Universität zu Köln

Uday, Anjana ORCID: 0000-0002-9719-0458 (2025). Superconducting Proximity Effect in Quantum Anomalous Hall Insulators. PhD thesis, Universität zu Köln.

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Abstract

When a thin film of a topological insulator (TI) is doped with magnetic impurities, it can exhibit the quantum anomalous Hall effect (QAHE). This phenomenon emerges from the breaking of time-reversal symmetry (TRS) in a system with strong spin-orbit coupling, resulting in a vanishing longitudinal resistance and a quantized Hall resistance of h/e² (where h is the Planck constant and e is the charge of an electron), even in the absence of an external magnetic field. Such a magnetic topological insulator is called a quantum anomalous Hall insulator (QAHI), where electrical current is carried by one-dimensional (1D) chiral edge states that propagate along the sample boundaries, while the two-dimensional (2D) bulk remains insulating. When superconducting pairing correlations are induced in such a material via the proximity to an s-wave superconductor, the resulting topological superconductivity is predicted to host chiral Majorana edge modes. In a Hall-bar device configuration, where a superconducting strip lies across the full width of a QAHI thin film, a quantized two-terminal conductance of 0.5(e²/h) was proposed as the smoking-gun evidence of the topological superconducting phase associated with a single chiral Majorana mode. This reduction in two-terminal conductance by a factor of two, compared to e²/h observed in a bare QAHI without the superconducting strip, has been experimentally reported. However, the origin of this 0.5(e²/h) conductance feature remains a topic of active debate, as alternative trivial mechanisms have also been proposed. This emphasizes the need for more robust experimental evidence to confirm the superconducting proximity effect in QAHIs. In this thesis, narrow superconducting electrodes of Nb on top of a QAHI thin film are investigated with widths ranging from 160 to 520 nm. By measuring the nonlocal `downstream' resistance with respect to the grounded superconducting electrode, a negative resistance contribution of -400Ω is observed for the narrowest superconducting electrode. This contribution decreases exponentially as the width of the SC increases. This negative nonlocal resistance is attributed to crossed Andreev reflection (CAR) taking place across the superconducting electrode. In the CAR process, an electron in the chiral edge state, arriving at the superconducting electrode with an energy eV smaller than the SC gap Δ, is converted into a hole in the chiral edge state leaving from the SC, carrying a potential of -V. Simultaneously, a Cooper pair is formed in the superconductor. The observation of a negative edge potential, measurable as a negative `downstream' resistance with respect to the grounded SC in our experiment, is a compelling signature of induced superconducting pair correlation in the chiral edge state of the QAHI. Moreover, the characteristic length over which the CAR process is suppressed with increasing the width of the SC is found to be significantly longer than the superconducting coherence length of Nb. This implies that the CAR process is mediated by the superconductivity induced in the QAHI film underneath the Nb electrode, rather than by the Nb superconductor itself. These findings are supported by a detailed Landauer-Büttiker analysis of the experimental set-up, accounting for all possible processes at the SC-QAHI interface, and by KWANT simulations that incorporate charge disorder in the QAHI film, as well as the metallization effects by the superconducting electrode. Having established a reliable method to proximitize a QAHI thin film using a superconducting Nb, the second part of this thesis re-evaluates the 0.5(e²/h) feature in two-terminal conductance measurements. Rather than only characterizing the device's two-terminal conductance, the potentials of all chiral edge states arriving at and leaving from the superconducting Nb electrode are determined in this thesis, providing a comprehensive understanding of the transport through the proximitized QAHI thin film. Two Hall-bar devices were fabricated for this purpose. In the first device, a Nb superconducting electrode spans the full width of the Hall-bar, forming a proximitized QAHI region beneath the SC. The second device serves as a control experiment, where the QAHI film is interrupted underneath the superconducting electrode, creating two separate QAHI Hall-bars connected in series through the Nb electrode. For both devices, a quantized resistance of h/e² is measured across the Nb electrode in a four-terminal configuration when the current flows through the QAHI film. This quantized resistance of h/e² in the four-terminal set-up employed in this thesis corresponds to a two-terminal conductance of 0.5(e²/h) for the device. No difference is observed between the devices with and without a continuous QAHI under the superconducting electrode. This indicates that the 0.5(e²/h) conductance feature is unrelated to chiral Majorana edge mode transport, as the interrupted QAHI in the control device prevents Majorana transmission underneath the superconducting electrode. In addition, the potentials of all chiral edge states arriving at and leaving from the superconducting electrode remain unchanged when the external magnetic field exceeds the upper critical field of Nb, which points to a trivial effect unrelated to (induced) superconductivity. By using the Landauer-Büttiker formalism, the experimental data are shown to be consistent with a model in which the superconductor equilibrates all the chiral edge states arriving at and leaving from the superconducting electrode. Lastly, no negative nonlocal edge potentials are observed in Hall-bar devices with a Nb strip, in contrast to the narrow Nb electrodes studied in the first part of this thesis. This suggests that signatures of the superconducting proximity effect in QAHI thin films are only observable within a length scale comparable to the superconducting coherence length. The findings in this thesis provide critical insights into the chiral edge transport at superconducting electrodes interfaced with QAHIs and prove the existence of the SC proximity effect in QAHIs, offering a foundation for future studies of topological superconductivity, Majorana physics, and the search for non-Abelian zero modes.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Uday, Anjana anjanauday11@gmail.com orcid.org/0000-0002-9719-0458 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-785746
Date:	2025
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute of Physics II
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Experimental solid state physics English Topological insulator English Quantum anomalous Hall insulator English Superconducting proximity effect English Crossed Andreev reflection English UNSPECIFIED English UNSPECIFIED English
Date of oral exam:	18 February 2025
Referee:	Name Academic Title Ando, Yoichi Professor Kurzmann, Annika Professor Rosch, Achim Professor
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/78574