Nearest-neighbor Hopping Research Articles

Porous Haldane model: topological phase transitions and flat bands

To investigate the influence of nanoholes on Chern insulators (CIs), we propose a porous Haldane model that considers the nearest-neighbor (NN) hoppings and next-NN (NNN) hoppings with staggered magnetic fluxes. This model supports multiple topological phases with different filling factors. At 2/5 filling, CI phases withC=±1,C = 2,C=±3,C=±4and higher-order topological insulator (HOTI) appear. At 9/20 filling, CI withC=±1,C = 2,C = 3, and HOTI phases are obtained. At half-filling, this model exhibits CI withC=±1,C = 2, andC=-3and HOTI phases. Unlike conventional HOTIs, these HOTI phases host gapless edge states and robust corner states which are characterized by a quantized quadrupole. Additionally, there is a topological flat band (TFB) with a flatness ratio about 13 with the NN and NNN hoppings. Based on the TFB model, we further investigate aν=1/2fractional CI state with hard-core bosons filling.

The electronic and optical properties of graphene nanoribbons under the influence of the periodic strain

The electronic and optical properties of graphene nanoribbons under uniaxial periodic strain have been explored using various nearest-neighbor hopping patterns. It is found that by properly selecting hopping patterns, momentum-resolved gaps within minibands emerge, modifying the energy band structure to exhibit hollowed-out profiles, and enhancing peak intensity in local density of states but reducing peak count. The optical transitions are impacted by altered parity symmetry of wavefunctions, causing changes in optical selection rules. The parity of wavefunctions for strained GNRs has been established through rigorous mathematical proof, whereby the optical selection rule is determined for the strained GNRs. The absorption curves arise from a complex interplay between diminished velocity matrix elements and escalated joint density of states.

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 QDs particularly appealing for applications in nanoelectronic and quantum devices. Herein we study the gate-driven transition temperatures of electron hopping behavior in the upper Hubbard bands (UHBs) and lower Hubbard bands (LHBs) 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 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 UHBs and LHBs. 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.

Topological phase transitions and flat bands on a square-octagon lattice

We construct a square-octagon lattice model by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-nearest-neighbor (NNN) hoppings, where zero-Chern-number topological insulator (ZCNTI) phases emerge. At 1/4 filling, by tuning the staggered fluxes and NNN hopping potential, this model supports the phase transition from a Chern insulator (CI) with Chern number C = 2 to a ZCNTI phase. At half filling, we observe that staggered magnetic fluxes can induce a higher-order topological insulator (HOTI) state. Interestingly, the ZCNTI appears at 3/4 filling when considering the NN and NNN hoppings in the absence of staggered fluxes, which has been rarely reported in previous work. Contrary to conventional HOTIs, this ZCNTI phase hosts both robust corner states and gapless edge states which can be identified based on the quantized dipole and quadrupole moments. Additionally, a topological flat band (TFB) with flatness ratio about 24 appears. We further investigate ν = 1/2 fractional Chern insulator (FCI) state when hard-core bosons fill into this TFB model.

Thermal signature of a helical molecule: Beyond nearest-neighbor electron hopping

Thermal signature of a helical molecule: Beyond nearest-neighbor electron hopping

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.

A galactic approach to neutron scattering science

Neutron scattering science is leading to significant advances in our understanding of materials and will be key to solving many of the challenges that society is facing today. Improvements in scientific instruments are actually making it more difficult to analyze and interpret the results of experiments due to the vast increases in the volume and complexity of data being produced and the associated computational requirements for processing that data. New approaches to enable scientists to leverage computational resources are required, and Oak Ridge National Laboratory (ORNL) has been at the forefront of developing these technologies. We recently completed the design and initial implementation of a neutrons data interpretation platform that allows seamless access to the computational resources provided by ORNL. For the first time, we have demonstrated that this platform can be used for advanced data analysis of correlated quantum materials by utilizing the world's most powerful computer system, Frontier. In particular, we have shown the end-to-end execution of the DCA++ code to determine the dynamic magnetic spin susceptibility χ(q, ω) for a single-band Hubbard model with Coulomb repulsion U/t = 8 in units of the nearest-neighbor hopping amplitude t and an electron density of n = 0.65. The following work describes the architecture, design, and implementation of the platform and how we constructed a correlated quantum materials analysis workflow to demonstrate the viability of this system to produce scientific results.

