Neighbor Hopping Research Articles

Composite fermion state of graphene as a Haldane-Chern insulator

Graphene in the presence of a strong external magnetic field is a unique attraction for investigations of the fractional quantum Hall (fQH) states with odd and even denominators of the fraction. Most of the attempts to understand Graphene in the strong-field regime were made through exploiting the universal low-energy effective description of Dirac fermions emerging from the nearest neighbor hopping model of electrons on a honeycomb lattice. We highlight that accounting for the next-nearest-neighbor hopping terms in doped Graphene can lead to a unique redistribution of magnetic fluxes within the unit cell of the lattice. While this affects all the fQH states, it has a striking effect at a half-filled Landau-level state: it leads to a composite fermion state that is equivalent to the doped topological Chern insulator on a honeycomb lattice. At energies comparable to the Fermi energy, this state possesses a Haldane gap in the bulk proportional to the next-nearest-neighbor hopping and density of dopants. We argue that this microscopically derived energy gap survives the projection to the lowest band. We also conjecture that the gap should be present in a microscopic theory giving the recently proposed particle-hole symmetric Dirac composite fermion scenario of the half-filled Landau-level. The proposed gap is lower than the chemical potential, and is predicted to be parametrically separated from the Dirac point in the latter description. Finally we conclude by proposing experiments to detect this gap; the associated boundary mode; and encourage cold-atom setups to test other predictions of the theory.

Edge states, corner states, and flat bands in a two-dimensional PT -symmetric system

We study corner states on a flat band in the square lattice. To this end, we introduce a two dimensional model including Su-Schrieffer-Heeger type bond alternation responsible for corner states as well as next-nearest neighbor hoppings yielding flat bands. The key symmetry of the model for corner states is space-time inversion ($\cal PT$) symmetry, which guarantees quantized Berry phases. This implies that edge states as well as corner states would show up if boundaries are introduced to the system. We also argue that an infinitesimal $\cal PT$ symmetry-breaking perturbation could drive flat bands into flat Chern bands.

Influence of correlations on the orbital magnetization of the spin- 12 Haldane-Hubbard model

Orbital magnetization is known empirically to play an important role in several magnetic phenomena, such as permanent magnetism and ferromagnetic superconductivity. Within the recently developed ''modern theory of orbital magnetization'', theoretical insight has been gained into the nature of this often neglected contribution to magnetism, but is based on an underlying mean-field approximation. From this theory, a few treatments have emerged which also take into account correlations beyond the mean-field approximation. Here, we apply the scheme developed in a previous work [Phys. Rev. B ${\bf \text{93}}$, 161104(R) (2016)] to the Haldane-Hubbard model to investigate the effect of charge fluctuations on the orbital magnetization within the $GW$ approximation. Qualitatively, we are led to distinguish between two quite different situations: (i) When the lattice potential is larger than the nearest neighbor hopping, the correlations are found to boost the orbital magnetization. (ii) If the nearest neighbor hopping is instead larger than the lattice potential, the correlations reduce the magnetization.

Exploiting similarities of user friendship networks across social networks for user identification

User identification has been attracting considerable attention from academia. Due to the uniqueness and difficulty of faking friendship networks, some friendship-based methods have been presented to improve the identification performance. However, the information redundancies in k-hop (k > 1) neighbors and their contributions to user identification have not been fully analyzed in the existing work. Addressing these two issues helps to understand the problem of friendship-based user identification and to propose more effective solutions. In this paper, we first obtain ground-truth friendship networks across three popular social sites; then, we analyze the similarities of k-hop neighbors to fully characterize the information redundancies in the friendship network. We apply these information redundancies in several classifiers to study their contributions to user identification. Furthermore, we apply the friendship-based information redundancies jointly with the display-name-based information redundancies to perform user identification. The experiments show that (1) the similarities related to the 1-hop neighbors contribute to user identification much more than do the other similarities; (2) the information redundancies in the k-hop (k > 1) neighbors are also very useful for user identification; and (3) jointly applying display-name-based information redundancies can provide better performance and improve the universality of the identification method.

