[Paper Review] Why high Tc is exciting

Jan Zaanen|arXiv (Cornell University)|Mar 12, 2001

Physics of Superconductivity and Magnetism6 references3 citations

TL;DR

This paper argues that high-temperature superconductivity in cuprates arises from a hidden quantum phase transition driven by sublattice parity order—specifically, a form of geometric order in dynamical stripes—rather than conventional quasiparticle behavior. The authors propose that the disappearance of this order at a quantum critical point triggers superconductivity, with the underlying physics resembling a Z₂ gauge theory that may connect to quantum gravity, though the order remains experimentally elusive due to its quantum-disordered nature.

ABSTRACT

This piece has been written for local, educational purposes. If you are like me searching for the right words to explain your fascination with high Tc superconductivity to the outside world, you might find something useful in this text.

Motivation & Objective

• To challenge the conventional Fermi-liquid paradigm in strongly correlated electron systems.
• To explain the anomalous behavior of high-Tc cuprate superconductors as arising from a quantum phase transition driven by hidden order.
• To identify sublattice parity order as the key hidden order in the stripe phase, persisting even when charge and spin degrees of freedom are quantum disordered.
• To explore the connection between this hidden order and quantum gravity through a Z₂ gauge theory framework.
• To address the experimental challenge of detecting this order, which remains hidden due to its quantum fluctuations and non-local nature.

Proposed method

• Propose a theoretical framework based on dynamical stripes—nanoscale, fluctuating charge and spin order—with a geometric structure defined by sublattice parity.
• Model the quantum phase transition at which sublattice parity order disappears as a second-order transition in a Z₂ gauge theory, known to be well-understood and second-order.
• Use the gauge theory mapping to describe critical fluctuations in the effective spacetime of the electrons, linking them to quantum gravity analogs.
• Analyze the system's behavior under varying doping, showing that sublattice parity order persists until high doping, where it vanishes at the quantum critical point.
• Predict a novel quantum spin-nematic order as an indirect experimental signature, arising from the same underlying symmetry breaking.
• Address the fermion sign problem, acknowledging it as a major obstacle to a complete theoretical description.

Experimental results

Research questions

• RQ1 What is the nature of the hidden order underlying high-Tc superconductivity in cuprates?
• RQ2 How can a quantum phase transition occur without conventional order parameters being detectable?
• RQ3 Why does the Fermi-liquid paradigm fail in describing the electronic behavior in high-Tc superconductors?
• RQ4 Can the disappearance of sublattice parity order be described as a second-order phase transition in a gauge theory?
• RQ5 What experimental signatures might reveal the presence of a hidden geometric order like sublattice parity?

Key findings

• Sublattice parity order is proposed as the hidden order in high-Tc superconductors, persisting even when charge and spin degrees of freedom are quantum disordered.
• The quantum phase transition at which this order vanishes is identified as a second-order transition in a Z₂ gauge theory, which is analytically tractable.
• The critical fluctuations at the transition are not in spin or charge, but in the effective spacetime geometry of the electrons, suggesting a link to quantum gravity.
• The dynamical nature of the stripes makes the hidden order fundamentally difficult to detect directly, as it averages out over time.
• A novel quantum spin-nematic order is predicted as a potential experimental signature, though its realization remains uncertain.
• The fermion sign problem remains a significant theoretical obstacle, especially when matter fields are fermionic, limiting the completeness of the current description.