Synthesis of the phenomenology of the underdoped cuprates

The underdoped cuprates have a number of interesting and unusual properties that often seem hard to reconcile with one another. In this paper we show how many of these diverse phenomena can be synthesized into a single coherent theoretical picture. Specifically we present a description where a pseudogap and gapless Fermi arcs exist in the normal state above the superconducting transition temperature Tc but give way to the observed quantum oscillations and other phenomena at low temperature when the superconductivity is sup- pressed by a magnetic field. We show the consistency between these phenomena and observations of enhanced Nernst and diamagnetic signals above Tc. We also develop a description of the vortex core inside the super- conducting state and discuss its relation with the high-field phenomena. In the last several years, a large number of experiments have studied the properties of the underdoped cuprate mate- rials. The phenomenology of these materials is rather un- usual, and a unified theoretical picture of the diverse phe- nomena is yet to emerge. First below a temperature scale T there is the onset of the pseudogap in various probes. Re- markably angle resolved photoemission spectroscopy ARPES studies of the electron spectral function reveal the existence of gapless Fermi arcs in the pseudogap region above the superconducting SC transition. 1 The length of these Fermi arcs decreases with decreasing temperature T, possibly extrapolating to zero 2 in the limit T →0. Second in a fairly wide range of temperatures above Tc, but below the T line, there is an onset of local superconducting order with- out long-range phase coherence. 3,4 This is most strikingly evidenced by an enhancement of the Nernst effect and dia- magnetic response in this region. A third piece of the phe- nomenology comes from recent quantum oscillation studies of the state obtained by suppressing superconductivity in a high field at low temperature. 5,6 Remarkably sharp oscilla- tion frequencies are seen indicating the presence of a sharp Fermi surface with charge carriers that are fermionic Landau quasiparticles. The detailed behavior of the oscillation fre- quencies and other experiments have led to a suggestion that the oscillations are associated with gapless electron pockets centered near the antinodal region of the Brillouin zone. 7-10 Currently there is considerable confusion about how these various pieces of information about the normal i.e., nonsu- perconducting state of the underdoped cuprates fit together. The ARPES results at low field and high T seem to be in conflict with the existence of a closed Fermi surface at high fields and low T. Further the suggested electron pocket inter- pretation of the oscillation experiments also has a difficulty with ARPES and other probes at low field above Tc ;i t is precisely along the antinodal region that the pseudogap is seen in the electron spectrum. It is puzzling how a relatively modest field of 40 T can close the large antinodal gap. Fi- nally the high-field experiments in particular studies of the Hall effect 7 have questioned the correctness of the conclu- sions of Ong and co-workers 4 based on their Nernst/ magnetization experiments. In this paper we show how these various seemingly con- flicting results may be reconciled into a single coherent the- oretical picture. We are cognizant of other interesting phe- nomena that have attracted attention recently—notably signatures of time-reversal symmetry breaking. 11-13 The role they play in determining the electronic structure is not un- derstood, and we will not discuss them in this paper. Our theory is based on a small set of assumptions that we justify on various theoretical and empirical grounds. We then obtain a description of the underdoped cuprates where a pseudogap and gapless Fermi arcs occur above Tc but give way to the observed quantum oscillation and other phenomena at high fields. Further we show that there is no real conflict between the conclusions of the Nernst/diamagnetism experiments and the high-field oscillation experiments. As a bonus we obtain a description of the vortex core structure inside the supercon- ducting phase and discuss its relation with the phenomena described above. In a companion paper 14 we explore a spe- cific microscopic model that captures a number of aspects of the overall picture that emerges from the present one. We begin by stating and justifying our central assump- tions.