arXiv subjects

Sohan Lal

Publications and source records attributed to Sohan Lal.

12 recordsLinked to original sources

arXiv2023

Computational analysis of NM-polynomial based topological indices and graph-entropies of carbon nanotube Y-junctions

Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical molecule. The entropy of a graph is a topological descriptor that serves to characterize the complexity of the underlying molecular graph. The concept of entropy is a physical property of a thermodynamic system. Graph entropies are the essential thermophysical quantities defined for various graph invariants and are applied to measure the heterogeneity and relative stabilities of molecules. In this paper, several neighborhood degree sum-based topological indices including graph-based entropies of carbon nanotube Y-junction graphs are computed.

cond-mat.mes-hall↗

arXiv2022

On k-distance degree based topological indices of benzenoid systems

Topological indices are graph invariants numeric quantities, which are utilized by researchers to analyze a variety of physiochemical aspects of molecules. The goal of developing topological indices is to give each chemical structure a numerical value while maintaining the highest level of differentiation. Using these indices, the classification of various structures, and their physiochemical and biological properties can be predicted. In this paper, the leap and leap hyper Zagreb indices, as well as their polynomials for a zigzag benzenoid system $Z_{p}$ and a rhombic benzenoid system $R_{p}$ are determined. In addition, new $k$-distance degree-based topological indices such as leap-Somber index, hyper leap forgotten index, leap $Y$ index, and leap $Y$ coindex are also computed for the molecular graphs of $Z_p$ and $R_p$. Furthermore, their numerical computation and discussion are performed to determine the significance of their physiochemical properties.

math.CO↗

arXiv2022

Edge Resolvability of Crystal Cubic Carbon Structure

Chemical graph theory is commonly used to analyse and comprehend chemical structures and networks, as well as their features. The resolvability parameters for graph $G$= $(V,E)$ are a relatively new advanced field in which the complete structure is built so that each vertex (atom) or edge (bond) represents a distinct position. In this article, we study the resolvability parameters i.e., edge resolvability of chemical graph of crystal structure of cubic carbon $CCS(n)$

math.CO↗

arXiv2017

Studying the occupied and unoccupied electronic structure of LaCoO$_{3}$ by using DFT+embedded DMFT method with the calculated value of $\textit{U}$

In this work, we present a systematic study of the occupied and unoccupied electronic states of LaCoO$_{3}$ compound using DFT, DFT+$\textit{U}$ and DFT+embedded DMFT methods. The value of $\textit{U}$ used here is evaluated by using constrained DFT method and found to be $ \backsim $ 6.9 eV. It is found that DFT result has limitations with energy positions of PDOS peaks due to its inability of creating a hard gap although the DOS distribution appears to be fine with experimental attributes. The calculated value of $\textit{U}$ is not an appropriate value for carrying out DFT+$\textit{U}$ calculations as it has created an insulating gap of $ \backsim $ 1.8 eV with limitations in redistribution of DOS which is inconsistent with experimental spectral behaviour for the occupied states mainly. However, this value of $\textit{U}$ is found to be an appropriate one for DFT+embedded DMFT method which creates a gap of $\backsim $ 1.1 eV. The calculated PDOS of Co 3$\textit{d}$, La 5$\textit{d}$, La 4$\textit{f}$ and O 2$\textit{p}$ states are giving a remarkably good explanation for the occupied and unoccupied states of the experimental spectra in the energy range $\backsim $ -9.0 eV to $\backsim $ 12.0 eV.

cond-mat.str-el↗

arXiv2017

Studying the effect of different exchange correlation functionals on the structural and electronic properties of a half-Heusler NaAuS compound

Theoretically, NaAuS is predicted as topological insulator, while no detail electronic structure study has been done for this compound. Here, we report the structural and electronic properties of NaAuS by using LDA, PBEsol, PBE and revPBE exchange correlation functionals. The calculated values of equilibrium lattice constant for LDA, PBEsol, PBE and revPBE exchange correlation functionals are found to be $\sim$6.128 Å, $\sim$6.219 Å, $\sim$6.353 Å and $\sim$6.442 Å, respectively. The bulk modulus predicted by LDA, PBEsol, PBE and revPBE exchange correlation functionals is $\sim$66.6, $\sim$56.4, $\sim$46.5 and $\sim$39.3 GPa, respectively. Hence, the order of calculated values of bulk modulus is consistent with the order of calculated values of equilibrium lattice parameters for these exchange correlation functionals. The spread of total density of states below the Fermi level decreases as the exchange correlation functional changes from LDA to PBEsol to PBE to revPBE, which is also found to be consistent with the order of bulk modulus for these exchange correlation functionals. In presence of spin-orbit coupling, a direct band gap is observed in NaAuS compound, which is found to be $\sim$0.26, $\sim$0.25, $\sim$0.24 and $\sim$0.23 eV for LDA, PBEsol, PBE and revPBE exchange correlation functionals, respectively. Here, NaAuS is found to be topological insulator as it shows band inversion at $Γ$ point. The calculated values of band inversion strength for LDA (PBEsol) and PBE (revPBE) exchange correlation functionals are $\sim$1.58 eV ($\sim$1.57 eV) and $\sim$1.50 eV ($\sim$1.47 eV), respectively.

