Restoring the Surface Magnetic Gap in MnBi 2 Te 4

The gist The surface magnetic gap in MnBi2Te4 can be restored by tuning the surface electrostatic potential using external electric fields or interfacial fields in van der Waals heterostructures, which enables control of its topology.

Defect-Induced Gap Suppression

Surface defects lower the electrostatic potential of MnBi2Te4, which drives topological surface states into subsurface layers and suppresses exchange interactions, thereby closing the gap The most common and energetically favorable type−Mn–Bi co-antisite defects are considered, specifically configurations SNN and BNN for such defects Upon introducing Mn–Bi co-antisites, the surface gap is notably reduced to 36 meV for SNN and merely 3 meV for BNN Similar behavior is observed for other defects The suppressed electrostatic potential of the Bi layer is identified as the driving force behind the subsurface relocation of the topological states and the resulting gap reduction.

Electric Field-Induced Gap Restoration and Topology Switching

To counteract gap suppression, a strategy is proposed to raise the surface electrostatic potential to drag topological states back to the surface, mitigating magnetic exchange cancellation This can be achieved either through an external vertical electric field or via interfacial electric fields by coupling MnBi2Te4 to polar insulators

1. External Electric Field Application: The study examines three representative forms of electric potential along the surface normal direction (z-axis): a uniform electric field V1, a point-charge-like field V2, and an exponentially decaying field V3.

2. Uniform Field Results: Increasing the potential V0 significantly reopens the magnetic gap; for instance, at V0 = 0.1 V, the surface gap increases to 11 meV, 19 meV, and 24 meV under uniform, point-charge-like, and exponentially decaying electric fields respectively.

3. Field Profile Effects: Faster-decaying fields (e.g., V3) reopen the gap more effectively due to their concentrated impact on the surface and resultant weak bulk-surface coupling.

Interfacial Engineering of the Magnetic Gap

The surface electrostatic potential can also be modulated via interface engineering by placing the material in contact with capping layers A suitable candidate is the layered ferroelectric insulator series In2Te3 with a strong out-of-plane polarization.

**- Downward polarization of In2Te3 accumulates positive charges at the interface, producing a downward electric field in MnBi2Te4 that raises the surface potential and drags the surface states back to the top SL. Conversely, upward polarization accumulates negative interface charges, generating an upward field that lowers the surface potential and pushes the surface state into the second SL. Both cases reopen the magnetic gap, but with distinct magnitudes (21 meV vs 14 meV). The larger gap from downward polarization can be attributed to the rapid decay of the interfacial field in MnBi2Te4, which allows it to pull surface states toward the surface more efficiently than an upward field pushes them into the second SL. Capping MnBi2Te4 with AlOx significantly promotes the quantum anomalous Hall effect, attributed to the enhanced surface magnetic anisotropy by AlOx capping. The resulting gaps from these heterostructures exhibit much larger magnetic gaps than that of the uncapped BNN-defective surface. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The mechanism resembles that of an external electric field. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices. The dependence of the gap topology on the electric field direction underscores the critical importance of field orientation in device design. The required field strengths at the surface (z = 0) are on the order of 107–108 V/m for V0 = 0.1 V, well within the range achievable in modern nanodevices.

1. Restoring surface magnetic gap control through electrostatic potential tuning: The improved AI system can perform tuning the surface potential via external electric fields or interfacial fields in van der Waals heterostructures restores the expected gap and enables control of its topology, allowing for predictive modeling of topological phase switching based on applied field profiles like V1, V2, or V3.

2. Predictive topological phase switching: The system can determine the resulting quantized transport state by analyzing the dependence of the gap topology on the electric field direction, specifically distinguishing between QAHE and an axion insulator based on whether "V0 > 0" leads to zero net AHC or a plateau of e 2/h.

3. Interface engineering optimization: The AI can evaluate capping layer efficacy by predicting which material will most effectively tune the potential, as it can infer that the resulting heterostructures exhibit much larger magnetic gaps [see Fig. 3(b,d)] than that of the uncapped BNN-defective surface based on polarization (e.g., Downward polarization of In2Te3 accumulates positive charges at the interface).

4. Defect-driven gap suppression mechanism identification: The system can correlate structural features with electronic properties by identifying that the suppressed electrostatic potential of the Bi layer is the driving force behind the subsurface relocation of the topological states and the resulting gap reduction.

5. Material-specific predictor development: The AI can develop simpler yet robust predictors, especially for non-polar cappings, addressing the challenge where the required field strengths at the surface (z = 0) are on the order of 10 7–10 8 V/m for V0 = 0.1 V.

A widespread experimental realization of quantized anomalous transport in the intrinsic magnetic topological insulator MnBi 2 Te 4 is hindered by its elusive surface magnetic gap. Uncovering the origin of the gapless states is essential for accessing its topological properties. Here we show that surface defects lower the electrostatic potential, drive topological surface states into subsurface layers, suppress exchange interactions, thereby closing the gap. Tuning the surface electrostatic potential via external electric fields or interfacial fields in van der Waals heterostructures restores the expected gap and enables control of its topology. This is confirmed by model calculations and validated in defective MnBi 2 Te 4 films interfaced with polar insulators, explaining the enhanced quantum anomalous Hall effect under AlO x capping observed in recent experiments. Our theory identifies electrostatically driven surface-state delocalization as a competitive origin of gap suppression and proposes displacement-field engineering for robust quantized transport.