Second-neighbor Hopping Research Articles

Perturbative solution of fermionic sign problem in quantum Monte Carlo computations

We have developed a strong-coupling perturbation scheme for a general doped Hubbard model around a particle-hole-symmetric reference system, which is free from the fermionic sign problem. Our approach is based on the lattice determinantal Quantum Monte Carlo (QMC) method in both continuous and discrete time versions for large periodic clusters in a fermionic bath. By considering the first-order perturbation in the shift of the chemical potential and the second-neighbor hopping, we are able to obtain an accurate electronic spectral function for a range of parameters that correspond to optimally doped cuprate systems at temperatures of up to T = 0.1t, which are challenging to access using straightforward lattice QMC calculations. We also discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system with the interaction parameter U equal to the bandwidth and the optimal value of the next-nearest-neighbor hopping parameter 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} for high-temperature superconducting cuprates.

Tunning the tilt of the Dirac cone by atomic manipulations in 8Pmmn borophene

Two dimensional quantum materials possessing Dirac cones in their spectrum are fascinating due to their emergent low-energy Dirac fermions. In 8Pmmn borophene the Dirac cone is furthermore tilted, which is a proxy for spacetime geometry, since the future light-cone depends on the underlying metric. Therefore it is important to understand the microscopic origin of the tilt. Here, based on ab-initio calculations, we decipher the atomistic mechanism of the formation of tilt. First, nearest-neighbor hopping on a buckled honeycomb lattice forms an upright Dirac cone. Then, the difference in the renormalized anisotropic second-neighbor hopping, formed by virtual hoppings on one-dimensional chains of atoms, tilts the Dirac cone. We construct an accurate tight-binding model on honeycomb graph for analytical investigation, and we find that substitution of certain boron atoms by carbon provides a way to change the tilt of the cone.

Rashba spin-orbit coupling in the square-lattice Hubbard model: A truncated-unity functional renormalization group study

The Rashba-Hubbard model on the square lattice is the paradigmatic case for studying the effect of spin-orbit coupling, which breaks spin and inversion symmetry, in a correlated electron system. We employ a truncated-unity variant of the functional renormalization group which allows us to analyze magnetic and superconducting instabilities on equal footing. We derive phase diagrams depending on the strengths of Rasbha spin-orbit coupling, real second-neighbor hopping, and electron filling. We find commensurate and incommensurate magnetic phases which compete with $d$-wave superconductivity. Due to the breaking of inversion symmetry, singlet and triplet components mix; we quantify the mixing of $d$-wave singlet pairing with $f$-wave triplet pairing.

Second-Neighbor Hopping Effects in the Two-Dimensional Attractive Hubbard Model

The emergence of superconductivity (SC) in lattice models, such as the attractive Hubbard one, has renewed interest since the realization of cold-atom experiments. However, reducing the temperature in these experiments is a bottleneck; therefore, investigating how to increase the energy scale for SC is crucial to cold atoms. In view of this, we examine the effects of next-nearest-neighbor hoppings (t′) on the pairing properties of the attractive Hubbard model in a square lattice. To this end, we analyze the model through unbiased Quantum Monte Carlo simulations for fixed density n=0.87, and perform finite-size scaling analysis to the thermodynamic limit. As our main result, we notice that the existence of further hopping channels leads to an enhancement of the pairing correlations, which, in turn, increases the ground-state order parameter Δ. Finally, at finite temperatures, for t′/t≠0, this enhancement of pairing correlations leads to an increase in the critical temperature Tc. That is, the fine-tuning of second-neighbor hoppings increases the energy scales for SC, and may be a route by which cold-atom experiments can achieve such a phase and to help us further understand the nature of this phenomenon.