cond-mat.str-el↗

arXiv2017

Electronic structure study of vanadium spinels by using density functional theory and dynamical mean field theory

Theoretically, various physical properties of AV$_{2}$O$_{4}$ (A=Zn, Cd and Mg) spinels have been extensively studied for last 15 years. Besides of this, no systematic comparative study has been done for these compounds, where the material specific parameters are used. Here, we report the comparative electronic behaviour of these spinels by using a combination of density functional theory and dynamical mean-field theory, where the self-consistent calculated Coulomb interaction $U$ and Hund's coupling $J$ (determined by Yukawa screening $λ$) are used. The main features, such as insulating band gaps ($E_{g}$), degree of itinerancy of V 3$d$ electrons and position of lower Hubbard band are observed for these parameters in these spinels. The calculated values of $E_{g}$ for ZnV$_{2}$O$_{4}$, CdV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$ are found to be $\sim$0.9 eV, $\sim$0.95 eV and $\sim$1.15 eV, respectively, where the values of $E_{g}$ are close to experiment for ZnV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$. The position of lower Hubbard band are observed around $\sim$-1.05 eV, $\sim$-1.25 eV and $\sim$-1.15 eV for ZnV$_{2}$O$_{4}$, CdV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$, respectively, which are also in good agreement with the experimental data for ZnV$_{2}$O$_{4}$. The order of average impurity hybridization function of V site are found to be ZnV$_{2}$O$_{4}$$>$MgV$_{2}$O$_{4}$$>$CdV$_{2}$O$_{4}$. Hence, the degree of localization of V 3$d$ electrons is largest for CdV$_{2}$O$_{4}$ and smallest for ZnV$_{2}$O$_{4}$, which is in accordance with our earlier results. Hence, present work shows the importance of material specific parameters to understand the comparative electronic behaviour of these compounds.

cond-mat.str-el↗

arXiv2016

Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels

The inconsistency about the degree of geometrical frustration has been a long issue in AV$_{2}$O$_{4}$ (A $\equiv$ Zn, Cd and Mg) compounds, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. In the present study, we try to understand such inconsistency by using {\it ab initio} electronic structure calculations. The orbital degrees of freedom are found to play an important role in understanding the geometrically frustrated magnetic behaviour of these compounds. The inclusion of the orbital and spin angular momenta for calculating the frustration indices improves the understanding about the degree of geometrical frustration in these compounds. The calculated values of the frustration indices ($f$$_{\it J}$) are largest for MgV$_{2}$O$_{4}$ and smallest for CdV$_{2}$O$_{4}$ for 3.3$\leq$ $U \leq$5.3 eV. In this range of $U$, the calculated values of $Δ$M$_{2}$=M$_{\rm total}$-M$_{\rm exp}$ are largest for MgV$_{2}$O$_{4}$ and smallest for CdV$_{2}$O$_{4}$. Hence, the consistency about the degree of geometrical frustration is achieved. The absolute values of the nearest neighbour exchange coupling constant ({\it J$_{nn}$}) between V spins are found to be largest for MgV$_{2}$O$_{4}$ and smallest for CdV$_{2}$O$_{4}$, which indicate that the calculated absolute values of the Curie-Weiss temperature ($\varTheta$$_{CW}$)$_{\it J}$ are highest for MgV$_{2}$O$_{4}$ and smallest for CdV$_{2}$O$_{4}$ for 3.3$\leq$ $U \leq$5.3 eV. In this range of $U$, the magnetic transition temperature ($T$$_{N}$)$_{\it J}$ is found to be $\sim$150 K, $\sim$60 K and $\sim$22 K for MgV$_{2}$O$_{4}$, ZnV$_{2}$O$_{4}$ and CdV$_{2}$O$_{4}$, respectively, which shows that the order of ($T$$_{N}$)$_{\it J}$ is similar to that of ($T$$_{N}$)$_{\rm exp}$ for these compounds.

cond-mat.str-el↗

arXiv2016

Self-consistent evaluation of effective Coulomb interaction of V atom and its importance to understand the comparative electronic behaviour of vanadium spinels

