Nearest-neighbor Hopping Research Articles

First passage on disordered intervals.

We derive unexpected first-passage properties for nearest-neighbor hopping on finite intervals with disordered hopping rates, including (a) a highly variable spatial dependence of the first-passage time, (b) huge disparities in first-passage times for different realizations of hopping rates, (c) significant discrepancies between the first moment and the square root of the second moment of the first-passage time, and (d) bimodal first-passage time distributions. Our approach relies on the backward equation, in conjunction with probability generating functions, to obtain all moments, as well as the distribution of first-passage times. Our approach is simpler than previous approaches based on the forward equation, in which computing the mth moment of the first-passage time requires all preceding moments.

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).

Phenomenon of multiple reentrant localization in a double-stranded helix with transverse electric field

The present work explores the potential for observing multiple reentrant localization behavior in a double-stranded helical (DSH) system, extending beyond the conventional nearest-neighbor hopping (NNH) interaction. The DSH system is considered to have hopping dimerization in each strand, while also being subjected to a transverse electric field. The inclusion of an electric field serves the dual purpose of inducing quasi-periodic disorder and strand-wise staggered site energies. Two reentrant localization regions are identified: one exhibiting true extended behavior in the thermodynamic limit, while the second region shows quasi-extended characteristics with partial spreading within the helix. The DSH system exhibits three distinct single-particle mobility edges linked to localization transitions present in the system. The analysis in this study involves examining various parameters such as the single-particle energy spectrum, inverse participation ratio, local probability amplitude, and more. Our proposal, combining achievable hopping dimerization and induced correlated disorder, presents a unique opportunity to study phenomenon of reentrant localization, generating significant research interest.

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.

Doping dependence of superconductivity on a honeycomb lattice within the framework of kinetic-energy-driven superconductivity

Unconventional superconductivity on a honeycomb lattice has received increasing interest since the discovery of graphene primarily due to the similarities between materials with a honeycomb lattice and cuprate superconductors. Many theoretical studies have been conducted on superconductivity on a honeycomb lattice, however, a consistent picture is still lacking. In this paper, we have extended the theory of kinetic-energy-driven superconductivity, which has been developed to investigate unconventional superconductivity in cuprate superconductors, to explore superconductivity on a honeycomb lattice within the t-J model. Our results demonstrate that the charge-carrier pair gap parameter with [Formula: see text]-wave symmetry exhibits a dome-like shape as a function of doping, with superconductivity emerging at a certain doping concentration and disappearing at high doping levels, similar to what has been observed in cuprate and cobaltate superconductors. Furthermore, the charge-carrier pair gap parameter decreases with increasing the value of [Formula: see text] (the ratio between the antiferromagnetic exchange coupling constant and the nearest-neighbor hopping integral), and approaches zero when [Formula: see text] reaches a sufficiently large value. This indicates that the antiferromagnetic order will suppress the superconducting state and a sufficiently strong exchange coupling will completely destroy the superconductivity. Taking into account our present results together with the corresponding results of cuprate and cobaltate superconductors, it appears that the dome-like shape of the doping dependence of the charge-carrier pair gap parameter may be a common feature in doped Mott insulators.

Topological phases of monolayer and bilayer depleted Lieb lattices

Existence of nontrivial topological phases in a tight binding Haldane-like model on the depleted Lieb lattice is reported. This two-band model is formulated by considering the nearest-neighbor (NN), next-NN (NNN) and next-NNN hopping terms along with complex phase which breaks the time reversal symmetry of this semi-metallic system. Topological feature of this model is studied along with the presence of sublattice symmetry breaking staggered onsite energy. Combined effect of these two broken symmetries is found crucial for an additional transition between nontrivial and trivial phases. System exhibits two types of phase transitions, say, between two nontrivial phases and nontrivial to trivial phases. Nonzero Chern numbers, existence of Hall plateau and symmetry protected edge states confirm the presence of the nontrivial phases. This two-band system hosts four different types of phases where two are topological. Additionally topological properties of stacked bilayer of the depleted Lieb lattices is also studied with similar Haldane-like Hamiltonian. This four-band system is found to host Chern insulating phases, with higher values of Chern numbers supported by in-gap edge states.