Localization phenomena and electronic transport in irradiated Aubry–André–Harper systems

The role of light irradiation on electronic localization is critically investigated for the first time in a tight-binding lattice where site energies are modulated in the cosine form following the Aubry–André–Harper (AAH) model. The critical point of transition from delocalized-to-localized phase can be monitored selectively by regulating the light parameters that is extremely useful to have controlled electron transmission across the system. Starting with a strictly one-dimensional (1D) AAH chain, we extend our analysis considering a two-stranded ladder model which brings peculiar signatures in presence of irradiation. Unlike 1D system, AAH ladder exhibits a mixed phase (MP) zone where both extended and localized energy eigenstates co-exist. This is the fundamental requirement to have mobility edge in energy band spectrum. A mathematical description is given for decoupling the irradiated ladder into two effective 1D AAH chains. The underlying mechanism of getting a MP zone relies on the availability of two distinct critical points (CPs) of the decoupled chains, in presence of second-neighbor hopping between the two strands. Using a minimal coupling scheme the effect of light irradiation is incorporated following the Floquet–Bloch ansatz. The localization behaviors of different energy eigenstates are studied by calculating inverse participation ratio, and, are further explained in a more compact way by calculating two-terminal transmission probabilities together with average density of states. Finally, the decoupling procedure is extended for a more general multi-stranded AAH ladders where multiple CPs and thus multiple mobility edges are found. Our analysis may provide a new route of engineering localization properties in similar kind of other fascinating quasiperiodic systems.

Systematic Analysis Method for Nonlinear Response Tensors

We propose a systematic analysis method for identifying essential parameters in various linear and nonlinear response tensors without which they vanish. By using the Keldysh formalism and the Chebyshev polynomial expansion method, the response tensors are decomposed into the model-independent and dependent parts, in which the latter is utilized to extract the essential parameters. An application of the method is demonstrated by analyzing the nonlinear Hall effect in the ferroelectric SnTe monolayer for example. It is shown that in this example the second-neighbor hopping is essential for the nonlinear Hall effect whereas the spin–orbit coupling is unnecessary. Moreover, by analyzing terms contributing to the essential parameters in the lowest order, the appearance of the nonlinear Hall effect can be interpreted by the subsequent two processes: the orbital magneto-current effect and the linear anomalous Hall effect by the induced orbital magnetization. In this way, the present method provides a microscopic picture of responses. By combining with computational analysis, it stimulates further discoveries of anomalous responses by filling in a missing link among hidden degrees of freedom in a wide variety of materials.

Second-neighbor electron hopping and pressure induced topological quantum phase transition in insulating cubic perovskites

Perovskite structure is one of the five symmetry families suitable for exhibiting topological insulator phase. However, none of the halides and oxides stabilizing in this structure exhibit the same. Through density functional calculations on cubic perovskites (${\mathrm{CsSnX}}_{3}$; X = Cl, Br, and I), we predict a band insulator--Dirac semimetal--topological insulator phase transition with uniform compression. With the aid of a Slater-Koster tight binding Hamiltonian, we show that, apart from the valence electron count, the band topology of these perovksites is determined by five parameters involving electron hopping among the Sn-{$s,p$} orbitals. These parameters monotonically increase with pressure to gradually transform the positive band gap to a negative one and thereby enable the quantum phase transition. The universality of the mechanism of phase transition is established by examining the band topology of Bi based oxide perovskites. Dynamical stability of the halides against pressure strengthens the experimental relevance.

Mechanism for Unconventional Superconductivity in the Hole-Doped Rashba-Hubbard Model.

Motivated by the recent resurgence of interest in topological superconductivity, we study superconducting pairing instabilities of the hole-doped Rashba-Hubbard model on the square lattice with first- and second-neighbor hopping. Within the random phase approximation, we compute the spin-fluctuation-mediated pairing interactions as a function of filling. Rashba spin-orbit coupling splits the spin degeneracies of the bands, which leads to two van Hove singularities at two different fillings. We find that, for a doping region in between these two van Hove fillings, the spin fluctuations exhibit a strong ferromagnetic contribution. Because of these ferromagnetic fluctuations, there is a strong tendency towards spin-triplet f-wave pairing within this filling region, resulting in a topologically nontrivial phase.

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.