In present work, we try to understand the importance of effective Coulomb interaction ($U_{ef}$) between localized electrons of V atom to understand the comparative electronic behaviour of AV$_{2}$O$_{4}$ (A=Zn, Cd and Mg) compounds. The suitable values of $d$-linearization energy ($E_{d}$) of impurity V atom for calculating the $U_{ef}$ for these compounds are found to be $\geq$44.89 eV above the Fermi level. Corresponding to these values of $E_{d}$, the self-consistently calculated values of effective $U_{LSDA}$ ($U_{PBEsol}$) for ZnV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$ and CdV$_{2}$O$_{4}$ are $\sim$5.73 ($\sim$5.92), $\sim$6.06 ($\sim$6.22) and $\sim$5.59 ($\sim$5.71) eV, respectively. The calculated values of $\frac{t}{U_{ef}}$ ($t$ is the transfer integral between neighbouring sites) increases with decreasing V-V distance from CdV$_{2}$O$_{4}$ to MgV$_{2}$O$_{4}$ to ZnV$_{2}$O$_{4}$ and are found to be consistent with experimentally reported band gap. The values of $\frac{t}{U_{ef}}$ for ZnV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$ and CdV$_{2}$O$_{4}$ are found to be $\sim$0.023, $\sim$0.020 and $\sim$0.018, respectively. Hence, CdV$_{2}$O$_{4}$ with small (large) $\frac{t}{U_{ef}}$ (experimental band gap) as compared to ZnV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$ is found to be in localized-electron regime, while ZnV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$ are intermediate between localized and an itinerant-electron regime. The calculated values of lattice parameters $a_{LSDS}$ ($a_{PBEsol}$) are found to be $\sim$1.7\%, $\sim$2.0\% and $\sim$2.4\% ($\sim$0.6\%, $\sim$0.7\% and $\sim$0.7\%) smaller than $a_{exp}$ for CdV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$ and ZnV$_{2}$O$_{4}$, respectively, which indicates that the PBEsol functional predicts the lattice parameters in good agreement with the experimental data.

cond-mat.str-el↗

arXiv2016

The role of ionic sizes in inducing the cubic to tetragonal distortion in AV$_{2}$O$_{4}$ and ACr$_{2}$O$_{4}$ (A=Zn, Mg and Cd) compounds

Cubic to tetragonal distortion in spinel compounds have been a contentious issue for last two decades. Different groups have proposed different mechanisms to understand such a distortion in these spinels, which are: (i) spin lattice coupling mechanism known as the spin driven Jahn-Teller (JT) effect, (ii) the strong relativistic spin-orbit coupling, a moderate JT distortion and weak V-V interactions and (iii) the JT effect. Now, in order to know the possible cause for such a distortion, we have avoided these complexities (various interactions among spin, electronic, orbital and lattice degrees of freedom) by carrying out spin unpolarized calculations. The calculated values of bulk moduli for ZnV$_{2}$O$_{4}$ (ZnCr$_{2}$O$_{4}$), MgV$_{2}$O$_{4}$ (MgCr$_{2}$O$_{4}$) and CdV$_{2}$O$_{4}$ (CdCr$_{2}$O$_{4}$) are found to be $\sim$289 ($\sim$254), $\sim$244 ($\sim$243) and $\sim$230 ($\sim$233) GPa, respectively. For vanadates and chromates, the order of calculated values of lattice parameter $a$ are found to CdV$_{2}$O$_{4}$$>$MgV$_{2}$O$_{4}$$>$ZnV$_{2}$O$_{4}$ and CdCr$_{2}$O$_{4}$$>$MgCr$_{2}$O$_{4}$$>$ZnCr$_{2}$O$_{4}$, respectively and are consistent with the experimental results. The calculated values of cubic to tetragonal distortion (c/a), with c/a$<$1 for ZnV$_{2}$O$_{4}$ (ZnCr$_{2}$O$_{4}$), MgV$_{2}$O$_{4}$ (MgCr$_{2}$O$_{4}$) and CdV$_{2}$O$_{4}$ (CdCr$_{2}$O$_{4}$) are $\sim$0.996 ($\sim$0.997), $\sim$0.995 ($\sim$0.994) and $\sim$0.997 ($\sim$0.998), respectively. These values are in good agreement with the experimental data for ZnV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$, ZnCr$_{2}$O$_{4}$ and MgCr$_{2}$O$_{4}$ compounds. The present study clearly shows the role of ionic sizes in inducing the cubic to tetragonal distortion in these spinels. These mechanisms also appear to be responsible for deciding the other physical properties of these compounds.

