Induced superconducting correlations in a quantum anomalous Hall insulator

The study investigates whether superconducting pair correlations can be induced in the one-dimensional chiral edge states of a quantum anomalous Hall insulator (QAHI) via the superconducting proximity effect. Proximitizing such edges is a route to topological superconductivity with non-abelian excitations (e.g., chiral Majorana modes). Prior evidence of induced superconductivity exists for helical edges of 2D topological insulators (via Josephson junctions), and for quantum Hall chiral edges (via crossed Andreev reflection, CAR, and Andreev edge states). However, clear evidence for the superconducting proximity effect in a QAHI has been lacking, in part because QAHIs are insulating in both bulk and surface, complicating Andreev processes. The authors address this gap by designing nonlocal transport measurements across narrow Nb finger electrodes contacting the QAHI edge to detect CAR—where an upstream electron forms a Cooper pair in the superconductor while a hole emerges downstream—manifested as a negative nonlocal (downstream) resistance. The central hypothesis is that observation of CAR across the Nb finger evidences induced superconducting correlations in the QAHI edge/surface, with characteristic CAR length exceeding the intrinsic Nb coherence length if mediated by proximity in the QAHI.

- Induced superconductivity has been demonstrated in helical edge states of 2D topological insulators using Josephson junctions. - In quantum Hall systems, chiral edges exhibit signatures of superconducting correlations via crossed Andreev reflection (CAR) and Andreev edge states, producing negative nonlocal potentials downstream; CAR has even been observed in fractional quantum Hall edges. - For QAHIs (thin Cr/V-doped (Bi,Sb)2Te3 with magnetization-induced surface gap), prior attempts reported Andreev reflection only in metallic regimes of magnetic TI films; in the true QAHI regime clear Andreev signatures were absent, and some device geometries were suboptimal for detecting CAR. - Spin polarization differs between ν=1 quantum Hall and QAHI edges, potentially affecting Andreev processes. Theoretical works predict CAR and interference effects dependent on superconductor width and coherence length, and potential regimes involving topological superconductivity with chiral Majorana edge modes. - Experimental challenges include fragility of the QAHE to current and magnetic field, contribution from vortices (subgap states), and the need for nonlocal measurements without large external magnetic fields.

Materials and devices: - QAHI films: V-doped (Bi,Sb)2Te3 (~8 nm) grown on InP(111)A by MBE at 190 °C, with Bi:Sb beam-equivalent-pressure ratio 1:4 to tune chemical potential into the magnetic gap; capped ex situ with 4 nm Al2O3 by ALD (80 °C). - Device patterning: Hall bars by optical lithography. Superconducting contacts: Nb/Au (45 nm/5 nm) fingers defined by e-beam lithography with widths W_Nb from 160 to 520 nm; normal contacts: Ti/Au (5 nm/45 nm). Al2O3 cap selectively removed before sputtering Nb/Au and Ti/Au in UHV. Devices A–E fabricated on the same wafer; device F on a separate, later wafer. - Geometry: SC finger contacts the sample edge to intercept the chiral edge channel; other contacts Ti/Au with a few-ohm contact resistance. Measurement setup: - Transport measured in a dilution refrigerator at base 17–25 mK with an 8 T superconducting magnet. DC techniques (nanovoltmeters and current source); AC lock-in (3–7 Hz) used for additional checks. SQUID magnetometry characterized film magnetization (~−4 mT near zero field at 2 K). Measurement configurations and definitions: - Chiral edge direction anticlockwise for M>0. Current biased between upstream normal contact and grounded SC finger; downstream voltage V_D measured at a contact located after the SC finger along chiral direction. - Downstream resistance R_D = V_D/I consists of: R_QAHI (≈0 below breakdown), R_Nb,InP (Nb section on InP between film edge and SC pad; zero when Nb is superconducting), R_contact (Nb–QAHI interface/contact contribution in three-terminal setup), and the intrinsic downstream contribution R_D* reflecting CAR/CT. - CAR yields negative R_D (hole potential downstream), while co-tunnelling (CT) yields positive contributions. Suppression of superconductivity in Nb by magnetic field isolates normal-state contributions. Data acquisition and analysis: - Magnetic-field sweeps from 0 to above Nb H_c2 to track R_D(H), separating R_Nb,InP and changes due to CAR/CT. For device A (W_Nb=160 nm), negative R_D observed at low fields; R_D increases and saturates as Nb becomes normal. ΔR_D computed as [R_D(H_c2) − R_D(H>H_c2) − R_Nb,InP], attributed to CAR/CT (with R_QAHI≈0 and R_contact field-independent across H_c2). - I–V characteristics measured to confirm negative slope (R_D<0) at I→0 and to assess breakdown currents; temperature dependence of R_D and four-terminal R_xx measured to link CAR visibility to QAHE dissipationless regime. - Width dependence: Devices with W_Nb from 160 to ~520 nm measured; ΔR_b (same as ΔR_D) extracted per device. Fit of ΔR_b vs W_Nb to exponential ΔR_b = R0 exp(−W_Nb/ξ_CAR) to obtain characteristic CAR length. Simulations: - Quantum transport simulations (KWANT) using a Bogoliubov–de Gennes tight-binding model for a proximitized magnetic TI thin film. Parameters chosen to realize a proximitized topological superconducting (TSC) region under the SC finger (pairing on the top surface, local chemical potential shift). Disorder included (Gaussian, correlation length ~10 nm). Studied electron-to-hole conversion probability as a function of SC finger length L_SC and width W_SC to distinguish regimes: CAR-dominated for narrow fingers (W_SC≲ξ) and chiral Majorana interference for wide fingers (self-averaging to ~0.5 conversion).