A Distributed Framework for $k$-hop Control Strategies in Large-Scale Networks Based on Local Interactions

In this paper, we propose a distributed framework for large-scale networks to attain control strategies requiring $k$ -hop interactions. This research is motivated by the observation that in many practical applications and operational domains involving large-scale networks, such as environmental monitoring or traffic load balancing, agents may be required to collect only information concerning other agents located sufficiently close to them, that is agents topologically at most $k$ -hop away. In this setting, distributed observers available at the state of art, which typically estimates the full network state, may be inadequate due to scalability issues. Differently, we propose a distributed finite-time observer which allows each agent to estimate the state of its $k$ -hop neighbors by interacting only with the agents belonging to its 1-hop neighborhood. Furthermore, we demonstrate that for feedback control strategies based on $k$ -hop neighborhood information, which are input-to-state stable, the proposed distributed finite-time observer can be effectively used to design stable large-scale networked control strategies. Numerical results are provided to corroborate the theoretical findings.

Spin-valley density wave in moiré materials

We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.

Phase stiffness in an antiferromagnetic superconductor

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Neel order is included as a special case. Close to half-filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasi-particle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side, and smaller for electron doping. Hence, in the hole-doped regime near half-filling the ground state pairing gap sets the scale for the Kosterlitz-Thouless temperature T_c^{KT}, while in the slightly electron-doped regime T_c^{KT} is determined essentially by the ground state phase stiffness.

Decision Tree Based Routing Protocol (DTRP) for Reliable Path in MANET

In mobile ad hoc network due to node movements, there exists route failure in active data transmission which results in data loss and communication overheads. Hence, in such a dynamic network, routing through reliable path is one of the tedious tasks. In this paper, we propose a novel Decision Tree based Routing Protocol (DTRP) a data mining technique in route selection process from source to destination. The proposed DTRP protocol selects the one hop neighbors based on the parameters such as speed, Link Expiration Time, trip_time and node life time. Thus the performance of a route discovery mechanism is enhanced by selecting the stable one-hop neighbors along the path to reach the destination. The simulated results show that the lifetime of the route is increased and hence the data loss and end to end delay are minimized thereby increasing the throughput of the network using the proposed DTRP routing protocol compared to existing routing protocols.

Dielectric, impedance and modulus spectroscopy of Ta-based layered perovskite

ABSTRACTPbBi2Ta2O9 ceramic samples were fabricated by high-temperature mixed oxide method. X-ray diffraction determines the structure as orthorhombic. The scanning electron microscopy confirms the formation of densely packed grains in the sample. The dielectric measurements, complex impedance and complex modulus study were carried out in a frequency range of 1 kHz–1 MHz and a temperature rangeof 25–500°C. The conduction mechanism of the material is discussed in details using variable range hoping, nearest neighbor hopping relaxation model and dc activation energy at two different temperature regimes. From the J-E characteristics studies, the occurrence of non-linear curves endorses the non-Ohmic nature of the material.

Electrical conductivity of undoped bilayer Graphene: Beyond nearest neighbor approximation

We have addressed density of states and electrical conductivity of undoped biased bilayer graphene for both AA and AB stacking in the context of tight binding model hamiltonian. The effects of next nearest neighbor hopping amplitude for electrons and gap parameter on electronic density of states and electrical conductivity have been investigated. Green’s function approach has been implemented to find the behavior of electrical conductivity of bilayer graphene within linear response theory. We have found the temperature dependence of electrical conductivity for different values of gap parameter and bias voltage in the presence of neat nearest neighbor hopping integral. Our results for density of states of bilayer graphene in the presence of gap parameter show the increase of bias voltage reduces the band gap width. Also a peak in the dependence of thermal conductivity on temperature has been observed for all physical parameters. An anisotropic behavior for electrical conductivity of unbiased simple bilayer graphene in the presence of gap parameter has been resulted.