Realization of Yin–Yang kagome bands and tunable quantum anomalous Hall effect in monolayer V3Cl6

Kagome materials serve as crucial platforms for investigating the quantum anomalous Hall effect (QAHE) due to the presence of kagome bands in their electronic structures. However, despite the theoretical predictions being proposed, kagome band material realizations have been limited. In this work, through tight-binding (TB) model analysis, by setting the nearest-neighbor hopping integrals with opposite signs, we propose a Yin–Yang kagome band structure characterized by two stable enantiomorphic kagome bands. Furthermore, we design a monolayer V3Cl6 to confirm the TB model. Three V atoms are located in different coordination environments in V3Cl6, so opposite signs of the hopping integrals between two of their orthogonal d orbitals can be achieved, which is the key to realize Yin–Yang kagome band structures. The calculated band structures obtained from first principles are consistent with those from the TB model. Additionally, we find that the two enantiomorphic flat bands in monolayer V3Cl6 possess opposite Chern number after spin–orbit coupling is considered, which can also be confirmed from symmetry index analysis. The Chern numbers as well as the topological properties can be modulated by doping hole or adjusting the magnetization directions, so the QAHE can be tuned in monolayer V3Cl6. Our results provide a practicable pathway for realizing Yin–Yang kagome band structures and achieving tunable QAHE in them.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

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.

Universal chemical formula dependence of ab initio low-energy effective Hamiltonian in single-layer carrier-doped cuprate superconductors: Study using a hierarchical dependence extraction algorithm

We explore the possibility to control the superconducting transition temperature at optimal hole doping Tcopt in cuprates by tuning the chemical formula (CF). Tcopt can be theoretically predicted from the parameters of the low-energy effective Hamiltonian with one antibonding (AB) Cu3dx2−y2/O2pσ orbital per Cu atom in the CuO2 plane, notably the nearest-neighbor hopping amplitude |t1| and the ratio u=U/|t1|, where U is the onsite effective Coulomb repulsion. However, the CF dependence of |t1| and u is a highly nontrivial question. In this paper, we propose the universal dependence of |t1| and u on the CF and structural features in hole doped cuprates with a single CuO2 layer sandwiched between block layers. To do so, we perform extensive calculations of |t1| and u and analyze the results by employing a machine-learning method called hierarchical dependence extraction (HDE). The main results are (a) |t1| has a main-order dependence on the radii RX and RA of the apical anion X and cation A in the block layer. (|t1| increases when RX or RA decreases.) (b) u has a main-order dependence on the ionic charge ZX of X and the hole doping δ of the AB orbital. (u decreases when |ZX| increases or δ increases.) We elucidate and discuss the microscopic mechanism of items (a) and (b). We demonstrate the predictive power of the HDE by showing the consistency between items (a) and (b) and results from previous works. The present results provide a basis for optimizing superconducting properties in cuprates and possibly akin materials. Also, the HDE method offers a general platform to identify dependencies between physical quantities. Published by the American Physical Society 2024

Flat bands in three-dimensional lattice models with non-trivial Hopf index

We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.

Local Integrals of Motion in Dipole-Conserving Models with Hilbert Space Fragmentation.

Hilbert space fragmentation is an ergodicity-breaking phenomenon, in which the Hamiltonian shatters into exponentially many dynamically disconnected sectors. In many fragmented systems, these sectors can be labeled by statistically localized integrals of motion, which are nonlocal operators. We study the paradigmatic nearest-neighbor pair hopping model exhibiting the so-called strong fragmentation. We show that this model hosts local integrals of motion (LIOMs), which correspond to frozen density modes with long wavelengths. The latter modes become subdiffusive when longer-range pair hoppings are allowed. Finally, we make a connection with a tilted (Stark) chain. Contrary to the dipole-conserving effective models, the tilted chain is shown to support either a Hamiltonian or dipole moment as an LIOM. Numerical results are obtained from a numerical algorithm, in which finding LIOMs is reduced to a data compression problem.

