Static and dynamic properties of strongly correlated lattice models under electric fields (Dynamical Mean Field Theory approach)
Creator
Joura, Alexander V.
Advisor
Freericks, James K
Abstract
In this thesis we study the FalicovKimball model within the framework of Dynamical
Mean Field Theory (DMFT). We derive expressions for the electrical conductivity, electronic thermal conductivity, Seebeck coefficient (thermopower) and thermoelectric figure of merit (ZT) for the infinite dimensional hypercubic lattice and the Bethe lattice of infinite connectivity within linear response theory. We use these formulas to numerically calculate thermoelectric properties of the model away from halffilling. We also derive explicit analytic formulas for the retarded Green's function, the retarded selfenergy and the relaxation time near the pole in the insulating regime on the hypercubic lattice. Using these results we compare thermal and electric transport properties of the correlated insulator to that of a generic insulator in the small temperature regime. Using analytic expressions for the selfenergy near the pole in the insulator phase, we derive analytic formulas for the metalinsulator transition $U_{cr}$ on the hypercubic lattice. For the Bethe lattice we derive explicit analytic formulas for the electric conductivity, the electronic part of the thermal conductivity, the Seebeck coefficient, the Lorentz number and the figure of merit in the low temperature limit. We also examine the problem of calculating the density of states for singleband lattice Hamiltonians with an applied constant and uniform external electric field, when the field is large enough that nonlinear effects are important. To do this we develop a general formalism (based on the nonequilibrium KadanoffBaymKeldysh theory), which can be applied to a wide variety of different manybody Hamiltonians. We assume that the electric field was turned on in the distant past, so the system has reached the steady state. We present numerical solutions of the equations derived for the FalicovKimball model within the framework of dynamical meanfield theory. Finally, nonequilibrium properties of the Hubbard model in presense of an external electric field are studied. The transient nonequilibrium formalism is appied to study the total energy, double occupancy and electric current in a system under a strong electric field.
Description
Ph.D.
Permanent Link
http://hdl.handle.net/10822/709842Date Published
2014Subject
Type
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