Emergent gauge fields and the high-temperature superconductors.

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Materials Science

Background:

• Maxwell's theory describes electric and magnetic fields, but these can also emerge from quantum structures in matter.
• Fermi liquid (FL) theory explains electron behavior in metals via quasi-particles and the Luttinger theorem, assuming adiabatic continuity from free electrons.
• Long-range entanglement and emergent gauge fields can exist in metals, leading to states beyond standard FL theory.

Purpose of the Study:

• To review the theory of emergent gauge fields in insulators.
• To introduce and explain the fractionalized Fermi liquid (FL*) state in metals.
• To interpret experimental data from cuprate superconductors using the FL* framework.

Main Methods:

• Conceptual review of emergent gauge field theory in insulators.
• Theoretical analysis of the fractionalized Fermi liquid (FL*) state, highlighting its deviation from FL theory.
• Application of FL* theory to experimental observations in hole-doped cuprate superconductors.

Main Results:

• Emergent gauge fields originate from the quantum structure of many-electron states, not vacuum properties.
• The FL* state features electron-like quasi-particles and a Fermi surface, but violates the Luttinger theorem due to emergent gauge fields.
• The pseudogap regime in cuprate superconductors can be understood within the FL* theory.

Conclusions:

• Emergent gauge fields are crucial for understanding exotic metallic states like FL*.
• The FL* state represents a significant departure from conventional Fermi liquid theory, particularly in its violation of the Luttinger theorem.
• The FL* framework offers a promising avenue for interpreting complex phenomena in strongly correlated materials such as cuprate superconductors.