Three-dimensional Tight-binding Model Research Articles

Supercurrent-Induced Weyl Superconductivity

We show that Weyl superconductivity can be induced by finite supercurrent in noncentrosymmetric spin–orbit-coupled superconductors with line nodes. We introduce a three-dimensional tight-binding model of a tetragonal superconductor in a D+p-wave pairing state with a finite center-of-mass momentum, and elucidate that a line-nodal to point-nodal spectral transition occurs by applying an infinitesimal supercurrent. We also clarify that the higher-order effect in spin–orbit coupling is particularly important for this phenomenon. The point nodes are protected by topologically nontrivial Weyl charges, and therefore gapless arc states appear on the surface of the superconductor. Furthermore, both the positions and the Weyl charges of the point nodes depend on the direction of the current. In addition, a quantized Berry phase defined on high-symmetry planes characterizes the Weyl nodes when the in-plane supercurrent is considered. Our proposition paves a new way for controlling the superconducting gap structures by using an external field.

Eigenvalue analysis of the three-dimensional tight-binding model with non-Hermitian disorder

In this study, the level statistics of the three-dimensional tight-binding model with non-Hermitian disorder, introduced by Tzortzakakis, Makris, and Economou (TME), and its variants were analyzed. The shift-and-invert Arnoldi method was used to analyze the eigenvalues of the TME model up to a $48\ifmmode\times\else\texttimes\fi{}48\ifmmode\times\else\texttimes\fi{}48$ cubic lattice, which was larger than those used in previous studies. The results showed that the magnitude of critical disorders in the isotropic TME model was larger than that reported in previous numerical studies for smaller systems. The localization-delocalization transition in an anisotropic model was also investigated. The computational method adopted in this study was shown to be quite effective for large-scale analysis of the calculation of all eigenvalues of sparse non-Hermitian matrices.

Superconducting subphase and substantial Knight shift in Sr2RuO4

Recent nuclear magnetic resonance experiments measuring the Knight shift in $Sr_2RuO_4$ have challenged the widely accepted picture of chiral pairing in this superconductor. Here we study the implications of helical pairing on the superconducting state while comparing our results with the available experimental data on the upper critical field and Knight shift. We solve the Bogoliubov-de-Gennes equation employing a realistic three-dimensional tight-binding model that captures the experimental Fermi surface very well. In agreement with experiments we find a Pauli limiting to the upper critical field and, at low temperatures and high fields, a second superconducting transition. These transitions which form a superconducting subphase in the H-T phase diagram are first-order in nature and merge into a single second-order transition at a bicritical point $(T^\ast,H^\ast$), for which we find (0.8~K, 2.4~T) with experiment reporting (0.8~K, $\sim$ 1.2~T) [\textit{Phys. Rev. B} \textbf{93}, 184513 (2016)]. Furthermore, we find a substantial drop in the Knight shift in agreement with recent experiments.

K_{z} Selective Scattering within Quasiparticle Interference Measurements of FeSe.

Quasiparticle interference (QPI) provides a wealth of information relating to the electronic structure of a material. However, it is often assumed that this information is constrained to two-dimensional electronic states. We show that this is not necessarily the case. For FeSe, a system dominated by surface defects, we show that it is actually all electronic states with negligible group velocity in the z axis that are contained within the experimental data. By using a three-dimensional tight-binding model of FeSe, fit to photoemission measurements, we directly reproduce the experimental QPI scattering dispersion, within a T-matrix formalism, by including both k_{z}=0 and k_{z}=π electronic states. This result unifies both tunnelling based and photoemission based experiments on FeSe and highlights the importance of k_{z} within surface sensitive measurements of QPI.

