Order Fractionalization and Neutral Fermi Surfaces.
Center for Materials Theory, Physics and Astronomy, Rutgers University
Department of Physics, Royal Holloway University London.
Over the past two decades, research into quantum materials has reverberated
under the impact of new concepts, particularly those of topology and
fractionalization. This talk will discuss the merger of these ideas.
When a spin fractionalizes into a fermion, we argue that the resulting particle
can hybridize or pair with mobile electrons to develop
fractionalized order. This concept enables us to extend the concept of
off-diagonal order to encompass the formation of order parameters
with fractional quantum numbers, and it opens the way to new kinds of
ordered state with novel gapless excitations.
A controlled illustration of this phenomenon is provided by a model which
incorporates a solvable, gapless, Z2 spin liquid - the
"Yao-Lee-Kitaev model" into a Kondo lattice. This model explicitly
exhibits order fractionalization, and in its three dimensional formulation,
undergoes a transition into an order-fractionalized phase with a
Majorana Fermi surface, and a charge $e$, $S=1/2$ order parameter at at
arbitrarily weak Kondo coupling. The broader implications of these
considerations for Quantum Materials with neutral Fermis surfaces will be
- Work done in collaboration with Alexei M. Tsvelik, Brookhaven National
Laboratories, supported by US department of energy grants DE- SC0012704 (AMT) and DE-FG02-99ER45790 (PC).
 Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018).
 Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers
Coleman, arXiv:2112.07781, (2021).
 A solvable 3D Kondo lattice with a neutral Fermi surface, Piers Coleman,
Aaditya Panighri and Alexei Tsvelik, arXiv:2203.04104, (2022).