Order Fractionalization in a Kitaev-Kondo model

Abstract

We describe a mechanism for order fractionalization in a two-dimensional Kondo lattice model, in which electrons interact with a gapless spin liquid of Majorana fermions described by the Yao-Lee (YL) model. When the Kondo coupling to the conduction electrons exceeds a critical value, the model develops a superconducting instability into a state where the spinor order parameter carries charge 𝑒 and spin 𝑆 = 1/2. The broken symmetry state develops a gapless Majorana Dirac cone in the bulk. By including an appropriate gauge string, we can show that the charge 𝑒, spinorial order develops off-diagonal long range order that allows electrons to coherently tunnel arbitrarily long distances through the spin liquid.

Kitaev spin-orbital bilayers and their moiré superlattices

“…We study the zero-temperature phase diagram of bilayer versions of Kitaev spin-orbital models, initially proposed by Yao and Lee [20], with additional interlayer Heisenberg spin-exchange interactions. Spin-orbital models are generalizations of the original Kitaev model with extra local orbital degrees of freedom (DOF) and Kugel-Khomskii interactions involving both spin and orbital sectors [21], [20,[22][23][24][25][26][27][28][29][30]. Much like Kitaev's original proposal, spin and orbital DOF can each be represented in terms of three-flavored sets of Majorana fermions.…”

A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization

“…Recent work has hypothesized that hybridization between electrons and fractionalized excitations can give rise to a new kind of fractionalized order with half-integer quantum numbers [19,20]. Our Kondo lattice model provides a rigorous example of this phenomenon.…”

“…Once 𝑇 < 𝑇 𝑐1 the Wilson lines are not only constants of motion, but they are independent of the path between the two sites x and y. We can calculate the gauge invariant quantity in the gauge where 𝑢 (𝑖, 𝑗) = 1 so that 𝑊 = +1, and in this way, we can be sure that the gauge invariant density matrix asymptotically factorizes into a product of well-defined spinor order [20]. In short, once 𝑇 < 𝑇 𝑐1 where the absence of visons guarantees that typical Wilson lines are equal to +1, this fractionalized long-range order is guaranteed to develop.…”

Emergent Spinon Dispersion and Symmetry Breaking in Two-channel Kondo Lattices

“…The fractionalization S αβ ∼ b † α b β or b † α c aα ∼ χ a contraction are related to order parameter fractionalization [11,40]. In the long time/distance limit, correlation functions of b † α c aα and that of χ a are given by Σ χ and G χ , respectively and thus, have exponents that add up to zero.…”