Effect of Floquet engineering on the p-wave superconductor with second-neighbor couplings

The influence of the Floquet engineering on a particular one-dimensional p-wave superconductor, Kitaev model, with second-neighbor couplings is investigated in this paper. The effective Hamiltonians in the rotated reference frames have been obtained, and the convergent regions of the approximated Hamiltonian as well as the topological phase diagrams have been analyzed and discussed. We show that by modulating the external driving field amplitude, frequency as well as the second-neighbor hopping amplitude, the rich phase diagrams and transitions between different topological phases can be obtained.

Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model

Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength $U$, hole doping $\delta$ and temperature $T$. The N\'eel phase boundary is non-monotonic as a function of $U$ and $\delta$. Frustration induced by second-neighbor hopping reduces N\'eel order more effectively at small $U$. The doped AF is stabilized at large $U$ by kinetic energy and at small $U$ by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large $U$, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.

Correlation Between Charge Order and Second-Neighbor Hopping in Cuprate Superconductors

The correlation between the charge-order wave vector Q_{CD} and second-neighbor hopping t' in cuprate superconductors is studied based on the t-t'-J model. It is shown that the magnitude of the charge-order wave vector Q_{CD} increases with the increase of t', and then the experimentally observed differences of the magnitudes of the charge-order wave vector Q_{CD} among the different families of cuprate superconductors at the same doping concentration can be attributed to the different values of t'.

Floquet states in (LaNiO3)2/(LaAlO3)N heterostructures grown along the (111) direction

Using Floquet-Bloch theory we study the effect of circularly and linearly polarized light on the electronic structure of (LaNiO$_3$)$_2$/(LaAlO$_3$)$_N$ heterostructure grown along the (111) direction. In equilibrium, a tight-binding fit to the first principles band structure shows that nearest-neighbor hopping plays a dominant role while second-neighbor hopping breaks the particle-hole symmetry and determines the finer band features. The four bands of the LaNiO$_3$ bilayer exhibit both quadratic band touching points and Dirac points. By varying the amplitude of the incident light, one can independently tune the first and second-neighbor hopping for fixed frequency, which leads to considerable control over the Floquet band structure. We investigate this control in detail, and study how the quadratic and Dirac band touchings are influenced by the polarization and intensity of the light. We derive effective 2-band Hamiltonians (for both quadratic and Dirac band touching points) that accurately captures these results. We further study an extended model which explicitly includes oxygen $p$-orbitals and compare the results to the effective model that contains only the nickel $d$-orbitals. We conclude with a computation of the frequency dependent optical Hall conductivity using the full four band model and analyze the various inter-band contributions of the Floquet modes.

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

We theoretically analyze a discrete Schr\"odinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, the second-neighbor hopping has a strong impact on the band structure, leading to the emergence of a new extremum located inside the band, accompanied by a van Hove singularity in the density of states. The energy band is then divided into a subcritical regime with the usual unique correspondence between wave number and energy of the travelling waves, and a supercritical regime, in which waves of different wave number are degenerate in energy. We study the consequences of these features in a scattering setup, introducing a defect that locally breaks the translational invariance. The notion of a local probability current is generalized beyond the nearest-neighbor approximation and bound states with energies outside the band are discussed. At subcritical energies inside the band, an evanescent mode coexists with the travelling plane wave, giving rise to resonance phenomena in scattering. At weak coupling to the defect, we identify a prototypical Fano-Feshbach resonance of tunable shape and provide analytical expressions for its profile parameters. At supercritical energies, we observe coupling of the degenerate travelling waves, leading to an intricate wave packet fragmentation dynamics. The corresponding branching ratios are analyzed.

Hole-Doped Cuprate Panorama and the Second Neighbor Hopping

We consider the coexistent id-density wave order, at the antiferromagnetic wave vector Q = (π, π), representing the pseudo-gap state, and d-wave superconductivity, driven by an assumed attractive interaction, within the BCS framework for the two-dimensional fermion system on a square lattice starting with a meaneld Hamiltonian involving the singlet id-density wave and the d-wave superconductivity pairings. The second-neighbor hopping, which is known to be important for cuprates and frustrates the kinetic energy of electrons, leads to the Fermi surface sheets being not connected by Q. The signature of the particle hole asymmetry in the single-particle excitation spectrum of the pure id-density wave state is re ected in the coexisting id-density wave and d-wave superconductivity states, though the latter is characterized by the Bogoliubov quasi-particle bands a characteristic feature of superconducting state. Quite signi cantly, we nd that the coexistence is possible due to the non-nesting property.

