[Paper Review] Anomalous Magnetothermal Resistance of High-Tc Superconductors: Anomalous Cyclotron Orbits at a Dirac Point

Philip W. Anderson|ArXiv.org|Dec 3, 1998

Physics of Superconductivity and Magnetism1 references3 citations

TL;DR

This paper derives corrected equations of motion for quasiparticles near the nodes in the d-wave gap of high-Tc superconductors, accounting for the spatial phase dependence of the gap parameter. The model explains anomalous magnetothermal resistance measurements by predicting unusual cyclotron orbits near a Dirac point, consistent with experimental data from Ong and Krishana.

ABSTRACT

I derive equations of motion for quasiparticles near the nodes in the d-wave gap of high Tc superconductors. Previous versions have not properly taken into account the spatial dependence of the gap parameter phase. The results are compatible with magnetothermal conductivity measurements in the superconducting phase by Ong and Krishana.

Motivation & Objective

• To address inconsistencies in prior models of quasiparticle motion near d-wave superconductor nodes by incorporating the spatial phase dependence of the gap parameter.
• To reconcile theoretical predictions with experimental magnetothermal conductivity measurements in the superconducting state.
• To explain the origin of anomalous cyclotron orbits observed in high-Tc superconductors.
• To provide a self-consistent theoretical framework for quasiparticle dynamics in d-wave superconductors with non-uniform gap phases.

Proposed method

• Derives equations of motion for quasiparticles using a relativistic-like Hamiltonian near the Dirac point at the d-wave node.
• Incorporates the spatial variation of the d-wave gap phase, which was previously neglected in earlier models.
• Applies a semiclassical approach to track quasiparticle trajectories under magnetic fields.
• Uses the effective mass and velocity derived from the band structure near the node to model cyclotron orbits.
• Compares theoretical magnetothermal conductivity with experimental data from Ong and Krishana.
• Validated through consistency with observed anomalous resistance behavior in high-Tc superconductors.

Experimental results

Research questions

• RQ1 How does the spatial phase dependence of the d-wave gap parameter affect quasiparticle dynamics near the node?
• RQ2 Why do magnetothermal conductivity measurements in high-Tc superconductors show anomalous resistance behavior?
• RQ3 What causes the formation of unusual cyclotron orbits in d-wave superconductors under magnetic fields?
• RQ4 How can a theoretical model explain the observed deviations from standard Fermi liquid behavior in high-Tc superconductors?
• RQ5 What role does the Dirac point play in shaping the quasiparticle trajectories and transport properties?

Key findings

• The inclusion of spatial phase variation in the gap parameter leads to a significant correction in quasiparticle equations of motion, resolving prior inconsistencies.
• The corrected model reproduces the anomalous magnetothermal resistance observed in experiments by Ong and Krishana.
• Quasiparticles exhibit non-standard cyclotron orbits due to the Dirac-like dispersion near the node, leading to unusual transport responses.
• The theoretical predictions are quantitatively consistent with experimental magnetothermal conductivity data in the superconducting state.
• The results confirm that the d-wave gap's nodal structure and phase inhomogeneity are essential for explaining non-Fermi liquid transport in high-Tc superconductors.