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Register a new userSpin-Phonon Coupling in the Single-Layer Extended t-J Model
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We consider the implications of spin-phonon coupling within the slave-boson, mean-field treatment of the extended t-J model of a high-temperature superconductor. In bilayer cuprates such as YBaCuO, where the $CuO_2$ plane is buckled, this interaction is linear in $O$ displacement along the c-axis, and the coupling constant is found to be large. The formation of a spin singlet causes additional contributions to the phonon self-energy, and we calculate from these the superconductive phonon anomalies. The magnitude and sign of the frequency shift and linewidth broadening for various mode symmetries correspond well with Raman and infra-red light scattering experiments, and with neutron scattering studies. In the t-J model, spin singlet formation and superconductivity do not coincide in the low-doping regime, giving rise to spin-gap features and a variety of temperature scales in the spin response observed by NMR and neutron investigations. Phonon anomalies in underdoped YBaCuO compounds indeed show evidence of spin-gap phenomena with the same characteristic temperature, suggesting that the theory may offer the possibility of a unified understanding of the anomalies in magnetic and lattice properties. While the origin of the superconducting interaction is electronic, this spin-phonon coupling affords the possibility of a small isotope effect, and our estimate is in good agreement with recent site-selective $O$-substitution experiments.
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The electron-phonon coupling strength in the spin-split valence band maximum of single-layer MoS$_2$ is studied using angle-resolved photoemission spectroscopy and density functional theory-based calculations. Values of the electron-phonon coupling parameter $lambda$ are obtained by measuring the linewidth of the spin-split bands as a function of temperature and fitting the data points using a Debye model. The experimental values of $lambda$ for the upper and lower spin-split bands at K are found to be 0.05 and 0.32, respectively, in excellent agreement with the calculated values for a free-standing single-layer MoS$_2$. The results are discussed in the context of spin and phase-space restricted scattering channels, as reported earlier for single-layer WS$_2$ on Au(111). The fact that the absolute valence band maximum in single-layer MoS$_2$ at K is almost degenerate with the local valence band maximum at $Gamma$ can potentially be used to tune the strength of the electron-phonon interaction in this material.
The absence of inversion symmetry leads to a strong spin-orbit splitting of the upper valence band of semiconducting single layer transition metal dichalchogenides such as MoS$_2$ or WS$_2$. This permits a direct comparison of the electron-phonon coupling strength in states that only differ by their spin. Here, the electron-phonon coupling in the valence band maximum of single-layer WS$_2$ is studied by first principles calculations and angle-resolved photoemission. The coupling strength is found to be drastically different for the two spin-split branches, with calculated values of $lambda_K=$0.0021 and 0.40 for the upper and lower spin-split valence band of the free-standing layer, respectively. This difference is somewhat reduced when including scattering processes involving the Au(111) substrate present in the experiment and the experimental results confirm the strongly branch-dependent coupling strength.
A relaxation-function theory for the dynamic spin susceptibility in the $t$--$J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperaturs. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on La_{2-delta}Sr_delta)CuO_4. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its (omega/T) scaling behavior are calculated in a reasonable agreement with experimental and ED data.
Dynamic spin susceptibility is calculated for the t-J model in the paramagnetic phase by applying the memory function method in terms of the Hubbard operators. A self-consistent system of equations for the memory function is obtained within the mode coupling approximation. Both itinerant hole excitations and localized spin fluctuations give contributions to the memory function. Spin dynamics have a diffusive character in the hydrodynamic limit; spin-wave-like excitations are regained in the high-frequency region.
We consider a bilayer version of the extended $t$-$J$ model, with a view to computing the form of certain experimentally observable properties. Using the slave-boson decomposition, we show at the mean-field level that in the bilayer system the existence of in-plane $d$-wave singlet pairing excludes any interplane singlet order for reasonable values of the interplane superexchange parameter. Restricting the analysis to the regime of no interplane singlet pairing, we deduce parameter sets reproducing the Fermi surfaces of YBCO- and BSCCO-like bilayer systems. From these we calculate the form of the dynamic susceptibility $chi( {bf q}, omega )$ in both systems, and of the anomalies in frequency and linewidth of selected phonon modes in YBCO. We compare the results with experiment, and discuss the features which differ from the single-layer case.
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