[Paper Review] Quantum Ginzburg-Landau theory of doped Mott insulators

Qiang-Hua Wang|arXiv (Cornell University)|Jun 19, 2003

Physics of Superconductivity and Magnetism4 citations

TL;DR

This paper proposes a quantum Ginzburg-Landau theory for doped Mott insulators that unifies Cooper pair condensation and dual spin condensation via topological mutual duality, explaining key cuprate phenomena: the scaling of neutron resonance energy with superfluid density, vortex-induced quantized spin moments, and the compatibility of d-wave quasi-particle scattering with BCS-like behavior despite Mott physics.

ABSTRACT

We improve a previous theory of doped Mott insulators with duality between pairing and magnetism by a further duality transform. As the result we obtained a quantum Ginzburg-Landau theory describing the Cooper pair condensate and the dual of spin condensate. We address the superconductivity by doping a Mott insulator, which we call Mott superconductivity. Some fingerprints of such novelty in cuprates are the scaling between neutron resonance energy and superfluid density, and the induced {\it quantized} spin moment by vortices or Zn impurity (together with circulating charge supper-current to be checked by experiments).

Motivation & Objective

• To resolve the paradox of high-Tc superconductivity being 'normal' in terms of quasi-particles yet distinct in its doping-driven superfluid density and neutron resonance.
• To establish a field-theoretic framework that unifies superconductivity and magnetism in doped Mott insulators via topological duality.
• To explain the scaling of neutron resonance energy with superfluid density as a fingerprint of Mott superconductivity.
• To account for the absence of zero-energy states in vortex cores and the presence of quantized spin moments via dual vortex mechanisms.

Proposed method

• Derives a low-energy effective field theory from an exact all-boson representation of the t-J model, integrating out gauge fluctuations in the infrared limit.
• Constructs a Lagrangian $ L = L_c + L_m + L_{CS} $, where $ L_c $ describes the Cooper pair condensate (CC), $ L_m $ the dual spin magnetic condensate (MC), and $ L_{CS} $ a Chern-Simons term enforcing mutual duality.
• Uses gauge fields $ a^{h} $ and $ a^{m} $ to enforce flux attachment: CC sees $ S^z $-moments as $ 2\pi $ fluxes, and MC sees $ \delta\rho_c $ as $ 2\pi $ fluxes.
• Identifies the $ b $-photon as a dual gauge field that couples to both CC and MC currents, leading to a QED3-like theory for nodal quasiparticles.
• Analyzes vortex solutions: CC-vortices and dual M'C-vortices, showing that M'C-vortices capture quantized spin moments.
• Demonstrates that the $ b $-photon gap scales with superfluid density $ K_c \propto x $, matching the observed neutron resonance energy scaling.

Experimental results

Research questions

• RQ1 How can the scaling of neutron resonance energy with superfluid density in underdoped cuprates be explained within a unified field theory?
• RQ2 What is the physical origin of the induced quantized spin moment around vortices or Zn impurities in high-Tc superconductors?
• RQ3 How does the mutual duality between Cooper pair condensate and spin magnetic condensate explain the absence of zero-energy states in vortex cores?
• RQ4 Why do scanning tunneling microscopy experiments observe quasi-particle interference consistent with BCS theory despite the Mott insulator origin?
• RQ5 Can the duality between superconducting and magnetic order be consistently described in a quantum Ginzburg-Landau framework?

Key findings

• The neutron resonance energy in cuprates scales with the superfluid density $ K_c \propto x $, which the theory explains as a consequence of the $ b $-photon gap $ \omega_b \sim \sqrt{K_m(K_v + K_c)} \sim 1/\lambda_L $, tracing the Meissner penetration depth.
• Vortices in the Cooper pair condensate induce quantized spin moments via the dual M'C-vortex mechanism, with the spin moment captured in the vortex core and circulating supercurrents.
• The absence of zero-energy states in vortex cores is explained by the non-topological nature of the M'C-vortex, which disrupts supercurrent and suppresses zero modes.
• The theory predicts that the $ b $-photon, a dual gauge field, couples to both charge and spin currents, leading to a QED3-like low-energy theory for nodal quasiparticles.
• The effective theory reduces to a standard d-wave BCS-like description in the absence of vortices, explaining the observed quasi-particle scattering interference in STM experiments.
• The mutual duality ensures that spin excitations are perceived as gauge fields by the Cooper pair condensate, explaining the Anderson-Higgs mechanism for the neutron resonance as a response to spin fluctuations.