedure complete occlusion (Grade A, B) was achieved in 9 patients (60%) and adequate occlusion (Grade A, B, C) in 13 (86.6%). At 24‐hours follow‐up, 12 patients (80%) had complete occlusion and 15 (100%) achieved adequate occlusion. Six‐month complete occlusion rate (Grade A and B) was 100% (8/8). Interim results were site adjudicated. No cases of intraoperative rupture, or bleeding or re‐bleeding, or clinical stroke were observed. Conclusions The interim results of the PRE SEAL‐IT trial demonstrated promising complete occlusion rates at 24‐hour and 6 month follow‐up with no safety concerns. Trial enrollment will be completed in October, and final 24‐hour results will be presented at the 2022 SVIN Annual Meeting.

Random Uniform Attractors for First Order Stochastic Non-Autonomous Lattice Systems

Random Uniform Attractors for First Order Stochastic Non-Autonomous Lattice Systems

Observation of Mott instability at the valence transition of f-electron system.

Mott physics plays a critical role in materials with strong electronic correlations. Mott insulator-to-metal transition can be driven by chemical doping, external pressure, temperature and gate voltage, which is often seen in transition metal oxides with 3d electrons near the Fermi energy (e.g. cuprate superconductor). In 4f-electron systems, however, the insulator-to-metal transition is mostly driven by Kondo hybridization and the Mott physics has rarely been explored in experiments. Here, by combining the angle-resolved photoemission spectroscopy and strongly correlated band structure calculations, we show that an unusual Mott instability exists in YbInCu4 accompanying its mysterious first-order valence transition. This contrasts with the prevalent Kondo picture and demonstrates that YbInCu4 is a unique platform to explore the Mott physics in Kondo lattice systems. Our work provides important insight for the understanding and manipulation of correlated quantum phenomena in the f-electron system.

A resource efficient pseudo random number generator based on sawtooth maps for Internet of Things

AbstractThe strength of cryptographic keys rely on the random number generators (RNGs) to produce random seed values. Unfortunately there are not many RNGs options suitable for Internet of Things (IoTs) scenario, due to limited processing resources and bulk quantity of IoT data that needs to be secured. In this article, we studied sawtooth map which is a chaotic map. However, when implemented on a computer, the sawtooth map results on a non‐chaotic orbit due to the finite precision of computation. This can be avoided if we use the sawtooth map as the local map in a coupled map lattice (CML) system. We explore such coupled map systems for randomness through entropy and statistical analysis. Based on the results, we propose a lightweight hybrid pseudo random number generator (PRNG) based on sawtooth based CML system and SPONGENT hashing. The proposed PRNG is thoroughly tested against statistical attacks, entropy analysis, key space analysis and compared with existing state of the art solutions. The results provide evidence that the proposed PRNG produces random numbers that could produce sufficiently strong cryptographic keys for resource constrained IoT devices.

Hexagonal photonic crystal with nontrivial quadrupole topology

Topological theory of multipole moments in condensed matter physics have recently been generalized to classical systems such as photonic and sonic crystals and several types of quadrupole topological photonic crystals (QTPCs) have already been investigated. However, preceding reports relevant to this issue dealt mainly with square lattice. In this work, we reveal that quadrupole topological phases can also be appeared in hexagonal photonic lattices with the C3v-crystalline symmetry. For this purpose, we extend the topological theory of bulk and Wannier-sector polarizations to the affine coordinate system for analyzing the topological characteristics of non-square lattice systems. The calculation results show that the hexagonal photonic crystals with C3-crystalline symmetry have the quadrupole moments quantized to 1/3, provided that all photonic bands below the gap in consideration are non-degenerate. The hexagonal QTPCs support topological edge and corner states, which are much stronger confined compared with the edge and corner modes originating from nontrivial bulk polarizations. The presented results have fundamental importance and pave the way towards the broader applications of higher-order photonic topological insulators.

