Gapless state of interacting Majorana fermions in a strain-induced Landau level

TL;DR

This paper investigates a gapless, strongly interacting Majorana fermion state induced by strain in a 2D quantum system, revealing a novel Kitaev spin liquid with fractional quantum Hall-like properties.

Contribution

It demonstrates the existence of a gapless, strongly interacting Majorana fermion state with fixed half-filling, exhibiting complex symmetries and algebraic decay of correlations.

Findings

The state is gapless with ultra-short-ranged spin correlations.

Chirality correlators decay algebraically.

The system behaves like a fractional quantum Hall spin liquid.

Abstract

Mechanical strain can generate a pseudo-magnetic field, and hence Landau levels (LL), for low energy excitations of quantum matter in two dimensions. We study the collective state of the fractionalised Majorana fermions arising from residual generic spin interactions in the central LL, where the projected Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and particle-hole symmetries forbid any bilinear couplings, leading to an intrinsically strongly interacting system; also, they allow the definition of a filling fraction, which is fixed at 1/2. We argue that the resulting many-body state is gapless within our numerical accuracy, implying ultra-short-ranged spin correlations, while chirality correlators decay algebraically. This amounts to a Kitaev `non-Fermi' spin liquid, and shows that interacting Majorana Fermions can exhibit intricate behaviour akin to fractional quantum Hall physics in an insulating magnet.