Three-band Tight-binding Model Research Articles

Electronic structures and quantum capacitance of twisted bilayer graphene with defects based on three-band tight-binding model.

Twisted bilayer graphene (tBLG) with C vacancies would greatly improve the density of states (DOS) around the Fermi level (EF) and quantum capacitance; however, the single-band tight-binding model only considering pz orbitals cannot accurately capture the low-energy physics of tBLG with C vacancies. In this work, a three-band tight-binding model containing three p orbitals of C atoms is proposed to explore the modulation mechanism of C vacancies on the DOS and quantum capacitance of tBLG. We first obtain the hopping integral parameters of the three-band tight-binding model, and then explore the electronic structures and the quantum capacitance of tBLG at a twisting angle of θ = 1.47° under different C vacancy concentrations. The impurity states contributed by C atoms with dangling bonds located around the EF and the interlayer hopping interaction could induce band splitting of the impurity states. Therefore, compared with the quantum capacitance of pristine tBLG (∼18.82 μF cm-2) at zero bias, the quantum capacitance is improved to ∼172.76 μF cm-2 at zero bias, and the working window with relatively large quantum capacitance in the low-voltage range is broadened in tBLG with C vacancies due to the enhanced DOS around the EF. Moreover, the quantum capacitance of tBLG is further increased at zero bias with an increase of the C vacancy concentration induced by more impurity states. These findings not only provide a suitable multi-band tight-binding model to describe tBLG with C vacancies but also offer theoretical insight for designing electrode candidates for low-power consumption devices with improved quantum capacitance.

Calculation of shift current tensors in two-dimensional transition metal dichalcogenides

We investigate the shift current induced by optical excitation in two-dimensional transition metal dichalcogenides. Our approach is based on a second-order perturbation expansion of the semiconductor Bloch equations which are formulated in the basis of a three-band tight-binding model. From that, shift current tensors have been calculated for several different materials and their dependence on photon energy has been investigated and discussed.

Disorder effects on triple-point fermions

The stability of three-dimensional relativistic semimetals to disorder has recently attracted great attention, but the effect of disorder remains elusive for multifold fermions, that are not present in the framework of quantum field theory. In this paper, we investigate one type of multifold fermions, so-called triple-point fermions (TPFs), which have pseudospin-1 degrees of freedom and topological charges $\pm2$. Specifically, we consider the effect of disorder on a minimal, three-band tight-binding model, which realizes the minimal number of two TPFs. The numerically-obtained, disorder-averaged density of states suggests that, within a finite energy window, the TPFs are robust up to a critical strength of disorder. In the strong disorder regime, the inter-TPF scattering is the main mechanism for destroying a single TPF. Moreover, we study the effects of disorder on the distribution of Fermi arcs and surface Berry curvature. We demonstrate that the Fermi arc retains its sharpness at weak disorder, but gradually dissolves into the metallic bulk for stronger disorder. In clean limit, the surface Berry curvature exhibits a bipolar configuration in the surface Brillouin zone. With increasing disorder, the positive and negative surface Berry curvature start to merge at the nearby momenta where the Fermi arcs penetrate into bulk.

Edge magnetism in transition metal dichalcogenide nanoribbons: Mean field theory and determinant quantum Monte Carlo

Edge magnetism in zigzag transition metal dichalcogenide nanoribbons is studied using a three-band tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic gapped phase at the same edge filling as mean field theory, despite being sign-problematic for other fillings. The obtained results point to edge filling as yet another key ingredient to understand the observed magnetism in nanosheets. Moreover, the filling dependent edge magnetism gives rise to spin-polarized edge currents in zigzag nanoribbons which could be tuned through a back gate voltage, with possible applications to spintronics.