Exploiting underlying crystal lattice for efficient computation of Coulomb matrix elements in multi-million atoms nanostructures

Atomistic modeling of nanostructures often leads to computationally challenging problems involving millions of atoms and tens of thousands of Coulomb matrix elements. In our previous work, we presented a practical solution to this problem, where quasi-linear efficiency, both in time and memory, was obtained by utilizing the fast Fourier transform. Here, we present an updated version of our highly-parallelized computer program, named Coulombo-Lattice, that eliminates the necessity of introducing an auxiliary basis set for the wave-function transfer to the computational grid. Here, we instead exploit the properties of the underlying crystal lattice and run calculations on a regular three-dimensional grid superimposed on the original, lower-symmetry lattice. Due to removal of spurious interactions from other supercells, the resulting Coulomb matrix elements are, up to numerical precision, identical to those obtained by the direct summation O(N2) method, yet our code maintains O(Nlog⁡N) scaling. We illustrate our approach by calculations involving up to 1.7 million integrals, and number of atoms reaching up to 2.8 million, for the problem of dopant charging energy for a single phosphorus dopant embedded in a silicon lattice. Next, to emphasize the broad applicability of our code, we show the results for mixed zinc-blend/wurtzite lattice systems, also known as crystal phase quantum dots. Program summaryProgram Title: Coulombo-LatticeCPC Library link to program files:https://doi.org/10.17632/jwkvh5ycbf.1Licensing provisions: CC BY 4.0Programming language: C++Nature of problem: Computing the Coulomb matrix elements (Coulomb and exchange integrals), while being a demanding computational task, is a necessary step in a range of quantum mechanical calculations. For example, in the field of nanostructures, such as quantum dots and nanowires or novel single dopant devices, this stage of calculation (even after a series of approximations) is at least an O(N2) operation (a summation over all pairs of N atoms or grid points in the analyzed system). Moreover, calculating the full Coulomb matrix usually requires the computation of thousands of such elements, thus presenting a formidable computational challenge.Solution method: We provide a ready-to-use implementation for calculating Coulomb matrix elements for a given set of input wavefunctions in LCAO (linear combination of atomic orbitals) form resulting from tight-binding calculation. This implementation is based on the approach introduced in [1,2], by using a fast Fourier transform. In this work, we further significantly improved the method by eliminating the need to introduce wave-function transfer via auxiliary basis set.Additional comments including Restrictions and Unusual features: The implementation is fully parallelized in a distributed-memory model, using MPI and parallel routines from FFTW [3].

Higher rank chirality and non-Hermitian skin effect in a topolectrical circuit

While chirality imbalances are forbidden in conventional lattice systems, non-Hermiticity can effectively avoid the chiral-doubling theorem to facilitate 1D chiral dynamics. Indeed, such systems support unbalanced unidirectional flows that can lead to the localization of an extensive number of states at the boundary, known as the non-Hermitian skin effect (NHSE). Recently, a generalized (rank-2) chirality describing a 2D robust gapless mode with dispersion ω = kxky has been introduced in crystalline systems. Here we demonstrate that rank-2 chirality imbalances can be established in a non-Hermitian (NH) lattice system leading to momentum-resolved chiral dynamics, and a rank-2 NHSE where there are both edge- and corner-localized skin modes. We then experimentally test this phenomenology in a 2-dimensional topolectric circuit that implements a NH Hamiltonian with a long-lived rank-2 chiral mode. Using impedance measurements, we confirm the rank-2 NHSE in this system, and its manifestation in the predicted skin modes and a highly unusual momentum-position locking response. Our investigation demonstrates a circuit-based path to exploring higher-rank chiral physics, with potential applications in systems where momentum resolution is necessary, e.g., in beamformers and non-reciprocal devices.

