Disorder-Induced Topological Phases in a Two-Dimensional Chern Insulator with Strong Magnetic Disorder

TL;DR

This paper shows that strong magnetic disorder can induce topological phases in a two-dimensional Chern insulator, using a spinful Qi-Wu-Zhang model coupled to classical spins. By combining twisted boundary conditions and the topological Hamiltonian framework, it uncovers a rich m–J phase diagram with Chern numbers C ∈ {0, ±2} and reveals disorder-driven transitions driven not by clean-band inversions but by zeros of the disorder-averaged Green's function and by S-space topology. The study demonstrates robust disorder-induced topology even at arbitrarily large J, analyzes nonlocal self-energy effects, and introduces the S-space Chern number to capture topology across the spin-configuration manifold. These results deepen our understanding of how disorder can generate and stabilize topological phases beyond the clean-limit paradigm, with potential implications for experimental realizations in magnetic or engineered systems.

Abstract

Strong directional disorder in local magnetic moments coupled to a Chern insulator gives rise to topological phases that cannot be continuously connected to the clean limit and are therefore genuinely disorder-driven. We demonstrate this in a spinful Qi-Wu-Zhang model of a two-dimensional Chern insulator coupled to disordered classical spins of unit length. The topological phase diagram is computed numerically using two complementary approaches: twisted boundary conditions and the topological Hamiltonian technique. Our results show that strong disorder can act as a fundamental topological mechanism rather than merely a perturbation. For strong exchange coupling, tuning the mass parameter reveals a transition between phases with different Chern numbers $C$. Remarkably, this transition is driven by zeros, rather than poles, of the disorder-averaged Green's function crossing the chemical potential, and has no analogue in any clean system. We further identify a strong-coupling phase with $C = 0$ that is nonetheless topologically nontrivial, characterized by a distinct Chern number $C^{(\mathrm{S})} \neq 0$ over the manifold of classical spin configurations. This phase is also disorder-driven, as $C^{(\mathrm{S})} = 0$ in the clean limit.

Figures (10)

• Figure 1: Disorder-averaged Chern number (color code) as obtained from TBC approach as function of the mass parameter $m$ and disorder strength $J$. Results obtained for a system with $L_{x} \times L_{y} =10 \times 10$ sites and $N_{\rm conf.} = 50$ disorder configurations. Chemical potential $\mu=0$. See text for discussion of phases I, II, III, IV and the full yellow line.
• Figure 2: Upper panel: Standard deviation of the Chern number $C$ corresponding to the average shown in Fig. \ref{['fig:pd1']}. Lower panel: Disorder-averaged ($N_{\rm conf.}=300$) weight $\langle w_{\rm edge} \rangle$ of the zero-energy (spin-degenerate) chiral eigenstate at the edge sites of same system as in Fig. \ref{['fig:pd1']} but with open boundaries, as function of $m$ and $J$. The total weight summed over all sites is normalized to unity.
• Figure 3: Eigenenergies $\varepsilon$ and localization length $\xi_{\rm loc}$ (color code) of corresponding eigenstates, as function of the disorder strength $J$. Upper panel: $m=0$. Lower panel: $m=1$. $\xi_{\rm loc}$ as obtained from the inverse participation ratio, see text. The energy spectrum is normalized to the maximum eigenenergy $\varepsilon_{\rm max}$ for each $J$ (for $J=0$: $\varepsilon_{\rm max} = 2$ at $m=0$ and $\varepsilon_{\rm max} = 3$ at $m=1$). System size: $L_{x} \times L_{y} =10 \times 10$ sites. $N_{\rm config}=10$. Chemical potential $\mu=0$.
• Figure 4: Topological phase diagram (as in Fig. \ref{['fig:pd1']}) but now obtained from the topological-Hamiltonian approach with disorder self-energy averaged of the BZ. See the color code for the Chern number. Results obtained for a system with $L_{x} \times L_{y} =8 \times 8$ sites with periodic boundary conditions. The disorder-averaged Green's function is obtained for $N_{\rm conf.} = 50$ disorder configurations. Chemical potential $\mu=0$. $\eta=0.01$ in all calculations using the TH approach.
• Figure 5: Imaginary (upper panel) and real part (lower panel) of the retarded (${\boldsymbol k}$-averaged) disorder self-energy at $\omega=0$ for $\alpha = {\rm A}$ as function of $m$ in the range $-1 \le m \le 1$. Red: $J=4$, blue: $J=6$. Results as obtained for a system with $10 \times 10$ sites, and with $N_{\rm conf.} = 200$ disorder configurations. Lorentzian broadening $\eta=0.01$.