Electronic properties and quasiparticle model of monolayer MoSi2N4

By a combined study with first-principles calculations and symmetry analysis, we theoretically investigate the electronic properties of monolayer MoSi$_2$N$_4$. While the spin-orbital coupling results in bands splitting, the horizontal mirror symmetry locks the spin polarization along z-direction. In addition, a three-band tight-binding model is constructed to describe the low-energy quasi-particle states of monolayer MoSi$_2$N$_4$, which can be generalized to strained MoSi$_2$N$_4$ and its derivatives. The calculations using the tight-binding model show an undamped $\sqrt{q}$-dependent plasmon mode that agrees well with the results of first-principles calculations. Our model can be extended to be suitable for future theoretical and numerical studies of low-energy properties in MoSi$_2$N$_4$ family materials. Furthermore, the study of electronic properties of monolayer MoSi$_2$N$_4$ paves a way for its applications in spintronics and plasmonics.

Spin polarization in lateral two-dimensional heterostructures

In this work, we study the spin polarization in the MoS(Se)2–WS(Se)2 transition metal dichalcogenide heterostructures by using the non-equilibrium Green’s function method and a three-band tight-binding model near the edges of the first Brillouin zone. Although it has been shown that the structures have no significant spin polarization in a specific range of energy of electrons, by applying a transverse electric field in the sheet of the metal atoms, shedding light on the sample, and under a small bias voltage, a significant spin polarization in the structure could be created. Besides, by applying a suitable bias voltage between leads and applying the electric field, a noticeable spin polarization can be found even without shedding the light on the heterostructures.

Critical temperature Tc and Pauli limited critical field of Sr2RuO4 : Uniaxial strain dependence

Variations of critical temperature $T_c$ and in-plane critical field $H_{c2}$ of $\text{Sr}_2\text{Ru}\text{O}_4$ under uniaxial stress have recently been reported. We compare the strain dependence of $T_c$ and $H_{c2}$ in various pairing channels ($d$-wave, extended s-wave and $p$-wave) with the experimental observations, by studying a three-band tight-binding model that includes effects of spin-orbit and Zeeman couplings and a separable pairing interaction. Our study helps narrow down the possibility of pairing channels. The importance of the multi-band nature of $\text{Sr}_2\text{Ru}\text{O}_4$ is also highlighted.

Superconducting dome driven by intervalley phonon scattering in monolayer MoS2

We combine first-principles calculations, a three-band tight-binding model, and Bardeen–Cooper–Schrieffer theory to explore the physical mechanism for a dome-shaped dependence of superconducting transition temperature of monolayer MoS2 on electron doping concentration, which has been observed experimentally (2012 Science 338 1193). We find that in the process of doping more electrons contribute to superconducting pairing, but above some doping value the effective attractive interaction decreases so greatly that it starts to reduce the pairing strength, forming a superconducting dome. Therefore, the dome behavior can be attributed to the competition between the growing Fermi pocket (corresponding to an increase of the number of intervalley phonon scatterings) and the screened intervalley phonon scattering (corresponding to a decrease of scattering probability).

Optical injection of spin current into a zigzag nanoribbon of monolayer MoS2 with antiferromagnetic Kekule distortion

The Kekule pattern of the (anti)ferromagnetic exchange field on monolayer MoS2 can be induced by proximity to the (111) surface of BiFeO3 on both sides. The three-band tight binding model of the MoS2 layer with Kekule patterned exchange field is applied to describe the heterostructures. The tight binding model is justified by the first principle calculations. The magnetization orientations of the substrates control the pattern of the exchange field, which then switches the band structures of the lowest zigzag edge states between being metallic and insulating. The lowest four zigzag edge bands provide conducting channels with a spin-polarized current. Optical excitation of carriers in these bands generates sizable spin and charge currents, which are theoretically modeled by the perturbation solution of the semiconductor Bloch equation. The injected spin currents have multiple resonant peaks at a few frequencies, which can be switched off by rotating the magnetization orientations of the substrates.