Entanglement entropy and topological properties in a long-range non-Hermitian Su–Schrieffer–Heeger model

We employ entanglement entropy to investigate the topological properties of the extended long-range non-Hermitian Su–Schrieffer–Heeger (SSH) model. We show how long-range hopping, nearest-neighbor hopping, and the non-Hermitian term influence the entanglement entropy in the SSH model, which serves as a valuable tool for examining the topological features of the SSH model. Our research reveals a remarkable phenomenon: entanglement entropy exhibits singular behavior in specific regions that precisely align with the spatial locations of topological phase transitions in the extended long-range SSH model. These findings are further supported by the application of winding numbers and energy spectra, offering comprehensive evidence for the topological aspects of both Hermitian and non-Hermitian SSH models. As a result, the singularity in entanglement entropy provides a robust framework for characterizing topological phase transitions.

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.

Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems

We study if the interplay between dynamical localization and interactions in periodically driven quantum systems can give rise to anomalous thermalization behavior. Specifically, we consider one-dimensional models with interacting spinless fermions with nearest-neighbor hopping and density-density interactions, and a periodically driven on-site potential with spatial periodicity m=2 and m=4. At a dynamical localization point, these models evade thermalization either due to the presence of an extensive number of conserved quantities (for weak interactions) or due to the kinetic constraints caused by drive-induced resonances (for strong interactions). Our models therefore illustrate interesting mechanisms for generating constrained dynamics in Floquet systems which are difficult to realize in an undriven system.

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.

Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain

We present a feasible scheme to implement a planar and tunable quantum state transfer (QST) via topologically protected zero-energy mode in a splicing Y-junction Su–Schrieffer–Heeger (SSH) chain. The introduction of the elaborate nearest-neighbor (NN) hopping enables one to generate a topological interface at the central site of the Y-junction. By modulating the NN hopping adiabatically in the chain, the quantum state initially prepared at the central site can be simultaneously transferred to the three endpoints of the Y-junction with the equal/unequal probabilities. The planar distribution of QST is expected to realize a quantum router, whose function is to make the quantum information on the central site (input port) appear equally/unequally at the three endpoints (output ports) with different directions. Moreover, the numerical simulations demonstrate that the scheme possesses the robustness on the fluctuations of the NN hopping and the on-site potential in the system. Furthermore, we show that the number of the output ports with different directions can be flexibly increased in an extended X-junction SSH chain, and the experimental feasibility for implementing special QST in a superconducting qubit-resonator system is briefly discussed. Our work extends the space distribution of QST from linear distribution to planar distribution and promotes the construction of large-scale quantum networks.

On the structural and electrical properties of MgFe2O4, MgMn0.2Fe1.8O4, and Mn3O4

Charge carrier transport via donor/acceptor pairs of similar elements is dominant in n-type MgFe2O4 and p-type Mn3O4 spinels. The temperature-independent activation energy in the form of the nearest neighbor hopping model is applied for Fe2+/Fe3+ pairs of cubic MgFe2O4 spinel in the temperature range of 423–523 K (150–250 °C). At such high temperatures, even for this relatively narrow temperature range, the constant energy barrier deviates to a variable range hopping energy barrier in the case of Mn3O4, due to Jahn-Teller active octahedral sites. Replacing 10 mol% of Fe at octahedral sites with Mn has significantly increased the electron hopping energy barrier and electrical conductivity of MgFe2O4, while keeping the nearest neighbor hopping model dominant. The observed high energy barrier is due to donor/acceptor pairs of different elements (Mn/Fe). Due to a lack of structural distortion, deviation from the nearest neighbor hopping mechanism with temperature-independent activation energy was not observed. Rietveld refined XRD patterns and FT-IR spectra are utilized to support the argument on electrical conductivity mechanisms.