cond-mat.str-el↗

arXiv2016

Constrained DFT+$U$ approach for understanding the magnetic behaviour of ACr$_{2}$O$_{4}$ (A=Zn, Mg, Cd and Hg) compounds

In this work, we try to understand the inconsistency reported by [Yaresko, Phys. Rev. B. {\bf 77}, 115106 (2008)] in the theoretically estimated nature and the variation of magnitude of nearest neighbour exchange coupling constant ($\arrowvert${\it J$_{1}$}$\arrowvert$) with increasing $U$ in ACr$_{2}$O$_{4}$ (A=Zn, Cd, Mg and Hg) compounds by using density functional theory. In unconstrained calculations, the nature and variation of $\arrowvert${\it J$_{1}$}$\arrowvert$ as a function of $U$ in the present study are not consistent with the experimental data and not according to the relation, {\it J$_{1}$}$\propto$$\frac{t^{2}}{U}$ especially for CdCr$_{2}$O$_{4}$ and HgCr$_{2}$O$_{4}$ for $U >$3 eV and U=2-6 eV, respectively. Such an inconsistent behavior of $\arrowvert${\it J$_{1}$}$\arrowvert$ is almost similar to that of Yaresko for these two compounds for $U$=2-4 eV. For ZnCr$_{2}$O$_{4}$ and MgCr$_{2}$O$_{4}$, the nature and the variation of $\arrowvert${\it J$_{1}$}$\arrowvert$ in the present work are in accordance with the experimental data and above mentioned relation for $U$=2-6 eV and are similar to that of Yaresko for ZnCr$_{2}$O$_{4}$ for $U$=2-4 eV. However, in constrained calculations the nature and variation of $\arrowvert${\it J$_{1}$}$_{c}$$\arrowvert$ in the present work are according to experimental data and above above mentioned relation for all four compounds. Hence, the present study shows the importance of constrained calculations in understanding the magnetic behaviour of these spinels. The values of magnitude of Curie-Weiss temperature [$\arrowvert$($\varTheta$$_{CW}$)$_{c}$$\arrowvert$] for ZnCr$_{2}$O$_{4}$$>$MgCr$_{2}$O$_{4}$$>$CdCr$_{2}$O$_{4}$$>$HgCr$_{2}$O$_{4}$ for $U$=2-5 eV, which are according to the order of experimentally observed values for these spinels.

cond-mat.str-el↗

arXiv2016

Density matrix approach to the orbital ordering in the spinel vanadates: A case study

In this work we apply the density matrices approach to orbital ordering (OO) in order to study the OO of the spinel vanadates AV$_{2}$O$_{4}$ (A $\equiv$ Zn, Cd and Mg), which is normally believed to be responsible for the structural transition from cubic to tetragonal phase observed in these compounds. The density matrices of vanadium atoms are obtained by using {\it state-of-the-art} full-potential linearized augmented plane wave method based GGA+U calculations. In the absence of spin-orbit coupling, the present study shows the existence of anti-ferro OO in the global (local octahedral) coordinate system where $d_{xz}$ and $d_{yz}$ ($d_{xz}$+$d_{yz}$ and $d_{xz}$-$d_{yz}$) orbitals are mainly occupied at the neighboring V sites for all the compounds.

cond-mat.str-el↗

arXiv2016

Limitations of unconstrained LSDA+$U$ calculations in predicting the electronic and magnetic ground state of a geometrically frustrated ZnV$_{2}$O$_{4}$ compound

In the present work, we investigate the applicability of the LSDA+$U$ method in understanding the electronic and magnetic properties of a geometrically frustrated ZnV$_2$O$_4$ compound, where the delicate balance of electrons, lattice, orbital and spin interactions play an important role in deciding its physical properties. In the ferromagnetic solution of the compound, only one type of orbital solution is found to exist in all ranges of $U$ studied here. However, in antiferromagnetic (AFM) phase, two types of orbital solutions, AFM(OS1) and AFM(OS2), exist for $U >$3 eV. If the difference of the electronic occupancy of $d_{xz}$ and $d_{yz}$ orbitals is less than 0.25, then AFM(OS1) solution is stabilized, whereas for higher values AFM(OS2) solution is stabilized. The use of unconstrained calculations within the fully localized double counting scheme is unable to predict the AFM ground state for $U \leqslant$3 eV. Our results clearly suggest the importance of constrained calculations in understanding the electronic and magnetic properties of a compound, where various competing interactions are present. In the AFM solution, the orbital ground state of the compound changes with varying $U$, where AFM(OS1) is found to be the ground state for $U \leqslant$3 eV and for higher values of $U$, AFM(OS2) is the ground state. The analysis of the band gap suggests that the AFM(OS2) is the real ground state of the compound.

cond-mat.str-el↗