Magnetic phase diagram of the infinite- U Hubbard model with nearest- and next-nearest-neighbor hoppings

We study the infinite-U Hubbard model on ladders of 2, 4 and 6 legs with nearest (t) and next-nearest (t') neighbor hoppings by means of the density-matrix renormalization group algorithm. In particular, we analyze the stability of the Nagaoka state for several values of t' when we vary the electron density $(\rho)$ from half-filling to the low-density limit. We build the two-dimensional phase diagram, where the fully spin-polarized and paramagnetic states prevail. We find that the inclusion of a non-frustrating next nearest neighbor hopping stabilizes the fully spin-polarized phase up until |t'/t|=0.5. Surprisingly, for this value of t', the ground state is fully spin-polarized for almost any electron density 1 $\gtrsim \rho \gtrsim$ 0, connecting the Nagaoka state to itinerant ferromagnetism at low density. Also, we find that the previously found checkerboard insulator phase at t'=0 and $\rho$=0.75 is unstable against t'.

Hop-Count Quantization Ranging and Hybrid Cuckoo Search Optimized for DV-HOP in WSNs

Localization technology occupies a very important position in wireless sensor network (WSN). Distance vector-hop (DV-HOP) algorithm is range-free localization algorithm and has advantages of low overhead and can handle the case where a normal node has less than three neighbor anchors. However, considering the problem of high localization error of DV-HOP algorithm in WSN. An hybrid DV-HOP localization algorithm based on hop-count quantization anchor and modified cuckoo search (HMCS-D) is proposed. The algorithm using the correction factor to correct the number of hops that can reduce the error caused by the recording inaccurate minimum hops. The nodes of the hop neighbor nodes in the network are divided into three disjoint subsets and the distance between the nodes is estimated according geometric method. Then according to the weight of each anchor node to select average jump distance of unknown nodes. Finally, introduced hybrid cuckoo search which can dynamically adjust the search step size and using the search algorithm to calculate the node coordinates instead of the maximum likelihood estimation method. Simulation results show that compare with DV-HOP and cuckoo search DV-HOP algorithm, the average positioning error of HMCS-D algorithm decrease 39.7%, 10.6% respectively. Prove that the HMCS-D algorithm effectively improve the node localization accuracy, reduce the positioning error and without affecting the hardware cost.

An Algorithm based on VANET Technology to Count Vehicles Stopped at a Traffic Light

Vehicular Ad hoc Networks (VANETs) have gained considerable attention in the past few years due to their promising applicability in relation to the Intelligent Transportation Systems (ITSs). This emerging new technology will provide timely information to develop adaptive traffic light control systems that will allow a significant optimization of the vehicular traffic flow. In this paper, we introduce a novel algorithm for counting vehicles stopped at a traffic light using VANET technology. The algorithm is based on the idea of the propagation of a count request message from the RSU (originating unit) toward the vehicles that are at the end of the waiting line, and the propagation of a response message (with the number of vehicles counted) in the opposite direction, that is, from the vehicles at the end of the line toward the RSU. For this, our algorithm uses BEACON messages periodically to exchange the necessary information between any two 1-hop neighbors. Using the data received from BEACON messages, each vehicle can maintain its own neighbors list. To validate and evaluate the performance of our proposal, we use Veins (Vehicle in Network Simulation) and TraCI (Traffic Control Interface). The former is a framework that ties together a network simulator (OMNeT++) with a road traffic simulator (SUMO), and the latter is an API for the communications between both simulators by providing TCP connections between each other. The results of the simulations performed in different scenarios are encouraging since they indicate that the proposed algorithm efficiently computes a number of vehicles very close to the real one, using a few control messages.

