Mind the gap

A particularly striking example of a new quantum state of matter is the pseudogap state found in high-temperature cuprate superconductors. The temperature-doping phase diagram of the cuprates contains a large region between the antiferromagnetic Mott insulator and superconducting phases known as the pseudogap region. Many observed properties are that of a metal in which the density of states is suppressed near the Fermi energy. The pseudogap state is a distinctive feature of the cuprates and understanding its origin and relationship to superconductivity is highly contentious. A nice review by Norman, Pines, and Kallin (based on a workshop in 2004) considers three alternative schematic phase diagrams (temperature T versus doping x) for the cuprate superconductors.


The solid line denotes the superconducting transition temperature Tc and the dashed line the pseudogap temperature T*. A key question is whether T* is a crossover temperature or is actually associated with a phase transition. In (2) there is a quantum phase transition at the hole doping level xc which is close to the value at which the superconducting transition temperature Tc is maximal (i.e., optimal doping).

Proposals for the physical origin of the pseudogap include:
• pre-formed superconducting pairs
• resonating valence bonds (RVB)
• short-range spin correlations
• a new state of matter such as a d-density wave
• long-range antiferromagnetic spin fluctuations due to a magnetic quantum critical point.

It has been established by ARPES (angle-resolved photoemission spectroscopy) that the magnitude of the pseudogap varies over the Fermi surface. The wavevector dependence of the magnitude of the pseudogap has a d-wave character similar to that of the superconducting state. Furthermore, the quasi-particle excitations have a much longer lifetime at wavevectors near where the nodes in the pseudogap occur. Outstanding questions, besides the physical origin of the pseudogap ,include:

• Does the pseudogap temperature T* correspond to an actual phase transition (i.e., a new state of matter)23 or is it just a crossover temperature? If the former is there an order parameter and a broken symmetry associated with the pseudogap state?
• In the absence of superconductivity (e.g., if it is suppressed by a large magnetic field) does T* vanish at a particular doping corresponding to a quantum critical point? If so, is this point responsible for the optimal Tc and/or the non-Fermi liquid properties of the metallic phase at optimal doping?
• Can a pseudogap cause the temperature and frequency dependence of the interlayer and the intralayer conductivity to be distinctly different?
• How ubiquitous is anisotropic pseudogap in strongly correlated electron materials?
Specifically, does it occur in layered organic superconductors, overdoped cuprates, electron doped cuprates, heavy fermion metals, and iron pcinitides?
• Can the pseudogap be closed with a Zeeman magnetic field?
• Is there a change in the topology of the Fermi surface between the left and right sides of the phase diagrams in Figure above (i.e., as one goes from underdoped to overdoped) ?