Order Fractionalization in a Kitaev-Kondo model I: Introduction to the model. Piers Coleman and Alexei Tsvelik

The phenomenon of fractionalization, in which excitations break-up into

emergent particles with fractional quantum numbers, such as spinons, anyons or

Majorana fermions, well established, and may play an important role in quantum

materials that appear to form neutral Fermi surfaces, such as SmB₆[1],

YbB₁₂[2] and \alpha-RuCl₃[3].  "Order fractionalization" is

conjectured [4] to occur when such fractional quasiparticles pair with

conventional electrons, forming an order parameter fractional quantum numbers.

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 with charge e spinor order. By

including an appropriate gauge string, we can explicitly show that spinorial

order develops off-diagonal long range order.

[1]  B. S. Tan et al, Science 349, 287 (2015).

[2]  Y. Sato et al, Nature Physics 15, 954-959 (2019). 

[3]  P. Czajka et al, Nature Physics 17, 915-919 (2021).

[4]  Y. Komijani et al, arXiv:1811.11115 (2018).