Magnetotransport in a zigzag monolayer MoS2 nanoribbon with ferromagnetic electrodes

In this research, using the three-band tight-binding model combined with a non-equilibrium Green's function technique, spin-dependent electron transport was investigated in the quantum structure of zigzag monolayer molybdenum disulfide with ferromagnetic electrodes. It was shown that in parallel configurations, the conductance exhibited a quantized oscillating phenomenon, while in the antiparallel configurations with increasing magnetization, the conductance showed a zero platform in a large-energy region. We observed a giant magnetoresistance effect. Moreover, the length of the central part of the structure had a certain influence on the magnetoresistance ratio. It was found that as the length of the middle region increased, the magnetoresistance ratio decreased gradually. The results not only extended our understanding of novel electronic structures of monolayer MoS2 but also provided the possibility for the technological applications of spintronics device.

Spin-dependent transport in Normal/Ferromagnetic/Normal monolayer zigzag molybdenum disulfide nanoribbon junction

In this paper, with the three-band tight-binding model, we investigate spin transport in Normal/Ferromagnetic/Normal monolayer zigzag molybdenum disulfide nanoribbon junction with double electric barriers using Green’s function technique. We discuss the influence of the height of the double electric barrier on spin transport. The results demonstrate that spin conductance has relatively large dependence on electric field modulation. We can obtain large spin polarization in low energy region which may be applied as a spin filter. In addition, we study the effect of magnetic field, and we find that we can obtain a larger spin polarization area which may provide a theoretical basis for spin filter application.

Magnetization-direction tunable nodal-line and Weyl phases

We propose a spinless symmetry-based three-band tight-binding model with the coexistence of nodal-line and Weyl points, after considering spin-orbital coupling and different magnetization directions. It is confirmed that the number of Weyl points and nodal lines can be tuned by the magnetization direction. The combination of time-reversal symmetry and mirror reflection symmetry plays a crucial role in protecting the degeneracy of nodal lines. Moreover, we put forward a different class of materials ${\mathrm{C}}_{4}\mathrm{Cr}{X}_{3}$ ($X=\text{Ge}$ and Si) which host such a nontrivial semimetallic phase.

Spin Transport in Electric-Barrier-Modulated Ferromagnetic/Normal/Ferromagnetic Monolayer Zigzag MoS2 Nanoribbon Junction

In this paper, with the three-band tight-binding model and non-equilibrium Green’s function technique, we investigate spin transport in electric-barrier-modulated Ferromagnetic/Normal/Ferromagnetic (F/N/F) monolayer (ML) zigzag MoS2 nanoribbon junction. The results demonstrate that once the double electric barriers structure emerges, the oscillations of spin conductances become violent, especially for spin-down conductance, the numbers of resonant peaks increase obviously, thus we can obtain [Formula: see text] spin polarization in the low energy region. It is also found that with the intensity of the exchange field enhancement, the resonant peaks of spin-up and spin-down conductances move in the opposite direction in a certain energy region. As a consequence, the spin-down conductance can be filtered out completely. The findings here indicate that the present structure may be considered as a good candidate for spin filter.

Strain-induced topological phase transition at zigzag edges of monolayer transition-metal dichalcogenides

The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced superconductivity is studied using a minimal 3-band tight-binding model. The unstrained system shows a topological phase with Majorana zero modes localized at the boundaries of the one-dimensional (1D) zigzag edges. By direct inspection of the spectrum and wave functions we examine the evolution of the topological phase as an in-plane, uniaxial deformation is imposed. It is found that strain shifts the energy of 1D edge states, thus causing a topological phase transition which eliminates the Majorana modes. For realistic parameter values, we show that the effect of strain can be changed from completely destructive -- in which case a small built in strain is enough to destroy the topological phase -- to a situation where strain becomes an effective tuning parameter which can be used to manipulate Majorana zero modes. These two regimes are accessible by increasing the value of the applied Zeeman field within realistic values. We also study how strain effects are affected by the chemical potential, showing in particular how unwanted effects can be minimized. Finally, as a cross-check of the obtained results, we reveal the connection between 1D Majorana zero modes in the zigzag edge and the multi-band Berry phase, which serves as a topological invariant of this system.