On Topologies Induced by Graphs Under Some Unary and Binary Operations

Let G = (V (G),E(G)) be any simple undirected graph. The open hop neighborhood of v ϵ V(G) is the set 𝑁_𝐺^2(𝑣) = {u ϵ V(G): 𝑑_𝐺 (u,v) = 2}. Then G induces a topology τ_G on V (G) with base consisting of sets of the form F_G^2[A] = V(G) \ N_G^2 [A] where N_G^2 [A] = A ∪ {v ϵ V(G):  𝑁_𝐺^2(𝑣) ∩ A ≠∅ } and A ranges over all subsets of V (G). In this paper, we describe the topologies induced by the complement of a graph, the join, the corona, the composition and the Cartesian product of graphs.

Generating Functions for Lattice Gauge Models with Scaled Fermions and Bosons

Recently, employing an imaginary-time functional integral formulation, we considered abelian and nonabelian $$(a{\mathbb {Z}})^d$$ lattice quantum field gauge theories with new a-dependent locally scaled Wilson Fermi and Bose fields in $$d\le 4$$ spacetime dimensions and neglecting the pure gauge interaction. The use of scaled fermions and bosons preserves Osterwalder–Schrader positivity and the spectral content of the models since the decay rates of correlations in the infinite-time limit are unchanged. In addition, scaled fields also result in a less singular, more regular behavior in the continuum limit. The scaled field gauge models are thermodynamically stable, which shows that stability does not depend on the presence of a pure gauge, plaquette term in the action. The finite lattice free energy is bounded with a bound independent of the number of points of the lattice and the lattice spacing $$a\in (0,1]$$ . Recall that the expansion of the fermionic exponential bond factor, arising from the interacting nearest neighbor hopping terms in the action, is finite by Pauli exclusion. The Bose-Gauge models we consider here have a finite truncation of the bond factor; the Fermi-mimicking truncated Bose models still obey Osterwalder–Schrader positivity. We show boundedness of the n-point scaled field generating functions and n-point scaled field correlations. The bounds are independent of the number of lattice points and the lattice spacing $$a\in (0,1]$$ . For the truncated Bose models, the bound is also independent of the location of the n points. No renormalization of the parameters is needed. The precise a-dependent factors have been extracted and isolated from the unscaled field partition functions and correlations so that the scaled field free energies and correlations are not singular for $$a\in (0,1]$$ .

Topological property of a t2g5 system with a honeycomb lattice structure

A $t_{2g}^5$ system with a honeycomb lattice structure such as Na$_2$IrO$_3$ was firstly proposed as a topological insulator even though Na$_2$IrO$_3$ and its isostructural materials in nature have been turned out to be a Mott insulator with magnetic order. Here we theoretically revisit the topological property based on a minimal tight-binding Hamiltonian for three $t_{2g}$ bands incorporating a strong spin orbit coupling and two types of the first nearest neighbor (NN) hopping channel between transition metal ions, i.e., the hopping ($t_1$) mediated by edge-shared ligands and the direct hopping ($t_1'$) between $t_{2g}$ orbitals via $dd\sigma$ bonding. We demonstrate that the topological phase transition takes place by varying only these hopping parameters with the relative strength parametrized by $\theta$, i.e., $t_1=t\cos\theta$ and $t_1'=t\sin\theta$. We also explore the effect of the second and third NN hopping channels, and the trigonal distortion on the topological phase for the whole range of $\theta$. Furthermore, we examine the electronic and topological phases in the presence of on-site Coulomb repulsion $U$. Employing the cluster perturbation theory, we show that, with increasing $U$, a trivial or topological band insulator in the absence of $U$ can be transferred into a Mott insulator with nontrivial or trivial band topology. We also show that the main effect of the Hund's coupling can be understood simply as the renormalization of $U$. We briefly discuss the relevance of our results to the existing materials.