The direction of the d-vector in a nematic triplet superconductor

We investigate the states of triplet pairing in a candidate nematic superconductor versus typical material parameters, using the mean field theory for two- and three-dimensional tight-binding models with local triplet pairing in the Eu representation of the D3d, the point group of the system. In the two-dimensional model, the system favors the fully gapped chiral state for weaker warping or lower filling level, while a nodal and nematic state is favorable for stronger warping or higher filling, with the d-vector aligned along the principle axis. In the presence of lattice distortion, relative elongation along one of the principle axes, , tends to rotate the nematic d-vector orthogonal to , resulting in the nematic state at sufficient elongation. Three-dimensionality is seen to suppress the chiral state in favor of the nematic ones. Our results may explain the variety in the probed direction of the d-vector in existing experiments.

Topological metal bands with double-triple-point fermions in optical lattices

Novel fermionic quasiparticles with integer pseudospins in some energy bands, such as pseudospin-1 triple-point fermions, recently attract increasing interest since they are beyond the conventional spin-$1/2$ Dirac and Weyl counterparts. In this paper, we propose a class of pseudospin-1 fermioic excitations emerging in topological metal bands, dubbed double-triple-point (DTP) fermions. We first present a general three-band continuum model with $C_4$ symmetry in three dimensions, which has three types of threefold degenerate points in the bands classified by their topological charges $C=\pm4,\pm2,0$, respectively. They are dubbed DTPs as spin-1 generalization of double-Weyl points. We then construct two-dimensional and three-dimensional tight-binding lattice models of topological metal bands with exotic DTP fermions near the DTPs. In two dimensions, the band gaps close at a trivial DTP with zero Berry phase, which occurs at the transition between the normal and topological insulator phases. In three dimensions, the topological properties of three different DTP fermions in lattice systems are further investigated, and the effects of breaking $C_4$ symmetry are also studied, which generally leads to splitting each quadratic DTP into two linear triple points and gives topological phase diagrams. Using ultracold fermionic atoms in optical lattices, the proposed models can be realized and the topological properties of the DTP fermions can be detected.

Geometric effect on quantum anomalous Hall states in magnetic topological insulators

An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We numerically investigate this dissipative behavior of QAHE in MTIs with a three-dimensional tight-binding model and non-equilibrium Green’s function formalism. It is found that, in clean samples, the geometric mismatch between the detecting electrodes and the MTI sample leads to additional scattering in the central Hall bar, which is similar to the effect of splitting gates in the traditional Hall effect. As a result, while the Hall resistance remains quantized, the longitudinal resistance deviates from zero due to such additional scattering. It is also shown that external magnetic fields as well as disorder scattering can suppress the dissipation of the longitudinal resistance. These results are in good agreement with previous experimental observations and provide insight on the fabrication of QAHE devices.

Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct twoand three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named asMaxwell fermions.We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions,Maxwell points may have nontrivial monopole charges of \pm2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

Disorder-induced phase transitions of type-II Weyl semimetals

Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.

Filling of magnetic-impurity-induced gap in topological insulators by potential scattering

We show that the energy gap induced by ferromagnetically aligned magnetic impurities on the surface of a topological insulator can be filled, due to scattering off the non-magnetic potential of the impurities. In both a continuum surface model and a three-dimensional tight-binding lattice model, we find that the energy gap disappears already at weak potential scattering as impurity resonances add spectral weight at the Dirac point. This can help explain seemingly contradictory experimental results as to the existence of a gap.

(3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions

Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of spinless interacting fermions that reproduces, in the low energy limit, a (3+1)-dimensional Abelian topological quantum field theory called BF model. By employing a mechanism equivalent to the Haldane's Chern insulator, we can turn the non-interacting model into a three-dimensional chiral topological insulator. We then isolate energetically one of the two Fermi points of the lattice model. In the presence of suitable fermionic interactions, the system, in the continuum limit, is equivalent to a generalised (3+1)-dimensional Thirring model. The low energy limit of this model is faithfully described by the BF theory. Our approach directly establishes the presence of (2+1)-dimensional BF theory at the boundary of the lattice and it provides a way to detect the topological order of the model through fermionic density measurements.

