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Title:  Coupled one dimensional electron systems and stripe phases of high temperature superconductors 
Author(s):  Jaefari, Akbar 
Director of Research:  Fradkin, Eduardo H. 
Doctoral Committee Chair(s):  Phillips, Philip W. 
Doctoral Committee Member(s):  Fradkin, Eduardo H.; Mason, Nadya; Stack, John D. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  High Temperature Superconductivity
Stripe phases Spin gap Local density of states Hubbard model Pair density wave Charge density wave dimensional crossover 
Abstract:  In this dissertation, I will consider the problem of coupled one dimensional electronic systems particularly in connection with the stripe phases of high temperature superconductors. Three major problems have been addressed in this dissertation. In chapter one, I consider the problem of the Local Density of States for spingapped onedimensional charge density wave (CDW) states and Mott insulators in the presence of a hardwall boundary. I calculate the boundary contribution to the singleparticle Green function in the lowenergy limit using field theory techniques and analyze it in terms of its Fourier transform in both time and space. The boundary LDOS in the CDW case exhibits a singularity at momentum $2k_\mathrm{F}$, which is indicative of the pinning of the CDW order at the impurity. Several dispersing features has been observed at frequencies above the spin gap, which provide a characteristic signature of spincharge separation. This demonstrates that the boundary LDOS can be used to infer properties of the underlying ``bulk' system. In the presence of a boundary magnetic field midgap states localized at the boundary emerge with signature in the LDOS. I discuss implications of these results for STM experiments on quasi1D systems such as twoleg ladder materials like Sr$_{14}$Cu$_{24}$O$_{41}$. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of onedimensional Mott insulators. In the second chapter, I study an extended HubbardHeisenberg model on two types of two leg ladders, a model without flux and a model with flux $\pi$ per plaquette. In the case of the conventional (fluxless) ladder the Pair density wave state arises for certain filling fractions when commensurability conditions is satisfied. For the flux $\pi$ ladder the pair density wave phase is generally present. The PDW phase is characterized by a finite spin gap and a superconducting order parameter with a finite (commensurate in this case) wave vector and powerlaw superconducting correlations. In this phase the uniform superconducting order parameter, the $2k_F$ chargedensitywave (CDW) order parameter and the spindensitywave N\'eel order parameter exhibit short range (exponentially decaying) correlations. In particular the PDW phase appears even at weak coupling when the bonding band of the ladder is half filled. This state is shown to be dual to a uniform superconducting (SC) phase with quasi long range order. By making use of bosonization and the renormalization group, the phase diagram of the spingapped regime has been determined and the quantum phase transitions therein has been discussed. The phase boundary between PDW and the uniform SC ordered phases is found to be in the Ising universality class. This analysis is generalized to the case of other commensurate fillings of the bonding band, where higher order commensurate PDW states are found. The form of the effective bosonized field theory is determined and the corresponding phase diagram is discussed. We show that the formation of PDW order in the ladder embodies the notion of intertwined orders. The last topic discussed here is the competition between a superconducting (SC) ordered state with a charge density wave (CDW) state in stripe phases of high $T_c$ superconductors. An effective model for each stripe, motivated by studies of spingapped electronic ladder systems, has been considered. The problem of dimensional crossover arising from interstripe SC and CDW couplings has been analyzed using nonAbelian bosonization and renormalization group (RG) arguments and an effective $O(4)$symmetric nonlinear $\sigma$model in $D=2+1$ has been derived for the case when both interstripe couplings are of equal magnitude as well as equally RG relevant. By studying the effects of various symmetry lowering perturbations, the structure of the phase diagram has been determined and it has been shown that, in general, it has a broad regime in which both orders coexist. The quantum and thermal critical behavior is discussed in detail, and the phase coexistence region is found to end at associated $T=0$ as well as $T>0$ tetracritical points. The possible role of hedgehog topological excitations of the theory is considered and argued to be RG irrelevant at the spatially anisotropic higher dimensional lowenergy fixed point theory. These results are also relevant to the case of competing N\'eel and valence bond solid (VBS) orders in quantum magnets on 2D isotropic square as well as rectangular lattices interacting via nearest neighbor Heisenberg exchange interactions. 
Issue Date:  20130203 
URI:  http://hdl.handle.net/2142/42272 
Rights Information:  Copyright 2012 Akbar Jaefari 
Date Available in IDEALS:  20130203 
Date Deposited:  201212 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois