Author: Kevin Y. Lin
Affiliation: Freshman, Southern University of Science and Technology (SUSTech), Shenzhen, Guangdong, China
Date: July 8, 2025

Background

In Kagome materials with strong spin-orbit coupling and out-of-plane magnetization, spin-polarized Dirac fermions are theoretically possible, analogous to the Haldane model. However, ideal quantum materials are lacking, posing experimental challenges.

Key Findings / Evidence of Quantum-limit Chern Magnet

1. Spin-polarized Dirac Cones with Landau Quantization

  1. Zero-field STM peak shifts linearly with magnetic field due to the Zeeman effect:

    $$ \Delta E = \pm \tfrac{1}{2} g \mu_B B $$

    → Indicates spin-polarized electronic states.

  2. STM ( dI/dV ) maps under high magnetic fields show discrete Landau quantization, revealing:

    • Clear Dirac dispersion
    • Characteristic ( E_n ) vs. ( B ) dependence

  3. ARPES measurements confirm Dirac fermions in the Brillouin Zone.

2. Chern Gap

  1. Landau fan observed in high-bias STM measurements at varying magnetic fields shows two parallel straight lines, revealing a finite Chern gap.

  2. Landau-level fitting formula:

    $$ E_n(B) = \pm \sqrt{\left(\frac{\Delta}{2}\right)^2 + 2 e \hbar v_F^2 |n| B} - \frac{1}{2}g \mu_B B $$

  3. Fitted parameters from experimental data:

    $$ \Delta = 34 \pm 2,\mathrm{meV}, \quad E_D = 130,\mathrm{meV}, \quad v_F = 4.2 \times 10^5,\mathrm{m/s} $$

3. Bulk-Boundary Correspondence and Dissipationless Edge States

  • STM ( dI/dV ) mapping (Fig. 4a) shows localized in-gap edge states at step edges (interfaces between Kagome layers).

  • These topological edge states arise due to the bulk Chern gap:

    $$ n_{\text{edge}} = C $$

    where ( C ) is the Chern number.

  • Low QPI peaks observed in Fourier-transformed STM maps (Fig. 4b) indicate dissipationless propagation of edge modes.

4. Quantum Limit

  1. Low carrier concentration:
    Fermi level is very close to the Dirac point → extremely low carrier density and symmetric electron-hole excitations [PRX 2024].

  2. Discrete and sparse Landau levels are clearly resolved in STM (Fig. 2b), confirming the system is in the quantum limit.

5. Anomalous Hall Effect (AHE)

  • AHE arises due to intrinsic Berry curvature. Empirical relation:

    $$ \rho_{xy}^{\mathrm{AHE}} = \alpha \rho_{xx} + \beta \rho_{xx}^2 + \gamma \rho_{xy}^2 $$

  • Experimental data show strong quadratic dependence → confirms intrinsic mechanism.

  • Theoretical Chern conductivity from Berry curvature:

    $$ \sigma_{xy} = -\frac{e^2}{h} \frac{1}{N} \sum_{n} \int_{\mathrm{BZ}} \frac{d^2k}{(2\pi)^2} f_n(\mathbf{k}) \Omega_n(\mathbf{k}) $$

  • Substituting experimental values:

    • ( \Delta \approx 34,\mathrm{meV} )
    • ( E_D \approx 130,\mathrm{meV} )

    yields:

    $$ \sigma_{xy}^{\mathrm{Berry}} = 0.13, \frac{e^2}{h} $$

    → Consistent with experimentally measured:

    $$ 0.14, \frac{e^2}{h} $$

Research Significance

  • Provides first experimental evidence of a quantum-limit Chern topological magnet.

  • Establishes a complete framework connecting:

    • Bulk Dirac fermions
    • Finite Chern gap
    • Topological edge states
    • Berry curvature transport

  • Paves the way for future quantum material designs and topological electronics.

References

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