Neighbor Hopping Research Articles

Gate-driven transition temperatures of electron hopping behaviors in Hubbard bands formed by dopant-induced QD array in silicon nanowire

Abstract Dopant atoms confined in silicon nanoscale channel can be ionized to form quantum dots (QDs). Several dopant atoms couple with each other forming energy bands, where the electron hopping behavior can be described by the Hubbard model. This characteristic renders dopant-induced quantum dots particularly appealing for applications in nanoelectronic and quantum devices. Herein we study the gate-driven transition temperatures of electron hopping behavior in upper and lower Hubbard bands formed by dopant-induced QD array in junctionless silicon nanowire transistors. The gate-dependent transition temperatures are calculated for three stages of electron hopping behaviors including Efros-Shklovskii Variable Range Hopping (ES-VRH), Mott Variable Range Hopping (Mott-VRH) and Nearest Neighbor Hopping (NNH). Our experimental results indicate that the ES-VRH in arrays of dopant atoms occurs in the domination of a long-range Coulomb interaction, in which the hopping distance relies on the Coulomb gap. Furthermore, the localization length of ES-VRH can be modulated by gate voltages.Those factors lead to the significant difference of transition temperatures between the upper and lower Hubbard bands. In addition, we find that the source-drain bias voltage can effectively modulate the transition temperatures between VRH and NNH by thermal activation energies under different bias voltages Vds.

Symmetry and Value of the Order Parameter in 2d Nematic Superconductors

We derive equations for the superconducting nematic order parameter and chemical potential for the hexagonal lattice by accounting for nearest- and next-nearest-neighbor hoppings of electrons. By analyzing the energy of the superconducting ground state, we have found that the symmetry of the order parameter and some other superconducting properties of the system strongly depend on the sign and the magnitude of the next-nearest neighbor hopping. As we will demonstrate, both extended s- and d-pairings significantly contribute to the pairing in the system, that be tuned by changing the hopping parameters. We discuss a possible connection of the obtained results to the properties of several doped monolayer superconductors – graphene and transition metal dichalcogenides.

Localized dopant motion across the 2D Ising phase transition

I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings JJ, the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude tt. The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J|kBT/|J|, and on the ratio of the spin coupling to the hopping J/tJ/t. I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.

Tilted stripes origin in La1.88Sr0.12CuO4 revealed by anisotropic next-nearest neighbor hopping

Spin- and charge- stripe order has been extensively studied in the superconducting cuprates, among which underdoped La2−xSrxCuO4 (LSCO) is an archetype with static spin stripes at low temperatures. An intriguing, but not completely understood, phenomenon in LSCO is that the stripes are tilted away from the high-symmetry Cu-Cu directions. Using high-resolution neutron scattering on LSCO with x = 0.12, we find two coexisting phases at low temperatures, one with static spin stripes and the other with fluctuating ones, both sharing the same tilt angle. Our numerical calculations using the doped Hubbard model elucidate the tilting’s origin, attributing it to anisotropic next-nearest neighbor hopping t′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${t}^{{\\prime} }$$\\end{document}, consistent with the material’s slight orthorhombicity. Our results underscore the model’s success in describing specific details of the ground state of this real material and highlight the role of t′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${t}^{{\\prime} }$$\\end{document} in the Hamiltonian, revealing the delicate interplay between stripes and superconductivity across theoretical and experimental contexts.

Variational Monte Carlo study of stripes as a function of doping in the t−t′ Hubbard model

We perform variational Monte Carlo simulations of the single-band Hubbard model on the square lattice with both nearest (t) and next-nearest (t′) neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair–pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.

Realizing Altermagnetism in Fermi-Hubbard Models with Ultracold Atoms.

Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.

KNN-GNN: A powerful graph neural network enhanced by aggregating K-nearest neighbors in common subspace

It has been proven that graph neural networks (GNNs) are effective for a variety of graph learning-based applications. Typical GNNs iteratively aggregate messages from immediate neighbors under the homophily assumption. However, there are a larger number of heterophilous networks in our daily life, where the ability of these GNNs is limited. Recently, some GNN models have been proposed to handle networks with heterophily via some key designs like aggregating higher-order neighbors and combining immediate representations. But ”noise” information transmitted from different-order neighbors will be injected into the representations of nodes. In this paper, we propose a new GNN model, called KNN-GNN, to effectively perform the node classification task for networks with various homophily levels. The main idea of KNN-GNN is to learn a comprehensive and accurate representation for each node by integrating not only the local information from its neighborhood but also the non-local information held by its similar nodes decentralized in the network. Specifically, the local information of a node is generated from itself and its 1-hop neighbor. Then, we project all nodes into a common subspace, where similar nodes are desired to be close to each other. The non-local information of a node is gathered by aggregating its K-Nearest Neighbors searched in the common subspace. We evaluate the performance of KNN-GNN on both real and synthetic datasets including networks with diverse homophily levels. The results demonstrate that KNN-GNN outstrips the state-of-the-art baselines. Moreover, the ablation experiments show that the core designs in KNN-GNN play a critical role in node representation learning.

Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement

Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX−YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan–Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin–spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.

Hydrogenation-controlled band engineering of dumbbell graphene

The stability of the dumbbell structure has been confirmed by previous theory and experiment. Based on first-principles calculations, we proposed hexagonal dumbbell graphene (HDB C10) and rectangular dumbbell graphene (RDB C10) monolayers containing periodically raised C (CR) atoms. They turn out to have high mobility semiconductor properties. By adsorbing H atoms on these CR atoms, their band structures can be widely tuned from semiconductor to semimetal. When considering adsorption of two/four H atoms on the unit cell of the dumbbell structure, the bandgap can be increased, and isolated flat band structures can be obtained by further adding or removing H atoms. Remarkably, two different Dirac band structures can be found in the HDB/RDB C10H2-I monolayers. The HDB C10H2-I shows a Dirac cone with isotropic Fermi velocities, while the RDB C10H2-I monolayer exhibits a quasi-one-dimensional Dirac nodal line with varying Fermi velocities along the XS path. Tight-binding (TB) models are constructed including nearest neighbor (NN) and next NN hopping in order to understand our DFT results. These TB models are related to the Su-Schrieffer-Heeger model, and are able to explain the tunable topological properties of the RDB C10H2-I monolayer. They not only are able to explain the different kinds of Fermi velocity, but also can predict the emergence of topological edge states, providing a good platform for research on Dirac fermions. The HDB/RDB C10 monolayer exhibits more freedom of tunable band structures and more stable hydrogen storage capacity, making it superior to graphene. Finally, possible experimental synthesis paths of these DB monolayers are provided.

Correlation between structural, morphological, and electrical transport properties of nano-dimensional Tellurium thin film by low energy ion beam irradiation

Tellurium (Te), an emerging semiconductor material, exhibits intriguing physical properties in low-dimensional forms. This study investigates the structural, morphological, and transport properties of low-dimensional Te thin film deposited by physical vapor deposition after 400 keV Kr2+ ion irradiation with varying fluences of 1 × 1013, 5 × 1013, and1 × 1014 ions-cm−2. The X-ray diffraction (XRD) pattern reveals the hexagonal phase of pristine Te. As ion fluence increases, intensity of the XRD peaks decreases and the full-width half maxima (FWHM) increases, indicating a reduction in crystallinity. The intensity of the Raman peak decreases upon irradiation, resulting in a red shift in the spectra of the irradiated sample. The evolution of morphology at different fluences has been examined with atomic force microscopy (AFM) measurements. The results indicate the segregation of grains and an increase in root mean square (RMS) roughness from 2.59 pm to 5.11 pm with ion fluence up to 5 × 1013 ions-cm−2. At the highest fluence, i.e., 1 × 1014 ions-cm−2, there is an agglomeration of grains, and hence a decrease in RMS roughness to 3.92 pm is observed. The DC resistivity measurement indicates the semiconducting nature of all films. Additionally, this measurement signifies the rapid decrease in activation energy at both band-to-band conduction and nearest neighbour hopping (NNH) conduction. Following irradiation, Hall measurement demonstrates a decrease in the concentration of charge carriers and an increase in resistivity due to scattering originating from grain boundaries. However, when the fluence is increased to 1 × 1014 ions-cm−2, there is a reduction in resistivity and an increase in carrier concentration with enhanced Hall mobility in comparison to pristine Te. Therefore, this study showcases that low-energy ion irradiation has a significant impact on the modification of the structure, morphology, and electrical transport properties of semiconducting Te thin film.

Effect of next-nearest neighbor hopping on the single-particle excitations at finite temperature

In the half-filled one-orbital Hubbard model on a square lattice, we study the effect of next-nearest neighbor hopping on the single-particle spectral function at finite temperature using an exact-diagonalization + Monte-Carlo based approach to the simulation process. We find that the pseudogap-like dip, existing in the density of states in between the Néel temperature T_NTN and a relatively higher temperature scale T^*T*, is accompanied with a significant asymmetry in the hole- and particle-excitation energy along the high-symmetry directions as well as along the normal-state Fermi surface. On moving from (\pi/2, \pi/2π/2,π/2) toward (\pi, 0)(π,0) along the normal state Fermi surface, the hole-excitation energy increases, a behavior remarkably similar to what is observed in the dd-wave state and pseudogap phase of high-T_cTc cuprates, whereas the particle-excitation energy decreases. The quasiparticle peak height is the largest near (\pi/2, \pi/2π/2,π/2) whereas it is the smallest near (\pi, 0)(π,0). These spectral features survive beyond T_NTN. The temperature window T_N ≲ T ≲ T^*TN≲T≲T* shrinks with an increase in the next-nearest neighbor hopping, which indicates that the next-nearest neighbor hopping may not be supportive to the pseudogap-like features.

