Doping the chiral spin liquid -- topological superconductor or chiral metal?

TL;DR

This paper explores two distinct chiral spin liquid states on the triangular lattice, their doping-induced conducting states, and how they relate to topological superconductors and quantum criticality.

Contribution

It identifies and characterizes two different chiral spin liquids, CSL1 and CSL2, and analyzes their doping-induced phases, revealing novel scenarios including topological superconductivity and bosonic quantum Hall states.

Findings

Doping CSL2 leads to a topological d+id superconductor.

Doping CSL1 can result in a chiral metal or a bosonic integer quantum Hall state.

The study connects theoretical models with recent numerical results on doped chiral spin liquids.

Abstract

We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $\nu =4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the effect of doping can be accessed by introducing charged holons. On doping CSL2, condensation of charged holons leads to a topological d+id superconductor. However on doping CSL1 , in sharp contrast , two different scenarios can arise: first, if holons condense, a chiral metal with doubled unit cell and finite Hall conductivity is obtained. However, in a second novel scenario, the internal magnetic flux adjusts with doping and holons form a bosonic integer quantum Hall (BIQH) state. Remarkably, the latter phase is identical to a $d+id$ superconductor. In this case the Mott insulator to superconductor transition is associated with a bosonic variant of the integer quantum Hall plateau transition for the holon. We connect the above two scenarios to two recent numerical studies of doped chiral spin liquids on triangular lattice. Our work clarifies the complex relation between topological superconductors, chiral spin liquids and quantum criticality .