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Fractionalized topological d+id superconductivity in the Yao-Lee-Kondo model

Chengzhi Tang, Hong Yao

TL;DR

The work addresses realizing 2D chiral topological superconductivity in a Kondo lattice where conduction electrons couple to a Yao-Lee spin liquid. It employs a perturbatively exact renormalization group analysis in the weak-coupling limit, leveraging the intact $Z_2$ gauge structure to integrate out Majorana spinons and derive an emergent electron-electron interaction that drives a Cooper instability. The leading inter-orbital antiferromagnetic interaction selects topological $d+id$ spin-singlet pairing with Chern number $C=\pm 2$, while the Yao-Lee Majorana sector remains gapless, yielding a fractionalized topological SC* phase; for sufficiently strong Kondo coupling, the system transitions to a heavy Fermi liquid phase with fractionalization (HFL*). The results establish a concrete mechanism for fractionalized topological superconductivity in correlated lattice systems and suggest potential material realizations of Yao-Lee-type spin liquids coupled to itinerant electrons, guiding future experimental searches for SC* and HFL* phases.

Abstract

A conclusive experimental realization of 2D chiral topological superconductivity remains elusive. Here we present a theoretical demonstration that a topological $d+id$ fractionalized superconducting phase (SC*) can emerge in the weak-coupling limit of a Kondo lattice model, where conduction electrons interact with a Yao-Lee spin liquid on the honeycomb lattice (the Yao-Lee-Kondo model). Using a renormalization-group analysis, we show that exchanging Majorana spinons from the Yao-Lee spin liquid generates effective interactions among the conduction electrons and drives a Cooper instability even for arbitrarily weak Kondo coupling. We further find that the induced leading inter-orbital antiferromagnetic interaction selects topological $d+id$ spin-singlet pairing with Chern number $C=\pm 2$. Meanwhile, the Majorana fermions in the Yao-Lee spin liquid remain gapless and deconfined in this regime, so the resulting state is a fractionalized topological $d+id$ superconductor (SC*). For sufficiently strong Kondo coupling, the system instead enters a heavy Fermi liquid phase with fractionalization (HFL*).

Fractionalized topological d+id superconductivity in the Yao-Lee-Kondo model

TL;DR

The work addresses realizing 2D chiral topological superconductivity in a Kondo lattice where conduction electrons couple to a Yao-Lee spin liquid. It employs a perturbatively exact renormalization group analysis in the weak-coupling limit, leveraging the intact gauge structure to integrate out Majorana spinons and derive an emergent electron-electron interaction that drives a Cooper instability. The leading inter-orbital antiferromagnetic interaction selects topological spin-singlet pairing with Chern number , while the Yao-Lee Majorana sector remains gapless, yielding a fractionalized topological SC* phase; for sufficiently strong Kondo coupling, the system transitions to a heavy Fermi liquid phase with fractionalization (HFL*). The results establish a concrete mechanism for fractionalized topological superconductivity in correlated lattice systems and suggest potential material realizations of Yao-Lee-type spin liquids coupled to itinerant electrons, guiding future experimental searches for SC* and HFL* phases.

Abstract

A conclusive experimental realization of 2D chiral topological superconductivity remains elusive. Here we present a theoretical demonstration that a topological fractionalized superconducting phase (SC*) can emerge in the weak-coupling limit of a Kondo lattice model, where conduction electrons interact with a Yao-Lee spin liquid on the honeycomb lattice (the Yao-Lee-Kondo model). Using a renormalization-group analysis, we show that exchanging Majorana spinons from the Yao-Lee spin liquid generates effective interactions among the conduction electrons and drives a Cooper instability even for arbitrarily weak Kondo coupling. We further find that the induced leading inter-orbital antiferromagnetic interaction selects topological spin-singlet pairing with Chern number . Meanwhile, the Majorana fermions in the Yao-Lee spin liquid remain gapless and deconfined in this regime, so the resulting state is a fractionalized topological superconductor (SC*). For sufficiently strong Kondo coupling, the system instead enters a heavy Fermi liquid phase with fractionalization (HFL*).

Paper Structure

This paper contains 2 sections, 34 equations, 4 figures.

Table of Contents

  1. A. The Detailed Derivation of $\delta S^{\mathrm{eff}}_{\mathrm{e-e}}$
  2. B. RG calculation of $e-e$ interaction

Figures (4)

  • Figure 1: (a) A schematic representation of the Yao-Lee-Kondo model on the honeycomb lattice. The first (black) layer represents the conduction electrons, which are Kondo coupled to the Yao-Lee spins residing in the second layer. In the Yao-Lee model, each localized electron carries both spin and orbital indices. (b) Quantum phase diagram of the Yao-Lee-Kondo model. In the weak-coupling regime, the system realizes a topological $d+id$ spin-singlet superconductivity coexisting with an underlying Yao-Lee spin liquid (SC*). At sufficiently strong coupling, a heavy Fermi-liquid phase arises from hybridization between the conduction electrons and Yao-Lee spins while the Yao-Lee orbital moments simultaneously form an underlying a quantum orbital liquid, realizing a fractionalized heavy Fermi liquid (HFL*).
  • Figure 2: Panel (a) represents the bare Kondo interaction. Panels (b), (c), and (d) show the induced Kondo interaction, e-e interaction, and $\chi$-$\chi$ interaction at the one-loop level, respectively. The following conventions are used in the Feynman diagrams: (i) electron propagators are denoted by thick lines with a single arrow; (ii) Majorana propagators are denoted by thin lines with double arrows; and (iii) fast modes to be integrated out are indicated by blue lines and the slow modes are indicated by black lines.
  • Figure 3: The figures present the mean-field results for superconductivity of the conduction electrons. Panels (a) and (b) show the order parameters and energies, respectively, as functions of the interaction strength $J^2/16tK$. Results obtained from three different initial conditions in the self-consistent calculations are displayed, corresponding to nodal $d$ wave SC, $d+id$ SC and $f$ wave SC.
  • Figure :