Modern Theory for the Orbital Moment in a Superconductor

Abstract

The chiral p-wave superconducting state is comprised of spin triplet Cooper pairs carrying a finite orbital angular momentum. For the case of a periodic lattice, calculating the net magnetisation arising from this orbital component presents a challenge as the circulation operator $\hat{\mathbf{r}}\times \hat{\mathbf{p}}$ is not well defined in the Bloch representation. This difficulty has been overcome in the normal state, for which a modern theory is firmly established. Here, we derive the extension of this normal state approach, generating a theory which is valid for a general superconducting state, and go on to perform model calculations for a chiral p-wave state in Sr${}_2$RuO${}_4$. The results suggest that the magnitude of the elusive edge current in Sr${}_2$RuO${}_4$ is finite, but lies below experimental resolution. This provides a possible solution to the long-standing controversy concerning the gap symmetry of the superconducting state in this material.

References in corpus (10)

• Topological superconductors: a review
• Introduction to topological superconductivity and Majorana fermions
• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Orbital magnetization in periodic insulators
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• Dichroic f-sum rule and the orbital magnetization of crystals
• Frequency and temperature dependence of the anomalous Hall conductivity in a chiral px+ipy superconductor with impurities
• Non-topological nature of the edge current in a chiral p-wave superconductor
• Impurity Induced Polar Kerr Effect in A Chiral p-wave Superconductor
• The Berry curvature of the Bogoliubov quasiparticle Bloch states in the unconventional superconductor Sr${}_2$RuO${}_4$

Cited by in corpus (6)

• Recent progress on superconductors with time-reversal symmetry breaking
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Conserved current of nonconserved quantities
• Magnetization amplification in the interlayer pairing superconductor 4Hb-TaS${}_2$
• Distinguishing $d_{xz}+i{d}_{yz}$ and $d_{x^2-y^2}$ pairing in $S{r}_{2}Ru{O}_4$ by high magnetic field H-T phase diagrams
• Semiclassical theory for the orbital magnetic moment of superconducting quasiparticles