Topological phase transitions and flat bands on an islamic lattice

We construct an islamic lattice by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-NN hoppings. This model supports abundant quantum phases for various values of filling fractions. At filling, Chern insulator (CI) phases with Chern numbers and a zero-Chern-number topological insulator (ZCNTI) phase exist. At filling, several CI phases with Chern numbers and the ZCNTI phase are obtained. For the filling fraction 3/4, CI phases with Chern numbers and two ZCNTI phase areas appear. Interestingly, these ZCNTI phases host both robust corner states and gapless edge states which can be characterized by the quantized polarization and quadrupole moment. We further find that staggered magnetic fluxes can give rise to the ZCNTI state at and fillings. Phase diagrams for filling fractions , , and are presented as well. In addition, flat bands are obtained for various filling fractions by tuning the hopping parameters. At 1/8 filling, a best topological flat band (TFB) with flatness ratio about 12 appears. Several trivial flat bands but with total Chern number emerge in this model and exactly flat band is found at 3/8 filling. We further investigate fractional Chern insulate state when hard-core bosons fill into this TFB model.

Isolated flat bands in 2D lattices based on a novel path-exchange symmetry

The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties. One such property is the presence of flat bands. Typically, the presence of these requires long-ranged hoppings, fine-tuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell. We provide a prescription based on carrying out projections from a parent system to generate different flat band systems. We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones. Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band. This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature. The prescription also eliminates the need for any fine-tuning. Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band. As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagomé, the Lieb, and the Dice lattices. Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagomé lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.

Strain control of a bandwidth-driven spin reorientation in Ca3Ru2O7

The layered-ruthenate family of materials possess an intricate interplay of structural, electronic and magnetic degrees of freedom that yields a plethora of delicately balanced ground states. This is exemplified by Ca3Ru2O7, which hosts a coupled transition in which the lattice parameters jump, the Fermi surface partially gaps and the spins undergo a 90∘ in-plane reorientation. Here, we show how the transition is driven by a lattice strain that tunes the electronic bandwidth. We apply uniaxial stress to single crystals of Ca3Ru2O7, using neutron and resonant x-ray scattering to simultaneously probe the structural and magnetic responses. These measurements demonstrate that the transition can be driven by externally induced strain, stimulating the development of a theoretical model in which an internal strain is generated self-consistently to lower the electronic energy. We understand the strain to act by modifying tilts and rotations of the RuO6 octahedra, which directly influences the nearest-neighbour hopping. Our results offer a blueprint for uncovering the driving force behind coupled phase transitions, as well as a route to controlling them.

Negative Hall coefficient in band conduction region in heavily Al-doped 4H-SiC

At low temperatures, the Hall coefficients in heavily Al-doped 4H-SiC are reported to be negative in the band conduction region as well as in the hopping conduction regions (i.e., nearest-neighbor hopping conduction region and variable-range hopping conduction region). A physical model was proposed to explain the negative sign of RH(T) in the hopping conduction regions. However, the negative value of RH(T) in the conduction band region remains unexplained. This study proposed a physical model to explain the negative value of RH(T) in the conduction band region. In addition to the valence band, doping copious amounts of Al acceptors in 4H-SiC causes a strong overlap of the wave functions of the excited states of Al acceptors, which results in the formation of allowed bands, referred to as allowed minibands. Although the holes can flow freely through the valence band as well as the allowed minibands, the energy–momentum relationship in the valence band and the allowed minibands determines the sign of RH(T). As elucidated here, if the holes flow primarily in the lower parts of the allowed minibands, the RH(T) in the band conduction region becomes negative, whereas if the holes flow primarily in the upper parts of the allowed minibands and the valence band, the RH(T) becomes positive.