Effect of short-range order on transport in one-particle tight-binding models

We investigate transport properties of topologically disordered three-dimensional one-particle tight-binding models, featuring site-distance-dependent hopping terms. We start from entirely disordered systems into which we gradually introduce some short-range order by numerically performing a pertinent structural relaxation using local site-pair interactions. Transport properties of the resulting models within the delocalized regime are analyzed numerically using linear response theory. We find that even though the generated order is very short ranged, transport properties such as conductivity or mean free path scale significantly with the degree of order. Mean free paths may exceed the site-pair correlation length. It is furthermore demonstrated that while the totally disordered model is not in accord with a Drude- or Boltzmann-type description, moderate degrees of order suffice to render such a picture valid.

A three-dimensional tight-binding model and magnetic instability of iron selenide [formula omitted

For a newly discovered iron-based high Tc superconducting parent material KFe2Se2, we present an effective three-dimensional five-orbital tight-binding model by fitting the band structures. The three t2g-symmetry orbitals of the five Fe 3d orbitals mainly contribute to the electron-like Fermi surface, which has a three-dimensional character, in agreement with recent angle-resolved photoemission spectroscopy experiments. To understand the groundstate magnetic properties, the two- and three-dimensional spin and charge susceptibilities within the random phase approximation are investigated. It obviously shows a sharp peak at wave vector q∼(π,π), indicating the magnetic instability of Néel-type antiferromagnetic rather than (π/2, π/2)-type or stripe (π, 0)-type antiferromagnetic ordering, while it exhibits a ferromagnetic instability between the nearest neighboring FeSe layers along c axis. The three-dimensional spin fluctuation may play an important role in pairing symmetry in superconducting materials AyFe2−xSe2(A=Rb,Cs,K, etc.).

Spin fluctuations and superconductivity in a three-dimensional tight-binding model forBaFe2As2

Despite the wealth of experimental data on the Fe-pnictide compounds of the KFe2As2-type, K = Ba, Ca, or Sr, the main theoretical work based on multiorbital tight-binding models has been restricted so far to the study of the related 1111 compounds. This can be ascribed to the more three dimensional electronic structure found by ab initio calculations for the 122 materials, making this system less amenable to model development. In addition, the more complicated Brillouin zone (BZ) of the body-centered tetragonal symmetry does not allow a straightforward unfolding of the electronic band structure into an effective 1Fe/unit cell BZ. Here we present an effective 5-orbital tight-binding fit of the full DFT band structure for BaFeAs including the kz dispersions. We compare the 5-orbital spin fluctuation model to one previously studied for LaOFeAs and calculate the RPA enhanced susceptibility. Using the fluctuation exchange approximation to determine the leading pairing instability, we then examine the differences between a strictly two dimensional model calculation over a single kz cut of the BZ and a completely three dimensional approach. We find pairing states quite similar to the 1111 materials, with generic quasi-isotropic pairing on the hole sheets and nodal states on the electron sheets at kz = 0 which however are gapped as the system is hole doped. On the other hand, a substantial kz dependence of the order parameter remains, with most of the pairing strength deriving from processes near kz = pi. These states exhibit a tendency for an enhanced anisotropy on the hole sheets and a reduced anisotropy on the electron sheets near the top of the BZ.

Effects of interfacial couplings on charge transport properties of DNA molecule

Using the three-dimensional tight-binding model and the matrix transfer method， effects of interfacial couplings on the charge transport properties of DNA molecule have been studied. The results indicate that when the interfacial couplings are ideal， both transmission coefficient and localization length of electrons are larger， the molecule shows higher conductivity， while the case is the contrary when the interfacial couplings are unideal. When the molecule and the metallic electrodes couple ideally， through voltage-current characteristic， it is found that the onset voltage of poly(dG)-poly(dC) DNA is lower than that for the poly(dA)-poly(dT) counterpart， and the current of the former is larger than that of the latter under the same bias voltage， so the conductivity of poly(dG)-poly(dC) DNA is higher than that of the poly(dA)-poly(dT) counterpart.

