Doping a Mott Insulator: Physics of High Temperature Superconductivity

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits the pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. We introduce Anderson’s idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. However, we argue that phase fluctuation can only explain the pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement the strong correlation constraint, and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the t-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We follow the historical order and first review the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here we digress with a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We emphasize the difference between the high energy gauge group in the formulation of the problem versus the low energy gauge group which is an emergent phenomenon. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which lead to the physics of fractionalization and spin-charge separation. We next describe the extension of the SU(2) formulation to nonzero doping. We focus on a part of the mean field phase diagram called the staggered flux liquid phase. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase. We emphasize that d-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. We apply these ideas to the high Tc cuprates, and discuss their implications for the vortex structure and the phase diagram. A possible test of the topological structure of the pseudogap phase is discussed.