Statistics-tuned phases of pseudofermions in one dimension

We show that a quadratic system of pseudofermions, with tunable fractionalised statistics, can host a rich phase diagram on a one dimensional chain with nearest and next nearest neighbor hopping. Using a combination of numerical and analytical techniques, we show that that by varying the statistical angle and the ratio of the hopping, the system stabilizes two Tomonaga-Luttinger liquids (TLL) with central charges c = 1 and 2 respectively along with the inversion symmetry broken bond ordered (BO) insulating phase. Interestingly, the two quantum phase transitions in the system - (1) between the two TLLs, and, (2) the c = 1 TLL and BO phase can be engendered by solely tuning the statistics of the pseudofermions. Our analysis shows that both these transition are continuous and novel with the former lacking a local order-parameter based description and the latter of Berezinskii-Kosterlitz-Thouless type. These phases and phase transitions can be of direct experimental relevance in context of recent studies of fermionic cold atoms.

Experimental investigation of the typical activation energy and distance of hopping electron transport in ZnO

Using experimental dependencies of conductivity and Hall coefficient on temperature we calculate values of typical activation energy and typical hopping distance in ZnO for different temperatures in the range between 13 and 70 K. For that a system of two nonlinear equations is solved numerically using the proposed iterative procedure. The obtained dependencies are compared with the predictions of the variable range hopping theory. Although there is some similarity between the compared curves, the dependencies obtained in this work are much weaker than the predicted ones. In the range between 13 and 35 K, in which Mott law holds in our sample, there is only 15% and 6.5% change in typical activation energy and typical hopping distance, respectively. We suggest nearest neighbor hopping model in this temperature range. The effects of widening and superposition of the occupied and empty bands of localized energy states in the impurity band with a Coulomb gap are discussed.

Light-cone and local front dynamics of a single-particle extended quantum walk

We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave fronts can be characterized as ordinary or extremal fronts with the latter exhibiting an anomalous sub-diffusive scaling behaviour in the front region. We investigate the dynamical global and local scaling properties of the cumulative probability distribution function for the extended walk with nearest and next-nearest neighbour hopping using analytical and numerical methods. The global scaling shows the existence of a 'causal light-cone' corresponding to excitations travelling with a velocity smaller than a maximal 'light velocity'. Maximal fronts moving with fixed 'light velocity' bound the causal cone. The front regions spread with time sub-diffusively exhibiting a local Airy scaling which leads to an internal staircase structure. At a certain critical next-nearest neighbour hopping strength, there is a transition from a phase with one 'causal cone' to a phase with two nested 'causal cones' and the existence of an internal staircase structure in the corresponding cumulative distribution profiles. We also connect the study to that in spin chain systems and indicate that a single particle quantum walk on the one dimensional lattice already captures the many body physics of a spin chain system. In particular, we suggest that the time evolution of a single particle quantum walk on the one dimensional lattice with an initially localized state is equivalent to the time evolution of a domain wall initial state in a corresponding spin chain system.

Bloom Hopping: Bloom Filter Based 2-Hop Neighbor Management in VANETs

Recent works have shown that it would be beneficial for nodes in wireless networks with very dynamic topology to maintain a list of 2-hop neighbors, namely, the neighbors of its neighbors. This is important, for example, for routing, clustering, and message dissemination to all the nodes in a given geographic vicinity. In this paper, we propose a scheme that uses Bloom filters for maintaining 2-hop neighborship information. Furthermore, we developed a novel 2-hop broadcast algorithm making use of the specific nature of our Bloom filter encoded neighbor information. We particularly focus on the Vehicular Ad Hoc Networks (VANETs) application scenario. Here, beaconing is a periodic broadcast of awareness messages by each vehicle to its immediate neighbors. A naive approach would be to include all 2-hop neighbors in each beacon message, which, however, would work only for small or sparse scenarios. We show that our approach significantly reduces the length of the beacon messages, thereby keeping channel load and collision probability considerably lower than in the naive scheme. We further demonstrate the application of our Bloom filter based 2-hop neighbor table for developing higher layer protocols and introduce a multi-hop broadcast protocol called Bloom Hopping.