Effects of Strong Electron-Electron Correlations on Band Insulators in Equilibrium and Non-Equilibrium

Abstract

In this thesis, several aspects of correlation effects in band insulators that were hitherto not addressed, both in equilibrium and non-equilibrium, are studied using the Ionic Hubbard model (IHM) at half-filling and Dynamical mean-field theory (DMFT). The IHM is an extension of the Hubbard model on a bipartite lattice with a staggered on-site “ionic" potential Δ added in. The Hubbard model by itself is a tight-binding model of electrons hopping between (orbitals localized on) lattice sites, with amplitudes t and t’ for first neighbor and second neighbor hopping respectively, together with a coulomb repulsion energy cost of U for double occupancy (i.e., with both up and down spin electrons) at any lattice site. The studies in this thesis address strong correlation effects in this model using DMFT techniques which map the lattice problem to a self consistently embedded quantum impurity problem. The impurity problem itself is solved using state of the art continuous time quantum monte-carlo (CTQMC) techniques (Ch.s 3 and 4) as well as the somewhat simpler Iterated Perturbation Theory (IPT) (Ch.s 3, 5 and 6). Chapter 3 of the thesis is devoted to a detailed analysis of the properties of the half-filled t-U-Δ IHM (i.e., with t’=0) on a Bethe lattice of infinite connectivity. It is shown conclusively here that for a finite Δ and at zero temperature (T=0), the IHM has a first order transition from the Band Insulator (BI) phase to an antiferromagnetic insulating (AFI) phase at a threshold U = UAF (which increases with Δ) such that the BI to AFI transition preempts the transition from the BI to the correlation induced paramagnetic metallic (PM) phase. Evidence is also presented for a quantum transition to a sliver of half-metal (HM) phase just after the AF order turns on, followed by a return to the AFI phase on further increasing U. With increasing T, the AF order is lost via a first-order transition for weak to intermediate U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, the transition from the AFI to the paramagnetic Mott insulating phase (adiabatically connected to the BI phase) is of second order. As T increases, the range of U over which the AF order is stable shrinks, collapsing eventually to a line of tricritical points that separates the surfaces of first- and second-order phase transitions in the T-U-Δ space. In Chapter 4 of the thesis the t-t’-U-Δ IHM on a square lattice is studied using DMFT+CTQMC. It is shown here that the presence of t’ frustrates the AF order for weak to intermediate correlations, resulting in the stabilization of the correlation induced PM phase over a broad region of the parameter space, although the AFI is always the stable phase for large enough U. In the intermediate coupling regimes, two other interesting phases show up as a result of the competition among U, Δ and t’ : a Ferrimagnetic metallic (FM) phase which has non-zero values of the uniform as well as staggered magnetization; and even more interesting, an anti-ferromagnetic half-metal (AFHM) phase, where only the staggered magnetization is non-vanishing, and in which one spin-species has gapless excitations while the other is gapped. A rich phase diagram involving these phases is obtained and compared with the one obtained using the simpler Hartree-Fock approximation. The same model is treated in Chapter 5 using DMFT+IPT, to obtain spectral functions not easy to obtain using the CTQMC techniques. The results are consistent with and reinforce the conclusions of Chapter 4. Questions as to how closed quantum systems approach equilibrium after a quench are of great current interest, especially so because of experiments in cold atom systems. Chapter 6 of the thesis is devoted to a study of the consequences of an ionic potential quench in the t-U-Δ IHM on a Bethe lattice using non-equilibrium DMFT+IPT techniques. Two types of ionic potential quench are studied: (1) From a nonzero Ionic potential Δi to a uniform state with Δf = 0, and (2) Ionic potential Δi = 0 to a non-zero Δf quench, at different values of U. The evolutions of the staggered density and the double occupancy towards their final equilibrium values are found to be oscillatory with envelope functions that have power law tails despite the presence of interactions, which behavior is intriguing and worthy of further exploration. The exponents of the power law increase with increasing U, consistent with interactions promoting faster relaxation. In addition to the above original contributions the thesis also contains an introductory chapter (Ch. 1), a methods chapter (Ch. 2), and several appendices that present technical details.