Narrow Results

We examine the imbalance thermodynamics of uncontaminated decoherence in graphene. In a uncontaminated decoherence process, no exchange of energy takes place directly between graphene and the surroundings. It is seen that due to decoherence heat dissolution takes place due to which energy of the environment cannot remain conserved. In this paper, we find out the energy eigenvalues and wave function in the graphene from the perturbed Hamiltonian to find out the density matrix and entropy of the system and their unique relation between the density matrix, momentum of the graphene and entropy where the graphene is taken as an open system. In graphene, the behavior of electrons is controlled by the massless Hamiltonian and ($2+1$) Dirac equation.

Structural, electronic, magnetic and optical properties of Cu₄Mn₂Te₄ have been reported earlier by the authors, and here, the transport properties of the same are discussed along with the band structure investigation of the neodymium-doped cubic material LMO (LiMn₂O₄), namely LiMn${}_{1.75}$Nd${}_{0.25}$O₄ compound, under spin polarized schemes through the First Principles calculations. The Full Potential-Linearized Augumented Plane Wave Method (FP-LAPW) method is adopted to investigate the electronic structures based on the framework of Density Functional Theory (DFT). Exchange potentials are treated using the Generalized Gradient Approximations (GGA). Cohesive energy calculations reveal that the ferromagnetic phase of LiMn${}_{1.75}$Nd${}_{0.25}$O₄ and the antiferromagnetic phase of Cu₄Mn₂Te₄ exhibits a stable phase. Of these, FM-LiMn${}_{1.75}$Nd${}_{0.25}$O₄ shows a semi-metallic-like behavior in spin-up channel and metallic behavior in spin-down channel whereas antiferromagnetic Cu₄Mn₂Te₄ exhibits a band gap in both spin-up and spin-down channels. Dirac points are identified at −0.0625eV in the band structure plot of FM-LiMn${}_{1.75}$Nd${}_{0.25}$O₄ at its high symmetry points $\mathrm{\Gamma }$ and W which is an indication of high electron mobility at ambient condition. The presence of flat and dispersive bands around the Fermi energy level is an indication of high thermopower, and it is present in both the compounds FM-LiMn${}_{1.75}$Nd${}_{0.25}$O₄ and AFM-Cu₄Mn₂Te₄. From the present computations, at 300K, a power factor range of ($S^2\sigma$ scaled by relaxation time in $\mu$W/msK²) $1.75\times 10^{20}\uparrow$ and $9.37\times 10^{21}\downarrow$ is obtained for ferromagnetic LiMn${}_{1.75}$Nd${}_{0.25}$O₄ compounds at up and down spins, respectively. A typical power factor ($\mu$Wm${}^{-1}$s${}^{-1}$K${}^{-2}$) of $4.79\times 10^{15}\uparrow$ and $2.97\times 10^{18}\downarrow$ is obtained for antiferromagnetic Cu₄Mn₂Te₄ at 325K required for good thermoelectric performance.

In this paper, we use the generalized Dirac structure beyond the linear regime of graphene. This is probed using the a deformation of the Dirac structure in graphene by the generalized uncertainty principle. Here, the Planck length is replaced by the graphene lattice spacing. As the graphene sheet is bounded by two boundaries, we analyze this system with suitable boundary conditions. We solve the perturbed Hamiltonian and derive the wave function for this system. We observe that the energy of this system gets corrected due to this deformation. We explicitly calculate these corrections to the energy of this system.