arXiv:2210.13548 · Physical Review Letters

Amorphous and Polycrystalline Routes toward a Chiral Spin Liquid

Adolfo G. Grushin, Cécile Repellin

Published May 2, 2023• 30 citations

Abstract

We show that a chiral spin liquid spontaneously emerges in partially amorphous, polycrystalline, or ion-irradiated Kitaev materials. In these systems, time-reversal symmetry is broken spontaneously due to a nonzero density of plaquettes with an odd number of edges n_{odd}. This mechanism opens a sizable gap, at small n_{odd} compatible with that of typical amorphous materials and polycrystals, and which can alternatively be induced by ion irradiation. We find that the gap is proportional to n_{odd}, saturating at n_{odd}∼40%. Using exact diagonalization, we find that the chiral spin liquid is approximately as stable to Heisenberg interactions as Kitaev's honeycomb spin-liquid model. Our results open up a significant number of noncrystalline systems where chiral spin liquids can emerge without external magnetic fields.

DOI: 10.1103/physrevlett.130.186702

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arXiv:2210.13548 · Physical Review Letters

Amorphous and Polycrystalline Routes toward a Chiral Spin Liquid

Adolfo G. Grushin, Cécile Repellin

Published May 2, 2023• 30 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.130.186702

Related papers

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^\circ

bond rotation that preserves Kitaev bond labels for edge-sharing octahedra and thereby enables exact solvability. These SW-type defects involve odd-sided plaquettes with

\pm π/2

fluxes, but can be created locally. An isolated defect hosts a time-reversal pair of ground-state flux configurations with large net chirality. Certain excitations are also chiral. The chirality manifests in Majorana local Chern marker and in scalar spin chirality, producing electronic orbital magnetization. T-matrix analysis and numerics at finite defect density

n_d

show that defect chiralities generate a topological gap of

11 n_d

protecting a Chern number

C=\pm 1

. Emergent ferromagnetic long range Ising interactions

r^{-γ}

with

2<γ< 3

between defect chiralities lead to a finite temperature

T_c

phase transition into the chiral spin liquid. The

T_c

is proportional to

n_d

and diverges when

γ\rightarrow 2

. We also consider additional solvable impurity potentials and find that

γ

can be reduced to below

2.3

and correspondingly enhance

T_c

. Our results offer applications to 2D Dirac cone systems with a finite density of fluctuating Ising magnetic impurities and to identifying spin liquids with lattice defects.

We study the interplay of competing interactions in spin-

\frac{1}{2}

triangular Heisenberg model through tuning the first- (

{J}_{1}

), second- (

{J}_{2}

), and third-neighbor (

{J}_{3}

) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate

{J}_{2}

and

{J}_{3}

regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the

U(1)

staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the

U(1)

Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero

{J}_{2}

and

{J}_{3}

, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.