Unconventional quantum criticality in a non-Hermitian extended Kitaev chain

We investigate the nature of quantum criticality and topological phase transitions near the critical lines obtained for the extended Kitaev chain with next nearest neighbor hopping parameters and non-Hermitian chemical potential. We surprisingly find multiple gap-less points, the locations of which in the momentum space can change along the critical line unlike the Hermitian counterpart. The interesting simultaneous occurrences of vanishing and sign flipping behavior by real and imaginary components, respectively of the lowest excitation is observed near the topological phase transition. Introduction of non-Hermitian factor leads to an isolated critical point instead of a critical line and hence, reduced number of multi-critical points as compared to the Hermitian case. The critical exponents obtained for the multi-critical and critical points show a very distinct behavior from the Hermitian case.

Electrical Properties of Heavily Al-Doped 4H-SiC

We investigate the temperature-dependent resistivity (ρ(T)) and Hall coefficient (RH(T)) of heavily Al-doped 4H-SiC and discuss the underlying conduction mechanisms. The sign of RH(T) changes from positive to negative in nearest-neighbor hopping (NNH) and variable-range hopping (VRH) conduction, whereas it is positive in band conduction because Al-doped 4H-SiC is a p-type semiconductor. We propose a general physical model to explain why RH(T) in hopping conduction becomes negative at low temperatures, which is applicable to both NNH and VRH conduction. Moreover, we elucidate why the activation energy for negative RH(T) becomes similar to that of ρ(T) in NNH conduction.

Engineering Robust Metallic Zero-Mode States in Olympicene Graphene Nanoribbons.

Metallic graphene nanoribbons (GNRs) represent a critical component in the toolbox of low-dimensional functional materials technology serving as 1D interconnects capable of both electronic and quantum information transport. The structural constraints imposed by on-surface bottom-up GNR synthesis protocols along with the limited control over orientation and sequence of asymmetric monomer building blocks during the radical step-growth polymerization have plagued the design and assembly of metallic GNRs. Here, we report the regioregular synthesis of GNRs hosting robust metallic states by embedding a symmetric zero-mode (ZM) superlattice along the backbone of a GNR. Tight-binding electronic structure models predict a strong nearest-neighbor electron hopping interaction between adjacent ZM states, resulting in a dispersive metallic band. First-principles density functional theory-local density approximation calculations confirm this prediction, and the robust, metallic ZM band of olympicene GNRs is experimentally corroborated by scanning tunneling spectroscopy.

Flat bands with high Chern numbers and multiple flat bands in multifold staggered-flux models

Topological flat bands (TFBs) have been proposed in Chern-insulator lattice models. Some two-dimensional monolayer systems can host TFBs with the Chern number $|\mathcal{C}|=1$, and some TFBs with higher Chern numbers are achieved in multilayer or multicomponent systems. In this work, we construct a series of TFBs with higher Chern numbers in the monolayer star lattice by adding several distant-neighbor hopping terms with staggered magnetic fluxes. By considering the third and the fourth nearest-neighbor hopping terms, we find the $|\mathcal{C}|=2$ and $|\mathcal{C}|=3$ TFBs with large flatness ratios, respectively. We also obtain the $|\mathcal{C}|=4$ and $|\mathcal{C}|=5$ TFBs when the fifth and the sixth nearest-neighbor hopping terms are added. Intriguingly, we also observe multiple flat bands with various Chern numbers by tuning the distant-neighbor hopping amplitudes and the staggered-flux parameters. Furthermore, a series of fractional Chern insulator (FCI) states have been numerically observed when hard-core bosons are filled into these TFB models, with fractional fillings $\ensuremath{\nu}=1/3, 2/5, 3/7$ and $\ensuremath{\nu}=1/4, 2/7$ in the $|\mathcal{C}|=2$ and $|\mathcal{C}|=3$ TFBs, respectively. Our findings provide an approach to search for more TFBs with higher Chern numbers and further investigate more interesting FCIs.