Magnetotransport in mesoscopic rings and cylinders: effects of electron-electron interaction and spin-orbit coupling

AbstractWe undertake an in-depth analysis of the magnetotransport properties in mesoscopic single-channel rings and multichannel cylinders within a tight-binding (TB) formalism. The main focus of this review is to illustrate how the long-standing anomalies between the calculated and measured current amplitudes carried by a small conducting ring upon the application of a magnetic flux ϕcan be removed. We discuss two different cases. First, we examine the combined effect of second-neighbor hopping integral and Hubbard correlation on the enhancement of persistent current in the presence of disorder. A significant change in current amplitude is observed compared to the traditional nearest-neighbor hopping model, and the current amplitude becomes quite comparable to experimental realizations. In the other case, we verify that in the presence of spin-orbit interaction, a considerable enhancement of persistent current amplitude takes place, and the current amplitude in a disordered ring becomes almost comparable to that of an ordered one. In addition to these, we also present the detailed band structures and some other related issues to get a complete picture of the phenomena at the microscopic level.

Renormalization of hopping integrals in coexistence phase of stripe and d-wave superconductivity in two-dimensional Hubbard model

Abstract We have performed a variational Monte Carlo simulation on a two-dimensional Hubbard model with first- and second-neighbor hopping terms in order to study the coexistence state of a static stripe state and a modulated d-wave superconductivity in the underdoped cuprates. In addition to a Gutzwiller, a Jastrow and a doublon-holon correlation effects, the band-renormalization effect was considered in the trial wave function. The condensation energies of an 8-period stripe state was computed as a function of a Coulomb energy under the hole-density x=1/8. Our results reveal that the renormalization of higher hopping parameters due to the strong correlation effect enhances the one-dimensional hole motion on a quarter-filled band in the stripe state, and brings quasi-Fermi surface close to the magnetic zone boundary in the coexistence state.

Topological insulators and fractional quantum Hall effect on the ruby lattice

We study a tight-binding model on the two-dimensional ruby lattice. This lattice supports several types of first- and second-neighbor spin-dependent hopping parameters in an $s$-band model that preserves time-reversal symmetry. We discuss the phase diagram of this model for various values of the hopping parameters and filling fractions and note an interesting competition between spin-orbit terms that individually would drive the system to a ${Z}_{2}$ topological insulating phase. We also discuss a closely related spin-polarized model with only first- and second-neighbor hoppings and show that extremely flat bands with finite Chern numbers result, with a ratio of the band gap to the band width of approximately 70. Such flat bands are an ideal platform to realize a fractional quantum Hall effect at appropriate filling fractions. The ruby lattice can be possibly engineered in optical lattices and may open the door to studies of transitions among quantum spin liquids, topological insulators, and integer and fractional quantum Hall states.

Superconductivity and ferromagnetism in charge-ordered metallic phases of extended hubbard models

We analyze the Fermi-surface instability of charge carriers in the charge-ordered metallic phases of a triangular-lattice extended Hubbard model at quarter filling and an extended Hubbard ladder near half filling. We derive and analyze strong-coupling effective Hamiltonians for the charge carriers, and then, we find f-wave superconductivity in the triangular-lattice model and ferromagnetism in the ladder model. The origin of these orderings can be associated with the following terms in the effective Hamiltonians: f-wave superconductivity is stabilized by the inter-site attraction and correlated hopping, and ferromagnetism results from positive second-neighbor hopping and an infinitely large on-site repulsion.

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions

We explore the momentum-sector-selective metal-insulator transitions recently found in the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid-like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin-correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.