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.

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.

Dome structure in pressure dependence of superconducting transition temperature for HgBa2Ca2Cu3O8 : Studies by ab initio low-energy effective Hamiltonian

The superconducting (SC) cuprate HgBa2Ca2Cu3O8 (Hg1223) has the highest SC transition temperature Tc among cuprates at ambient pressure Pamb, namely, Tcopt≃138 K experimentally at the optimal hole doping concentration. Tcopt further increases under pressure P and reaches 164 K at optimal pressure Popt≃30 GPa, then Tcopt decreases with increasing P>Popt generating a dome structure [Gao , ]. This nontrivial and nonmonotonic P dependence of Tcopt calls for a theoretical understanding and mechanism. To answer this open question, we consider the low-energy effective Hamiltonian (LEH) for the antibonding (AB) Cu3dx2−y2/O2pσ band derived generally for the cuprates. In the AB LEH for cuprates with Nℓ≤2 laminated CuO2 planes between block layers, it was proposed that Tcopt is determined by a universal scaling Tcopt≃0.16|t1|FSC [Schmid , ], where t1 is the nearest-neighbor hopping, and the SC order parameter at optimal hole doping FSC mainly depends on the ratio u=U/|t1| where U is the onsite effective Coulomb repulsion: The u dependence of FSC has a peak at uopt≃8.5 and a steep decrease with decreasing u in the region u<uopt irrespective of materials dependent on other parameters. In this paper, we show that |t1| increases with P, whereas u decreases with P in the Hamiltonian of Hg1223. Based on these facts, we show that the domelike P dependence of Tcopt can emerge at least qualitatively if we assume Hg1223 with Nℓ=3 follows the same universal scaling for Tcopt, and Hg1223 is located at the slightly strong coupling region u≳uopt at Pamb and u≃uopt at Popt by taking account of expected corrections to our calculation. The consequence of these assumptions is the following: With increasing P within the range P<Popt, the increase in Tcopt is accounted for by the increase in |t1|, whereas FSC is insensitive to the decrease in u around ≃uopt and hence to P as well. At P>Popt, the decrease in Tcopt is accounted for by the decrease in u below uopt, which causes a rapid decrease in FSC dominating over the increase in |t1|. We further argue the appropriateness of these assumptions based on the insight from studies on other cuprate compounds in the literature. In addition, we discuss the dependencies of u and |t1| on each crystal parameter (CP), which provides hints for design of even higher Tcopt materials. Published by the American Physical Society 2024

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.

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.

Quantum simulation of the bosonic Kitaev chain

Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analog of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the in situ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.

Solitons in binary compounds with stacked two-dimensional honeycomb lattices

We model the electronic properties of thin films of binary compounds with stacked layers where each layer is a two-dimensional honeycomb lattice with two atoms per unit cell. The two atoms per cell are assigned different on-site energies in order to consider six different stacking orders: ABC, ABA, AA, ABC′, ABA′, and AA′. Using a minimal tight-binding model with nearest-neighbor hopping, we consider whether a fault in the texture of on-site energies in the vertical, stacking direction supports localized states, and we find localized states within the bulk band gap for ABC, ABA, and AA′ stacking. Depending on the stacking type, parameter values, and whether the soliton is atomically sharp or a smooth texture, there are a range of different band structures including soliton bands that are either isolated or that hybridize with other states, such as surface states, and soliton bands that are either dispersive or flat, the latter yielding narrow features in the density of states. We discuss the relevance of our results to specific materials including graphene, hexagonal boron nitride, and other binary compounds. Published by the American Physical Society 2024