Doping a Mott Insulator: Physics of High Temperature Superconductivity

TL;DR

The paper argues that high-$T_c$ superconductivity in cuprates emerges from doping a Mott insulator and can be understood via a strong-coupling framework based on the $t$-$J$ model. It develops and compares two complementary gauge-theory approaches: a $U(1)$ slave-boson theory (with projected wavefunctions) and an $SU(2)$ slave-boson formulation, showing how spin liquids, spinons, holons, and gauge fluctuations can generate pseudogap behavior, Fermi arcs, and $d$-wave superconductivity upon doping. The work emphasizes the role of phase fluctuations, vortex physics, and the possibility of deconfined gauge fields, arguing that the pseudogap region may reflect a nearby quantum spin liquid state with observable signatures such as orbital-current fluctuations and distinctive vortex cores. The analysis provides a coherent framework linking microscopic models to a range of experimental phenomena, and proposes concrete tests (e.g., vortex-core orbital currents, vison-related effects) to validate the spin-liquid perspective on high-$T_c$ superconductivity.

Abstract

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. 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. 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 give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.

Figures (36)

• Figure 1: Schematic phase diagram of high $T_c$ superconductors showing hole doping (right side) and electron doping (left side). From DHS0373, DHS0373.
• Figure 2: The two-dimensional copper-oxygen layer (left) is simplified to the one-band model (right). Bottom figure shows the copper $d$ and oxygen $p$ orbitals in the hole picture. A single hole with $S = 1/2$ occupies the copper $d$ orbital in the insulator.
• Figure 3: The Knight shift for YB$_2$Cu$_4$O$_8$. It is an underdoped material with $T_c = 79$K. From CIS9777, CIS9777.
• Figure 4: (a) Knight shift data of YBCO for a variety of doping (from AOM8900, AOM8900). The zero reference level for the spin contribution is indicated by the arrow and the dashed line represents the prediction of the 2D $S = {1\over 2}$ Heisenberg model for $J = 0.13$ eV. (b) Uniform magnetic susceptibility for LSCO (from NOM9400, NOM9400). The orbital contribution $\chi_0$ is shown (see text) and the solid line represents the Heisenberg model prediction.
• Figure 5: The specific heat coefficient $\gamma$ for YBa$_2$Cu$_3$O$_{6+y}$ (top) and La$_{2-x}$Sr$_x$CuO$_4$ (bottom). Curves are labeled by the oxygen content $y$ in the top figure and by the hole concentration $x$ in the bottom figure. Optimal and overdoped samples are shown in the inset. The jump in $\gamma$ indicates the superconducting transition. Note the reduction of the jump size with underdoping. (From LMC9340, LMC9340 and LLC0159, LLC0159).