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Register a new userDynamical mean field theory for oxide heterostructures
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Transition metal oxide heterostructures often, but by far not always, exhibit strong electronic correlations. State-of-the-art calculations account for these by dynamical mean field theory (DMFT). We discuss the physical situations in which DMFT is needed, not needed, and where it is actually not sufficient. By means of an example, SrVO$_3$/SrTiO$_3$, we discuss step-by-step and figure-by-figure a density functional theory(DFT)+DMFT calculation. The second part reviews DFT+DMFT calculations for oxide heterostructure focusing on titanates, nickelates, vanadates, and ruthenates.
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We study layered systems and heterostructures of s-wave superconductors by means of a suitable generalization of Dynamical Mean-Field Theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively small number of active layers is embedded in an effective potential accounting for the effect of the rest of the system. We introduce a feedback of the active layers on the embedding potential that improves on previous approaches and essentially eliminates the effects of the finiteness of the active slab allowing for cheap computation of very large systems. We extend the method to the superconducting state, and we benchmark the approach by means of simple paradigmatic examples showing some examples on how an interface affects the superconducting properties. As examples, we show that superconductivity can penetrate from an intermediate coupling superconductor into a weaker coupling one for around ten layers, and that the first two layers of a system with repulsive interaction can turn superconducting by proximity effects even when charge redistribution is inhibited.
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.
We describe the use of coupled-cluster theory as an impurity solver in dynamical mean-field theory (DMFT) and its cluster extensions. We present numerical results at the level of coupled-cluster theory with single and double excitations (CCSD) for the density of states and self-energies of cluster impurity problems in the one- and two-dimensional Hubbard models. Comparison to exact diagonalization shows that CCSD produces accurate density of states and self-energies at a variety of values of $U/t$ and filling fractions. However, the low cost allows for the use of many bath sites, which we define by a discretization of the hybridization directly on the real frequency axis. We observe convergence of dynamical quantities using approximately 30 bath sites per impurity site, with our largest 4-site cluster DMFT calculation using 120 bath sites. We suggest coupled cluster impurity solvers will be attractive in ab initio formulations of dynamical mean-field theory.
Dynamical mean field methods are used to calculate the phase diagram, many-body density of states, relative orbital occupancy and Fermi surface shape for a realistic model of $LaNiO_3$-based superlattices. The model is derived from density functional band calculations and includes oxygen orbitals. The combination of the on-site Hunds interaction and charge-transfer between the transition metal and the oxygen orbitals is found to reduce the orbital polarization far below the levels predicted either by band structure calculations or by many-body analyses of Hubbard-type models which do not explicitly include the oxygen orbitals. The findings indicate that heterostructuring is unlikely to produce one band model physics and demonstrate the fundamental inadequacy of modeling the physics of late transition metal oxides with Hubbard-like models.
We derive an exact mapping from the action of nonequilibrium dynamical mean-field theory (DMFT) to a single-impurity Anderson model (SIAM) with time-dependent parameters, which can be solved numerically by exact diagonalization. The representability of the nonequilibrium DMFT action by a SIAM is established as a rather general property of nonequilibrium Green functions. We also obtain the nonequilibrium DMFT equations using the cavity method alone. We show how to numerically obtain the SIAM parameters using Cholesky or eigenvector matrix decompositions. As an application, we use a Krylov-based time propagation method to investigate the Hubbard model in which the hopping is switched on, starting from the atomic limit. Possible future developments are discussed.
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