One-dimensional projection of two-dimensional systems using spiral boundary conditions

The spiral boundary conditions can project any two-dimensional or three-dimensional lattice onto a one-dimensional periodic chain with translational symmetry. It enables one to apply efficiently the existing one-dimensional techniques, such as density-matrix renormalization group (DMRG), bosonization, Jordan-Wigner transformation, etc., to studies of lattice systems in higher dimensions. Here, the authors demonstrate the utility of spiral boundary conditions by performing analytical and DMRG calculations for square and honeycomb lattice problems. Thus, the spiral boundary conditions emerge as a principal option in condensed matter physics.

Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices

The Lieb lattice and the kagome lattice, which are both well known for their Dirac cones and flat bands, can be continuously converted into each other by a shearing transformation. During this transformation, the flat band is destroyed, but the Dirac cones remain and become tilted, with types I, II, and III occurring for different parameters. In this work, we first study these tilted Dirac cones using a tight-binding model, revealing how they can be engineered into the different types. We then demonstrate conical diffraction in a photonic lattice realization of the Lieb-kagome lattice using split-step beam propagation simulations, obtaining evidence of the presence of Dirac cones tilted in different directions. Finally, we performed experiments with photonic lattices laser-written in fused silica (SiO$_2$) to validate the results of the simulations. These studies advance the understanding of the Lieb-kagome lattice and tilted Dirac cones in general and provide a basis for further research into this interesting tunable lattice system.

Manipulating light–matter interaction into strong coupling regime for photon entanglement in plasmonic lattices

Enhancing light–matter interaction into the strong coupling regime attracts tremendous attention in both theory and experiment, which presents essential significance in research from nano-optics to quantum information. In this work, the entanglement effect is observed in the photons emitted from a plasmonic lattice as the coherent light–matter interaction occurs into the strong coupling regime with a Rabi splitting of 93.4 meV. A full quantum mechanical treatment based on the number state representation is established to reveal the underlying physics of the strong coupling phenomenon, especially the femtosecond dynamics of energy exchange and damping. The entangled split states display oscillating concurrence and negative Wigner quasiprobability distribution function, which demonstrates that this designed plasmonic lattice system can serve as an on-demand entangled photon source for quantum information.

Semiclassical bounds on the dynamics of two-dimensional interacting disordered fermions

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$-noise at strong disorder.

Magnetic‐Flux‐Induced Tunable Completely Flat Band and Topological Nearly Flat Band in Square Kagome Lattice

AbstractThe flat bands in a square kagome lattice containing square and triangle plaquettes, are respectively investigated, and the origin of the doubly degenerated completely flat bands and the corresponding compact localized states are elucidated. It is found that the introduction of external magnetic flux enriches the modulation parameters, making the system present many interesting results. In the case that the magnetic flux penetrates through each square plaquette, the tunable completely flat band has one more tunable parameter. And when the external magnetic flux penetrates through each triangle plaquette, excepting a completely flat band, the band dispersions of the system present the topological nearly flat band, which is very useful to realize the interesting fractional quantum Hall physics. The average density of states is also calculated to corroborate the completely FB generated by the highly localized eigenstates. Furthermore, the implementation of the square kagome lattice system based on the current photonic waveguide network technology is demonstrated. The scheme opens up a way to generate the tunable completely flat band and topological nearly flat band in square kagome lattice under multi‐parameter variable conditions.

Emergence of quasiperiodic behavior in transport and hybridization properties of clean lattice systems

Quasiperiodic behaviour is known to occur in systems with enforced quasiperiodicity or randomness, in either the lattice structure or the potential, as well as in periodically driven systems. Here, we present instead a setting where quasiperiodic behaviour emerges in clean, non-driven lattice systems. We illustrate this through two examples of experimental relevance, namely an infinite tight-binding chain with a gated segment, and a hopping particle coupled to static Ising degrees of freedom. We show how the quasiperiodic behaviour manifests in the number of states that are localised by the geometry of the system, with corresponding effects on transport and hybridisation properties.

Exact solutions to the conformable time-fractional discretized mKdv lattice system using the fractional transformation method

Exact solutions to the conformable time-fractional discretized mKdv lattice system using the fractional transformation method