Devanagari

These tables are designed for use by teachers and learners of Devanagari, and may be freely incorporated into course materials, printed for reference, or read online. Please acknowledge HUF! Many thanks to our calligraphers, Aruna Kharod and Bipul Pandey.Asian Studie

Power Series Correction to Single Particle Electron Green's Function: Application to 1D Holstein Chain

Electrons in materials undergo numerous complex interactions among themselves, the external fields, as well as the constituent atomic lattice. The strength of such many-body interactions depends on various factors such as the electronic configuration of the host material, the presence of doping and defects, spins of carrier and lattice elements, etc. In the thermodynamic limit, these interactions are often treated as bosons that interact with the electrons in the system and manifest as side bands (replicas or satellites) in the electronic band structure seeping spectral weight and renormalizing the band structure obtained from purely electronic calculations. In ab-initio calculations, when the strength of such electron-boson interaction is weak, it is not only justified to neglect these interactions completely but also pragmatic for reasons ranging from tractability to associated computational cost. This is because the effect of electron-boson interaction is minute compared to the electronic energy scale of the problem. However, in many systems, especially organic semiconducting materials, the bosonic vibrations (stretching modes) of the molecule are strongly coupled with the electron. Furthermore, the bosonic energy scale is comparable to the electronic energy scale in these problems. Hence, neglecting the effect of electron-boson interactions in electronic spectra in such systems is myopic at best and catastrophic at worst. In the context of a single electron two orbital Holstein system coupled to dispersionless bosons, we develop a general method to correct single-particle Green’s function and electronic spectral function using an integral power series correction (iPSC) scheme. We then outline the derivations of various flavors of cumulant approximation through the iPSC scheme and explain the assumptions and approximations behind them. Finally, we compute and compare iPSC spectral function with cumulant and exact diagonalized spectral functions and elucidate three regimes of this problem - two that cumulant explains and one where cumulant fails. We find that the exact and the iPSC spectral functions match within spectral broadening across all three regimes. In order to scale our method to large systems, we then develop an ODE-based Power series correction(dPSC) formalism that goes beyond the cumulant approximation. We implement it to a 1D Holstein chain for a wide range of coupling strengths in a scalable and inexpensive fashion at both zero and finite temperatures. We show that this first differential formalism of the power series is qualitatively and quantitatively in excellent agreement with exact diagonalization results on the 1D Holstein chain with dispersive bosons for a large range of electron-boson coupling strength. We also investigate carrier mass growth rate and carrier energy displacement across a wide range of coupling strengths. We also present a faster second differential formalism which is very much similar to self-consistent cumulant formalism. We show the regime where this method is applicable and where it diverges. Finally, we present a heuristic argument that predicts most of the rich satellite structure without explicit calculation

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Going beyond the Cumulant Approximation:Power Series Correction to the Single-Particle Green's Function in the Holstein System

In the context of a single-electron two orbital Holstein system coupled to dispersionless bosons, we develop a general method to correct the single-particle Green's function using a power series correction (PSC) scheme. We outline the derivations of various flavors of cumulant approximation through the PSC scheme explaining the assumptions and approximations behind them. Finally, we compare the PSC spectral function with cumulant and exact diagonalized spectral functions and elucidate three regimes of this problem - two where the cumulant explains and one where the cumulant fails. We find that the exact and the PSC spectral functions match within spectral broadening across all three regimes.</p

Going beyond the Cumulant Approximation:Power Series Correction to the Single-Particle Green's Function in the Holstein System

In the context of a single-electron two orbital Holstein system coupled to dispersionless bosons, we develop a general method to correct the single-particle Green's function using a power series correction (PSC) scheme. We outline the derivations of various flavors of cumulant approximation through the PSC scheme explaining the assumptions and approximations behind them. Finally, we compare the PSC spectral function with cumulant and exact diagonalized spectral functions and elucidate three regimes of this problem - two where the cumulant explains and one where the cumulant fails. We find that the exact and the PSC spectral functions match within spectral broadening across all three regimes.</p

Site substitution in GdMnO3: Effects on structural, electronic, and magnetic properties

We report on detailed structural, electronic, and magnetic studies of GdMn1-xCrxO3 for Cr doping levels; x = 0 &lt;= x &lt;= 1. X-ray diffraction studies suggest that GdMn0.5Cr0.5O3 has a monoclinic P2(1)/b structure with alternate arrangements of Mn and Cr atoms along the [001] direction. In the solid solutions, the Jahn-Teller distortion associated with Mn3+ ions gives rise to major changes in the be-plane sublattice and also an effective orbital ordering in the ab plane, which persist up to compositions x similar to 0.35. These distinct features in the lattice and orbital degrees of freedom are also correlated with be-plane anisotropy of the local Gd environment. A gradual evolution of electronic states with doping is also clearly seen in O K-edge x-ray absorption spectra. Evidence of magnetization reversal in field-cooled-cooling mode for x &gt;= 0.35 coinciding with the Jahn-Teller crossover suggests a close correlation between magnetic interaction and structural distortion. These observations indicate a strong entanglement between lattice, spin, electronic, and orbital degrees of freedom. The nonmonotonic variation of remnant magnetization can be explained by doping-induced modification of magnetic interactions. Density-functional-theory calculations are consistent with layer-by-layer-type arrangements of Cr ions and Mn ions with ferromagnetic (antiferomagnetic) coupling between Mn (Cr) ions for intermediate compounds (x = 0.5). For x = 0.25 compositions, we found alternate layers of Mn and mixed Mn-Cr atoms stacked along the c axis with intralayer ferromagnetic coupling and interlayer antiferromagnetic coupling. For x = 0.75 compositions, there exists strong antiferomagnetic coupling between half-filled t(2g) orbitals of in-plane Cr ions along with a feromagnetic Mn-Cr coupling