Evidence for Half-Quantized Chiral Edge Current in a C = 1/2 Parity Anomaly State

A single massive Dirac surface band is predicted to exhibit a half-quantized Hall conductance, a hallmark of the C = 1/2 parity anomaly state in quantum field theory. Experimental signatures of the C = 1/2 parity anomaly state have been observed in semi-magnetic topological insulator (TI) bilayers, yet whether it supports a half-quantized chiral edge current remains elusive. Here, we observe a robust half-quantized Hall conductance plateau in a molecular beam epitaxy (MBE)-grown asymmetric magnetic TI trilayer under specific in-plane magnetic field regimes, corresponding to the C = 1/2 parity anomaly state. Within this state, both nonlocal and nonreciprocal transport signals are greatly enhanced, which we identify as direct evidence for a half-quantized chiral edge current localized at the boundary of the top gapped surface. Our numerical simulations demonstrate that this half-quantized chiral edge channel is the essential carrier of the observed half-quantized Hall conductance plateau, analogous to the quantized chiral edge channel in the C = 1 quantum anomalous Hall state. Our results provide experimental evidence for the half-quantized chiral edge transport in a C = 1/2 parity anomaly state. This work establishes asymmetric magnetic TI trilayers as a platform for probing single Dirac fermion physics and paves the way to explore a series of exciting phenomena in the C = 1/2 parity anomaly state, including the topological magnetoelectric effect and quantized magneto-optical response.

💡 Research Summary

In this work the authors report the experimental realization of a half‑quantized Hall conductance plateau (σxy≈0.5 e²/h) associated with the C = ½ parity‑anomaly state, and they provide direct evidence for a half‑quantized chiral edge current localized at the boundary of the top gapped surface. The material platform consists of an asymmetric magnetic topological‑insulator (TI) trilayer grown by molecular‑beam epitaxy: a 3‑quintuple‑layer (QL) V‑doped (Bi,Sb)₂Te₃ layer, a 6‑QL undoped spacer, and a 3‑QL Cr‑doped (Bi,Sb)₂Te₃ layer. The spacer suppresses inter‑layer exchange so that the two magnetic layers can be tuned independently by an in‑plane magnetic field μ₀Hx.

When μ₀Hx is zero, both magnetic layers are out‑of‑plane, opening gaps on both surfaces and yielding a C = 1 quantum anomalous Hall (QAH) state with σxy≈e²/h. As μ₀Hx is increased, the magnetization of the Cr‑doped bottom layer tilts into the plane while the V‑doped top layer remains out‑of‑plane. Consequently the bottom surface of the central (Bi,Sb)₂Te₃ layer becomes gapless, whereas the top surface stays gapped. In this regime (μ₀Hx,b < |μ₀Hx| < μ₀Hx,t) the Hall conductance settles at σxy≈0.504 e²/h and the longitudinal conductance rises to σxx≈0.67 e²/h, defining the C = ½ parity‑anomaly state. Further increase of μ₀Hx aligns both magnetic layers in‑plane, closing the remaining gap and driving the system into a C = 0 metallic phase.

To probe whether the C = ½ state supports edge transport, the authors performed non‑local resistance measurements. In the QAH regime the non‑local resistances ρ16,34 and ρ16,45 vanish for one magnetization polarity (chiral edge channel propagates clockwise) and become finite for the opposite polarity, reflecting the unidirectional nature of the edge mode. In the C = ½ state a similar polarity dependence is observed, but the non‑local signals are markedly larger. This enhancement is interpreted as the half‑quantized edge channel hybridizing with dissipative currents on the gapless bottom surface, forcing current to flow through the side surfaces to satisfy charge conservation. The polarity‑dependent non‑local response disappears in the C = 0 metallic regime, where bulk conduction dominates.

Complementary direct‑current (DC) measurements reveal a pronounced non‑reciprocal behavior in the C = ½ state. By applying a 10 nA DC bias and measuring the longitudinal resistance on the left and right edges (ρxx,L and ρxx,R), the authors find that reversing the magnetization direction changes the edge resistance by ~800–1000 Ω, violating Onsager reciprocity. This non‑reciprocity stems from the reversal of the half‑quantized chiral edge channel, which scatters carriers asymmetrically along a given edge. In contrast, the QAH state shows only a tiny (~30 Ω) difference, consistent with residual inelastic edge channels, and the metallic state shows no non‑reciprocity.

Theoretical support is provided by a four‑band effective 3D TI Hamiltonian with Zeeman terms on the top and bottom surfaces. By varying the Zeeman field according to the experimental μ₀Hx, the simulations reproduce the sequence of Hall conductances (C = 1 → C = ½ → C = 0), the spatial distribution of chiral currents confined to the sample boundaries, and the quantized number of edge channels (Nc = 1 for QAH, Nc = ½ for the parity‑anomaly state). The calculations also show that the C = ½ state remains metallic, with dephasing stabilizing the half‑quantized Hall response, in stark contrast to the fully gapped QAH plateau.

Overall, the paper establishes three key advances: (i) asymmetric magnetic TI trilayers provide a robust, tunable platform for the C = ½ parity‑anomaly state; (ii) half‑quantized chiral edge transport is directly observed via enhanced non‑local and non‑reciprocal DC signals; and (iii) quantitative agreement between experiment and realistic band‑structure simulations confirms that the half‑quantized edge channel is the essential carrier of the observed σxy≈0.5 e²/h plateau. These results open pathways to explore exotic phenomena tied to the parity anomaly, such as the topological magnetoelectric effect, quantized magneto‑optical responses, and novel magnetoelectric devices based on single‑Dirac‑fermion physics.