Tailoring the electrical and magneto-electric transport properties of ZnO films via Ti ion implantation

A significant development toward semiconductor-based electronic devices is based on the electric and magneto-electric control of the transport properties of the charge carriers. This study unprecedentedly investigates the Ti implantation and thereafter the effect of structural defects on the electrical and magneto-electric transport properties of Ti-implanted RF-sputtered ZnO thin films. Theoretical stopping and range of ions in matter simulations along with the experimental structural and elemental studies reveal that Ti ion implantation generates a significant amount of oxygen vacancy (VO) defects apart from Ti-related impurities in post-implantation annealed films. The film implanted with 8 × 1015 ions/cm2 (TZO815) exhibits the lowest resistivity (4.68 × 10−3 Ω cm) and the highest carrier concentration (6.61 × 1020 cm−3) values. Resistivity measurements over a temperature range of 5-300K indicate semiconducting behavior for all the films implanted up to fluences of 5 × 1015 ions/cm2 identified with a grain boundary dominated thermally activated band, nearest neighbor hopping, and Mott and Efros–Shklovskii (ES) variable range hopping conduction mechanisms at various temperature intervals. Notably, the gradual decrease in both Mott and ES hopping ranges following Ti implantation indicates the formation of more localized states. Interestingly, the TZO815 film exhibits metal-semiconductor transition around 220 K, suggesting the formation of a degenerate band within the ZnO conduction band upon Ti implantation. Remarkably, the magnetoresistance results align with a semiempirical formula proposed by Khosla and Fischer, indicating that a negative magneto resistance in the TZO thin films is attributed to the spin-dependent scattering of conduction electrons by the localized magnetic moments induced mainly by the implantation induced VO defects.

Transitions of electrical conduction mechanism in graphene flake van der Waals thin film

The electrical conduction mechanism in 2D van der Waals (vdW) thin film made of graphene flakes can be characterized by the variable range hopping (VRH) over a wide range of temperature, followed by a transition into an Arrhenius type conduction at the higher temperature. Regarding the nature of the subsequent Arrhenius type conduction, a lack of consensus exists between the nearest neighbor hopping (NNH) and the band conduction (BC). We discuss how to assess the transition in conduction mechanism based on the transient behavior of the reduced activation energy (W) and the structure of electronic density of states (DOS) of the sample. With a multi-channel conduction model, we show that the transition from VRH to BC always accompany an increase in W, which is absent in the transition from VRH to NNH. Also discussed are the peculiarities of VRH in vdW thin film and what they imply towards the properties of defects. In most vdW flake thin films, the spread of defect band in DOS is governed by the intrinsic defect energy not by the Coulomb interaction between defects. It can further be deduced that the gap in DOS near Fermi level associated with Efros-Shklovskii VRH observed in vdW film is not a Coulomb gap as found in weakly doped crystalline semiconductor, but inherent in the distribution of defect intrinsic energy. For the graphene flake thin film we synthesized, Mott VRH and BC are identified.

Ubiquitous light real-space pairing from long-range hopping and interactions

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbor hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎, are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼0.1t‾, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

Improving Distinguishability of Class for Graph Neural Networks

Graph Neural Networks (GNNs) have received widespread attention and applications due to their excellent performance in graph representation learning. Most existing GNNs can only aggregate 1-hop neighbors in a GNN layer, so they usually stack multiple GNN layers to obtain more information from larger neighborhoods. However, many studies have shown that model performance experiences a significant degradation with the increase of GNN layers. In this paper, we first introduce the concept of distinguishability of class to indirectly evaluate the learned node representations, and verify the positive correlation between distinguishability of class and model performance. Then, we propose a Graph Neural Network guided by Distinguishability of class (Disc-GNN) to monitor the representation learning, so as to learn better node representations and improve model performance. Specifically, we first perform inter-layer filtering and initial compensation based on Local Distinguishability of Class (LDC) in each layer, so that the learned node representations have the ability to distinguish different classes. Furthermore, we add a regularization term based on Global Distinguishability of Class (GDC) to achieve global optimization of model performance. Extensive experiments on six real-world datasets have shown that the competitive performance of Disc-GNN to the state-of-the-art methods on node classification and node clustering tasks.