Topological aspect and transport property in multi-band spin-triplet chiral p-wave superconductor Sr2RuO4

Considering the superconductor Sr2RuO4, we analyze a three-band tight-binding model with one hole-like and two electron-like Fermi surfaces corresponding to the α, β and γ bands of Sr2RuO4 by means of a self-consistent Bogoliubov-de Gennes approach for ribbonshaped system to investigate topological properties and edge states. In the superconducting phase two types of gapless edge states can be identified, one of which displays an almost flat dispersion at zero energy, while the other, originating from the γ band, has a linear dispersion and constitutes a genuine chiral edge states. Not only a charge current appears at the edges but also a spin current due to the multi-band effect in the superconducting phase. In particular, the chiral edge state from the γ band is closely tied to topological properties, and the chiral p-wave superconducting states are characterized by an integer topological number, the so-called Chern number. We show that the γ band is close to a Lifshitz transition. Since the sign of the Chern number may be very sensitive to the surface condition, we consider the effect of the surface reconstruction observed in Sr2RuO4 on the topological property and show the possibility of the hole-like Fermi surface at the surface.

Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $MX_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contributed by the $d_{z^{2}}$, $d_{xy}$, and $d_{x^{2}-y^{2}}$ orbitals of $M$ atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all $MX_2$ monolayers. The TB model involving only the nearest-neighbor $M$-$M$ hoppings is sufficient to capture the band-edge properties in the $\pm K$ valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor $M$-$M$ hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions of $M$ atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between Mo$X_{2}$ and W$X_{2}$. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in $MX_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.

Anisotropic intrinsic anomalous Hall effect in ordered3dPt alloys

By performing first-principles calculations, we investigate the intrinsic anomalous Hall conductivity (AHC) and its anisotropy in ordered L1${}_{0}$ FePt, CoPt, and NiPt ferromagnets and their intermediate alloys. We demonstrate that the AHC in this family of compounds depends strongly on the direction of the magnetization $\mathbf{M}$ in the crystal. We predict that such pronounced orientational dependence in combination with the general decreasing trend of the AHC when going from FePt to NiPt leads to a sign change of the AHC upon rotating the magnetization direction in the crystal of CoPt alloy. We also suggest that, for a range of concentration $x$ in Co${}_{x}$Ni${}_{1\ensuremath{-}x}$Pt and Fe${}_{x}$Co${}_{1\ensuremath{-}x}$Pt alloys, it is possible to achieve a complete quenching of the anomalous Hall current for a certain direction of the magnetization in the crystal. By analyzing the spin-resolved AHC in $3d$Pt alloys, we endeavor to relate the overall trend of the AHC in these compounds to the changes in their densities of $d$ states around the Fermi energy upon varying the atomic number. Moreover, we show the generality of the phenomenon of anisotropic anomalous Hall effect by demonstrating its occurrence within the three-band tight-binding model.

Revealing exciton-exciton couplings in semiconductors using multidimensional four-wave mixing signals

We show that the femtosecond four-wave mixing signal from GaAs quantum wells generated in the phase-matching direction ${\mathbf{k}}_{1}+{\mathbf{k}}_{2}\ensuremath{-}{\mathbf{k}}_{3}$ can fully resolve the pure heavy-hole, pure light-hole, and the mixed two excitons by directly observing double quantum coherences. Time-dependent Hartree-Fock contributions for different types of two excitons may be completely separated from higher-order Coulomb correlations by specific pulse polarization configurations. Simulations performed on a one-dimensional three-band tight-binding model for a GaAs quantum well are analyzed using double-sided Feynman diagrams which reveal the Liouville space pathways contributing to the various peaks.