Ab initiocalculations ofHc2in type-II superconductors: Basic formalism and model calculations

Detailed Fermi-surface structures are essential to describe the upper critical field ${H}_{c2}$ in type-II superconductors, as first noticed by and Hohenberg and Werthamer [Phys. Rev. 153, 493 (1967)] and shown explicitly by Butler for high-purity cubic Niobium [Phys. Rev. Lett. 44, 1516 (1980)]. We derive an ${H}_{c2}$ equation for classic type-II superconductors that is applicable to systems with anisotropic Fermi surfaces and/or energy gaps under arbitrary field directions. It can be solved efficiently by using Fermi surfaces from ab initio electronic-structure calculations. Thus, it is expected to enhance our quantitative understanding on ${H}_{c2}$. Based on the formalism, we calculate ${H}_{c2}$ curves for Fermi surfaces of a three-dimensional tight-binding model with cubic symmetry, an isotropic gap, and no impurity scatterings. It is found that, as the Fermi surface approaches to the Brillouin zone boundary, the reduced critical field $h*(T∕{T}_{c})$, which is normalized by the initial slope at ${T}_{c}$, is enhanced significantly over the curve for the spherical Fermi surface with a marked upward curvature. Thus, the Fermi-surface anisotropy can be a main source of the upward curvature in ${H}_{c2}$ near ${T}_{c}$.

Electron-Phonon Scattering in Very High Electric Fields

ABSTRACTLarge-bandgap materials can support very high electric fields (>lMV/cm) without breaking down. The possibility then exists for an electron in a conduction band to become quasi-localized in Wannier-Stark states, a possibility that depends on the scattering rate being less than the Bloch oscillation frequency. If this condition is met the scattering rate itself is affected and the description of transport must be changed from the usual model in which the electron is assumed to be virtually free. Here, we examine the feasibility of obtaining this condition in GaN using a simple three-dimensional tight-binding model for the bandstructure and taking the dominant scattering mechanism to be the polar and non-polar interaction with optical phonons and short-wavelength acoustic phonons.

Stochastic resonances and the mobility edge in a three-dimensional tight-binding Anderson model.

We carry out a numerical study of the transmittance in a three-dimensional disordered Anderson model and study the weakly localized regime in the vicinity of the mobility edge, by the vector-recursion method of Godin and Haydock. This regime is straddled by stochastic resonant states and characterized by negative magnetoresistance. These stochastic resonances are very different in character to the strong fluctuations in the extended regime which arise due to lead-sample mismatch at the boundary.

A three-dimensional tight-binding model for trans-polyacetylene

We develop a three-dimensional (3-D) generalization of the one-dimensional (1-D), tight-binding Su-Schrieffer-Heeger (SSH) model for trans-(CH) x . Importantly, the model faithfully reflects the 3-D character of the band-edges state as found in ab initio Local-Density, Approximation (LDA) calculations but remains simple enough to be analytically solvable for the dimerized ground state. We examine the density of states and the optical absorption predicted within this model, paying special attention to the roles of the transverse coupling and the polarization of the probing field.

Universal behavior near the band edges for disordered systems: Numerical and coherent-potential-approximation studies.

The integrated densities of states (DOS) of one-, two-, and three-dimensional tight-binding models with diagonal and off-diagonal disorder are calculated numerically. Our results for the diagonal-disorder case confirm the expected universal behavior of the DOS, particularly near the band edges. The simple exponential behavior of the DOS is clearly displayed in the three-dimensional results. The off-diagonal-disorder case follows a universal behavior too, which agrees reasonably well with the coherent-potential-approximation (CPA) results. Our results are compared with the various phenomenological theories, with the CPA conclusions, and with previous numerical results.