Thesis advisor: Ziqiang Wang / One of the most unconventional electronic states in high transition temperature cuprate superconductors is the pseudogap state. In the temperature versus doping phase diagram, the pseudogap state straddles across the antiferromagnetic (AF) state near half filling and the superconducting (SC) dome on the hole doped side above the transition temperature Tc. The relationship between the pseudogap state and these two well known states - the AF state and the SC state is believed to be very important for understanding superconductivity and the emergent quantum electronic matter in doped Mott insulators. The pseudogap is characterized by the emergence of a soft gap in the single-particle excitation spectrum in the normal state in the temperature range between Tc and a characteristic temperature T*, i.e. Tc < T < T*. The most puzzling feature of the pseudogap is the nodal-antinodal dichotomy. Observed by ARPES in momentum space, the Fermi surface is gapped out in the antinodal region leaving a Fermi arc of gapless excitations near the nodes. Whether the pseudogap is an incoherent superconducting gap (onegap scenario) or it is a different gap governed by other mechanisms, other than superconductivity, (two-gap scenario) is still under debate. In this thesis I study the particle-particle channel and the particle-hole channel of the valence bond fluctuations away from half filling. Based on a strong-coupling analysis of the t-J model, I argue that the superexchange interaction J induced incommensurate bond centered density wave order is the driving mechanism for the pseudogap state. Low energy density of states (DOS) are eliminated by multiple incommensurate scatterings in the antinodal region at the Fermi level. I show that the interplay between the incommensurate bond centered d-wave density wave instability and the intrinsic electronic inhomogeneity in real cuprate materials is responsible for the observed pseudogap phenomena. Utilizing the spatially unrestricted Gutzwiller approximation, I show that the off-stoichiometric doping induced electrostatic disorder pins the low-energy d-wave bond density fluctuations, resulting in a VBG phase. The antinodal Fermi surface (FS) sections are gapped out, giving rise to a genuine normal state Fermi arc. The length of the Fermi arc shrinks with underdoping below the temperature T* determined by thermal filling of the antinodal pseudogap. Below Tc, the d-wave superconducting gap due to singlet pairing coexists and competes with the VBG pseudogap. The spatial, momentum, temperature and doping dependence of these two gaps are consistent with recent ARPES and STM observations in underdoped and chemically substituted cuprates. The temperature versus doping phase diagram captures the salient properties of the pseudogap phenomena and provides theoretical support for the two-gap scenario. In addition to resolving the complexities of the quantum electronic states in hole-doped cuprates, my unified theory elucidates the important role of the interplay between the strong electronic correlation and the intrinsic electronic disorder in doped transition metal oxides. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.