Crystal structure, cation distribution and electrical properties in NixAlyMn3−x−yO4 (0

NixAlyMn3−x−yO4 (0 < x < 0.6; 0 < y < 0.3) series NTC chip thermistors with homogeneous chemical compositions and high-pure spinel phases were fabricated via a tape casting-lamination-sintering process. The multi-variate cation distribution model was established as (Mn1-x+v2+Nix-v2+)Mn2-2v-y3+Mnv4+Niv2+Aly3+O4 (0 < v < 0.5). The conduction mechanism was proposed based on a nearest neighbor hopping (NNH) model. They were verified coherently by cation-oxyanion chemical compositions (XRF/EDS), valence states (XPS), phase structures and Rietveld refinements (XRD), IR vibrations and electrical analyses. The obtained NTC chips were well suitable for commercial applications with a high reliability and with regulable ρ25 (4080 ± 135 ∼ 15,760 ± 526 Ω cm) and B25/50 (4016 ± 20 ∼ 4251 ± 13 K).

Second order topology in a band engineered Chern insulator

Haldane model is a celebrated tight binding toy model of a Chern insulator in a 2D honeycomb lattice that exhibits quantized Hall conductance in the absence of an external magnetic field. In our work, we deform the bands of the Haldane model smoothly by varying one of its three nearest neighbour hopping amplitudes (t1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_1$$\\end{document}), while keeping the other two (t) fixed. This breaks the C3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_3$$\\end{document} symmetry of the Hamiltonian, while the Mx∗T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_x*T$$\\end{document} symmetry is preserved. The symmetry breaking causes the Dirac cones to shift from the K and the K′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$'$$\\end{document} points in the Brillouin zone (BZ) to an intermediate M point. This is evident from the Berry curvature plots which show a similar shift in the corresponding values as a function of the deformation parameter, namely t1t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{t_1}{t}$$\\end{document}. We observe two different topological phases of which, one is a topological insulator (TI) and the other is a second order topological insulator (SOTI). The Chern number (C) remains perfectly quantized at a value of C=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=1$$\\end{document} for the TI phase and it goes to zero in the SOTI phase. Furthermore, the evolution of the Wannier charge center (WCC) as the band is smoothly deformed shows a jump in the TI phase indicating the presence of conducting edge modes. We also study the SOTI phase and diagonalize the real space Hamiltonian on a rhombic supercell which shows the presence of in-gap zero energy corner modes. The polarization of the system, namely px\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_x$$\\end{document} and py\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_y$$\\end{document}, are evaluated, along the x and the y directions, respectively. We see that both px\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_x$$\\end{document} and py\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_y$$\\end{document} are quantized in the SOTI phase owing to the presence of the inversion symmetry of the system. Finally we establish the SOTI phase as an example of a topological phase with zero Berry curvature and provide an analogy with the two dimensional Su–Schrieffer–Heeger model.

Impact of the temperature on the conductive filament morphology in HfO2-based RRAM

In this letter, we study the impact of the temperature on the resistive switching effect of TiN/Ti/HfO2/W metal–insulator-metal devices. An analysis of the conduction mechanisms is made, with the low resistance state being ruled by nearest neighbor hopping, while the conduction in the high resistance state is dominated by Schottky emission. Taking into account the filamentary mechanism behind the resistive switching effect, a thorough analysis of the Schottky emission allows for the calculation of the gap between conductive filament tip and metal electrode in the high resistance state. We report an increase of this gap when temperature lowers below a certain value. Moreover, the mentioned gap adopts values of integer multiples of the the mean distance between traps obtained by the hopping model.

Observation of flat-band localized state in a one-dimensional diamond momentum lattice of ultracold atoms

We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple two- and four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.

Grundy Total Hop Dominating Sequences in Graphs

Let G = (V (G), E(G)) be an undirected graph with γ(C) ̸= 1 for each component C of G. Let S = (v1, v2, · · · , vk) be a sequence of distint vertices of a graph G, and let Sˆ ={v1, v2, . . . , vk}. Then S is a legal open hop neighborhood sequence if N2G(vi) \Si−1j=1 N2G(vj ) ̸= ∅for every i ∈ {2, . . . , k}. If, in addition, Sˆ is a total hop dominating set of G, then S is a Grundy total hop dominating sequence. The maximum length of a Grundy total hop dominating sequence in a graph G, denoted by γth gr(G), is the Grundy total hop domination number of G. In this paper, we show that the Grundy total hop domination number of a graph G is between the total hop domination number and twice the Grundy hop domination number of G. Moreover, determine values or bounds of the Grundy total hop domination number of some graphs.