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Register a new userModified group projectors: tight binding method
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Modified group projector technique for induced representations is a powerful tool for calculation and symmetry quantum numbers assignation of a tight binding Hamiltonian energy bands of crystals. Namely, the induced type structure of such a Hamiltonian enables efficient application of the procedure: only the interior representations of the orbit stabilizers are to be considered. Then the generalized Bloch eigen functions are obtained naturally by the expansion to the whole state space. The method is applied to the electronic pi-bands of the single wall carbon nanotubes: together with dispersion relations, their complete symmetry assignation by the full symmetry (line) groups and the corresponding symmetry-adapted eigen function are found.
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We have performed systematic tight-binding (TB) analyses of the angle-resolved photoemission spectroscopy (ARPES) spectra of transition-metal (TM) oxides A$M$O$_3$ ($M=$ Ti, V, Mn, and Fe) with the perovskite-type structure and compared the obtained parameters with those obtained from configuration-interaction (CI) cluster-model analyses of photoemission spectra. The values of $epsilon_d-epsilon_p$ from ARPES are found to be similar to the charge-transfer energy $Delta$ from O $2p$ orbitals to empty TM 3d orbitals and much larger than $Delta-U/2$ ($U$: on-site Coulomb energy) expected for Mott-Hubbard-type compounds including SrVO$_3$. $epsilon_d-epsilon_p$ values from {it ab initio} band-structure calculations show similar behaviors to those from ARPES. The values of the $p-d$ transfer integrals to describe the global electronic structure are found to be similar in all the estimates, whereas additional narrowing beyond the TB description occurs in the ARPES spectra of the $d$ band.
Motivated by recent nuclear magnetic resonance (NMR) experiments, we present a microscopic sp3 tight-binding model calculation of the NMR shifts in bulk Bi2Se3, and Bi2Te3. We compute the contact, dipolar, orbital and core polarization contributions to the carrier-density-dependent part of the NMR shifts in Bi209, Te125 and Se77. The spin-orbit coupling and the layered crystal structure result in a contact Knight shift with strong uniaxial anisotropy. Likewise, because of spin-orbit coupling, dipolar interactions make a significant contribution to the isotropic part of the NMR shift. The contact interaction dominates the isotropic Knight shift in Bi209 NMR, even though the electronic states at the Fermi level have a rather weak s-orbital character. In contrast, the contribution from the contact hyperfine interaction to the NMR shift of Se77 and Te125 is weak compared to the dipolar and orbital shifts therein. In all cases, the orbital shift is at least comparable to the contact and dipolar shifts, while the shift due to core polarization is subdominant (except for Te nuclei located at the inversion centers). By artificially varying the strength of spin-orbit coupling, we evaluate the evolution of the NMR shift across a band inversion but find no clear signature of the topological transition.
We propose a simple and effective approach to construct the empirical tight-binding parameters of ternary alloys in the virtual crystal approximation. This combines a new, compact formulation of the strain parameters and a linear interpolation of the hamiltonians of binary materials strained to the alloy equilibrium lattice parameter. We show that it is possible to obtain a perfect description of the bandgap bowing of ternary alloys in the InGaAsSb family of materials. Furthermore, this approach is in a good agreement with supercell calculations using the same set of parameters. This scheme opens a way for atomistic modeling of alloy-based opto-electronic devices without extensive supercell calculations.
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.
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
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