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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 Urbana-Champaign 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 spin-gapped one-dimensional charge density wave (CDW) states and Mott insulators in the presence of a hard-wall boundary. I calculate the boundary contribution to the single-particle Green function in the low-energy 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 spin-charge 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 mid-gap states localized at the boundary emerge with signature in the LDOS. I discuss implications of these results for STM experiments on quasi-1D systems such as two-leg 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 one-dimensional Mott insulators. In the second chapter, I study an extended Hubbard-Heisenberg 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 (flux-less) 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 power-law superconducting correlations. In this phase the uniform superconducting order parameter, the $2k_F$ charge-density-wave (CDW) order parameter and the spin-density-wave 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 spin-gapped 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 spin-gapped electronic ladder systems, has been considered. The problem of dimensional crossover arising from inter-stripe SC and CDW couplings has been analyzed using non-Abelian 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 inter-stripe 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 low-energy 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: 2013-02-03 URI: http://hdl.handle.net/2142/42272 Rights Information: Copyright 2012 Akbar Jaefari Date Available in IDEALS: 2013-02-03 Date Deposited: 2012-12
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