Aspects of Spin - Charge Separation in high Tc Cuprates

High T, cuprates have a number of features that are anomalous from the point of view of the conventional theory of metals, i.e. the Fermi liquid theory. These include the high Tc itself, the linear resistivity in optimally doped cuprates, the "spin gap" phenomena, and antiferromagnetic fluctuations. Some of the basic features of the high T, phase diagram can be readily understood from slave boson mean field theories of the t-J model that yield a variety of phases like the uRVB phase (strange metal), d-wave RVB phase (spin gap), and the superconducting phase. This thesis is concerned with improving this picture by considering important fluctuations around the mean fields. This leads to certain gauge theories in which neutral spin 1/2 fermions ("spinons") and charged spinless bosons ("holons") are coupled to gauge fields. If the gauge field is not "confining", the spin and charge degrees of freedom are separated to some extent, and an unconventional picture for transport and magnetic properties is expected. Following an introduction and overview, the first half of the main body of this thesis analyzes a simple model of a degenerate two-dimensional Bose liquid interacting with a fluctuating gauge field, with the goal of studying the charge degree of freedom in the cuprates. It is shown that the fluctuating gauge field efficiently destroys superfluidity even in the Bose degenerate regime. The nature of the resulting normal state is discussed in terms of the geometric properties of the imaginary-time paths of the bosons. Charge response functions are studied numerically (by path integral Monte Carlo methods); it is found that the transport scattering rate behaves as h/Ttr 2kBT, consistent with the experiments on the cuprates in the normal state, and that the density correlations of our model resemble the charge correlations of the t-J model. The second half considers the magnetic properties of cuprates from the point of view of a gauge theory of spinons, with emphasis on the underdoped regime. Despite the spin gap, there is a substantial antiferromagnetic correlation in the underdoped cuprates, as evidenced by the q-space scan of Neutron scattering cross section and different temperature dependences of the Copper and Oxygen site relaxation rates, features which are not captured well by mean field theories. As a concrete illustration of the gauge-fluctuation restoration of the antiferromangetic correlation and the feasibility of the 1/N perturbation theory, a U(1) gauge theory of id Heisenberg spin chain is worked out exactly, and then perturbatively. The difference between the behavior of uniform and staggerd spin correlation functions is discussed in terms of conserved and nonconserved currents. The 1/N-perturbative treatment of the gauge theory in 2+1D (which can be motivated from the mean field Flux phase of the Heisnberg model) leads to a dynamical mass generation corresponding to an antiferromagnetic ordering, but it is argued that in a similar gauge theory with an additional coupling to a Bose (holon) field, symmetry breaking does not occur, but antiferromagnetic correlations are improved, which is the situation in the underdoped cuprates. Thesis Supervisor: Patrick A. Lee Title: William and Emma Rogers Professor of Physics