Correlation effects in dilute Fermi liquids: Nonequilibrium spin systems and graphene

We use Landau Fermi liquid theory to study the thermodynamics and spin dynamics of polarized nonequilibrium (PNEQ) spin systems. The PNEQ systems are paramagnetic systems in which nonequilibrium magnetization is imposed in the absence of external magnetic fields. These systems are successfully created in liquid helium, in systems used in the study of spintronics, and in cold atom systems of alkali metals. Some of the popular methods in use are the rapid melting, optical pumping and spin injection. We show that the correlation makes it possible to create PNEQ systems. We argue that in the presence of the finite correlation, steady states of the PNEQ systems can be created. We predict that such steady states can have gapless collective modes; which is a completely new observation for paramagnetic systems. We suggest that the effect of the nonequilibrium magnetization on the spin diffusion coefficient, which can be determined using the spin echo experiment, can be used to test the existence of the gapless collective modes. We have also shown that the correlation has nontrivial effects on the dispersion relations of the modes and their dynamical properties.;We also study the effects of correlation on the electronic properties of single and bilayer graphene, specifically on the possibility of the charge inhomogeneity. Analytically, we show that the electrons in the single layer graphene always remain in homogeneous (liquid) phase. We also solve a real space tight binding model numerically to determine the average occupation of electrons on the lattice sites of the single and bilayer graphene by varying the strength of the long range Coulomb interaction. For single layer graphene the occupation number of electrons is same at each lattice site which reinforces the idea that the electrons in single layer graphene remain in liquid state. In contrary, the bilayer graphene supports inhomogeneous distribution of the electrons on the lattice sites. The inhomogeneous state is a lattice commensurate triangular charge density wave state.;We apply Gutzwiller method to solve Hubbard model to study the importance of the on-site interaction in single layer graphene. The idea is to look at the effect of the on-site Coulomb repulsion on the renormalization of the kinetic energy, which is a direct measure of the correlation effect. We find that the renormalization of the kinetic energy is very small. Hence, we infer that neither the on-site nor the long range Coulomb interaction plays an important role in determining the electronic properties of the single layer graphane.;By solving a real space Green's function method we also study the impurity states in bilayer graphene as a function of the interlayer hopping energy and external bias. We find that energy of the impurity states can be controlled by tuning these parameters. It is shown that the physics of the impurity states in the bilayer graphene has more interesting features than that in the single layer graphene. We have discussed the effects of the electron-electron and electron-phonon interactions on the impurity states.