- Direct evidence of crossed Andreev reflection (CAR) in a QAHI edge: Negative downstream resistance R_D observed for a narrow Nb finger (device A, W_Nb=160 nm) at low magnetic fields; negative slope in I–V at I→0 robust across magnetic histories. - Quantification for device A: As magnetic field suppresses Nb superconductivity, R_D increases by ~520 Ω. After subtracting the normal-state Nb contribution R_Nb,InP≈120 Ω, the CAR contribution is ΔR_D≈−400 Ω. This corresponds to ~3% of the maximum negative downstream resistance −h/2e^2 expected for 100% CAR. - Temperature dependence: R_D departs from zero below 50 mK, but above ~50 mK the QAHE becomes dissipative (R_xx>0), and the 2D bulk contribution masks CAR; by T≥100 mK, bulk dominates R_D. - Width dependence and characteristic length: Across devices A–E (W_Nb up to ~500 nm), finite negative ΔR_b observed. Fit to ΔR_b = R0 exp(−W_Nb/ξ_CAR) yields R0≈−750 Ω and ξ_CAR≈100 nm. - ξ_CAR greatly exceeds the superconducting coherence length of dirty Nb (~30 nm), implying CAR is mediated by proximity-induced superconductivity in the QAHI beneath the Nb rather than through Nb alone. - Interface quality effects: Device F (W_Nb=160 nm, aged wafer) had larger R_contact (~420 Ω). Despite no sign change in raw R_b, a sizable CAR contribution remained (ΔR_b≈−170 Ω), demonstrating robustness of CAR to poorer contacts. - Consistency check: Verified R_xx − R_D = h/e^2 in wider-finger devices, consistent with Andreev processes whose contributions cancel in this combination. - QAHE fragility: Breakdown currents decrease with magnetic field; negative R_D visible only within the dissipationless QAHE regime at very low temperatures and small bias currents.

The observation of negative nonlocal downstream resistance across a superconducting finger in the QAHI regime demonstrates the presence of induced superconducting pair correlations in the chiral edge/surface. The magnitude and magnetic-field dependence of ΔR_D, together with the exponential suppression with finger width and the extracted characteristic length ξ_CAR≈100 nm, show that the process is not limited by the intrinsic Nb coherence length (~30 nm) but instead involves superconductivity induced in the QAHI beneath the superconductor. This supports the central hypothesis that proximitized QAHI edges can host superconducting correlations necessary for realizing topological superconductivity. Two scenarios can account for the data: (1) a trivial proximitized superconducting region, where CAR dominates for narrow fingers (W_SC<ξ) and Andreev edge-state transport dominates for wide fingers; and (2) a topological superconducting (TSC) region with a single chiral Majorana edge mode, where wide fingers lead to self-averaged electron–hole conversion (R≈0) due to interference of counter-propagating chiral Majorana modes, while narrow fingers allow bulk CAR to dominate (R<0). Quantum transport simulations qualitatively reproduce these regimes, including sensitivity to finger dimensions. The experimentally observed stable dominance of CAR (negative R) for narrow fingers, more robust than naive simulations suggest, indicates additional real-device physics (e.g., vortex-related dissipation channels, disorder averaging, contact specifics) that tip the balance toward hole transmission. Overall, the results provide the clearest evidence to date of proximity-induced superconductivity in a QAHI and establish a platform to explore chiral Majorana modes, interferometry, and non-abelian zero modes using engineered superconducting structures on QAHIs without large external magnetic fields.

The work demonstrates superconducting proximity-induced correlations in a quantum anomalous Hall insulator by detecting crossed Andreev reflection across narrow Nb finger electrodes. Negative downstream resistance and its dependence on magnetic field, temperature, and SC finger width provide quantitative evidence, with a characteristic CAR decay length (~100 nm) far exceeding Nb’s coherence length, implicating proximitized QAHI regions as the CAR mediator. This establishes a practical route to engineer topological superconductivity in QAHIs. Future directions include: designing long, narrow SC fingers to enhance CAR; fabricating geometries enabling controlled interference of chiral Majorana modes (e.g., fingers wide enough to avoid self-averaging); realizing closely spaced SC fingers to form Josephson junctions for injecting and manipulating edge vortices (non-abelian zero modes); systematic control of interface transparency and vortex dynamics; and refined theoretical modeling incorporating dissipation and disorder specific to QAHI devices.

- CAR visibility is restricted to the low-temperature, low-bias regime where the QAHE remains dissipationless (R_xx≈0); above ~50 mK bulk conduction masks CAR. - The three-terminal configuration always includes an unknown contact resistance R_contact, complicating absolute quantification and requiring field-dependent subtraction. - Device-specific disorder and magnetic history affect the magnitude of R_D, introducing variability. - Possible trapped vortices and subgap states in the SC can provide dissipative channels, altering CAR and CT contributions. - Contact/interface quality degrades over time (aging), increasing R_contact and reducing raw negative signal, though ΔR remains detectable. - Simulations are qualitative and use reduced system sizes/parameters; they do not capture all experimental physics (e.g., vortices, long-length self-averaging), limiting direct quantitative comparison. - The study evidences induced superconducting correlations via CAR but does not directly demonstrate chiral Majorana modes; additional interferometric or vortex-based experiments are required.