Magnetic texture modulated superconductivity in superconductor/ferromagnet shells of semiconductor nanowires

This study demonstrates that superconductivity in full-shell InAs/EuS/Al nanowires is exclusively induced by the multi-domain magnetic texture of the EuS shell, enabling the reconfigurable and position-dependent control of superconducting regions via small external magnetic fields, which holds promise for applications in topological qubits and superconducting logic.

The Gist

Imagine a tiny, one-dimensional wire made of three layers, like a microscopic candy cane. The core is a semiconductor, the middle layer is a magnet (EuS), and the outer shell is a superconductor (Aluminum).

Usually, magnets and superconductors don't get along. If you put a strong magnet next to a superconductor, the magnet's "push" (called a Zeeman field) usually kills the superconductivity, stopping electricity from flowing without any resistance.

The Big Discovery
This paper found a clever loophole. The researchers discovered that superconductivity doesn't just disappear everywhere in the wire; it survives in specific "safe zones" created by the magnet's internal structure.

Think of the magnet layer not as a single, solid block of magnetism, but like a crowd of people holding signs.

• The "Saturated" State: If you push the magnet hard enough, everyone in the crowd points their sign in the exact same direction (North). This creates a strong, uniform magnetic field that kills the superconductivity completely. The wire becomes a normal, resistive wire.
• The "Multi-Domain" State: If you relax the magnetic push, the crowd splits up. Some people point North, others point South. These groups are called "domains."
  • The Safe Zone: Where a "North" group meets a "South" group, there is a boundary called a domain wall. At this exact boundary, the magnetic push cancels out. It's like a peace treaty zone where the fighting stops.
  • The Result: In these calm, neutral zones (either at the boundaries or in a mix of tiny North/South groups), the superconductivity wakes up and starts flowing again.

What They Did
The team used two main tools to watch this happen:

1. A Super-Sensitive Magnet Camera (SQUID): This allowed them to take pictures of the magnetic "signs" inside the wire. They saw that when the wire was in a "multi-domain" state, the magnetic signs were mixed up. When they pushed the wire into a single direction, the signs all lined up.
2. Electrical Testing: They measured the wire's resistance. They found that the wire only became a superconductor (zero resistance) when the magnet was in that mixed-up, multi-domain state. As soon as they forced the magnet to line up perfectly (single domain), the superconductivity vanished.

The "Magic" Control Knob
The most exciting part is that they can move these "safe zones" around.

• By making tiny, almost invisible changes to the external magnetic field (less than the strength of a fridge magnet), they could push a specific boundary (a domain wall) along the wire.
• They found that for every tiny bit of magnetic push, the boundary moved about 5.5 micrometers (roughly the width of a human hair).
• The Analogy: Imagine a train track where the "superconducting train" can only run on a specific, short stretch of track. The researchers found a way to slide that stretch of track back and forth along the wire just by turning a dial slightly.

Why It Matters (According to the Paper)
The authors suggest that because you can move these superconducting "safe zones" around with magnetic fields, this could be useful for:

• Topological qubits: A type of building block for future quantum computers.
• Andreev spin qubits: Another type of quantum bit that uses electron spin.
• Superconducting logic and memory: Creating switches or memory devices that work without generating heat.

In short, the paper shows that by playing with the magnetic "texture" of a nanowire, you can turn superconductivity on and off and move it around like a spotlight, all without needing to change the temperature or the physical structure of the wire.

Technical Summary

Technical Summary: Magnetic Texture Modulated Superconductivity in Superconductor/Ferromagnet Shells of Semiconductor Nanowires

Problem and Context
Hybrid semiconductor nanowires with epitaxial superconducting shells (specifically InAs/Al) serve as a versatile platform for quantum devices, including the search for Majorana bound states and Andreev spin qubits. However, integrating ferromagnetic layers (such as EuS) to induce Zeeman shifts for creating exotic topological states often suppresses superconductivity due to the strong exchange field. Theoretical models suggest that superconductivity might survive in such hybrid systems only where the Zeeman field is locally suppressed. Two primary mechanisms are proposed:

1. Domain Wall Superconductivity (DWS): Superconductivity surviving near magnetic domain walls (MDWs) where the net magnetization is zero.
2. Multi-Domain-Averaged Superconductivity (MDAS): Superconductivity surviving in multi-domain states where individual domains are smaller than the superconducting coherence length ($\xi$), causing the net magnetization to average to nearly zero over that length scale.

While DWS has been observed in quasi-2D heterostructures, its manifestation in full-shell nanowires and the interplay with the specific magnetic texture of the ferromagnet remained unexplored.

Methodology
The authors investigated full-shell InAs nanowires coated with epitaxial bilayers of EuS (3–10 nm) and Al (4–10 nm). The study employed a dual-approach methodology:

• Scanning SQUID Magnetometry: Used to image the stray magnetic fields and domain textures of the EuS shell at 4.2 K. The SQUID measured the out-of-plane magnetic flux, allowing for the visualization of domain nucleation, propagation, and annihilation as external axial magnetic fields ($H_a$) were swept through hysteresis loops.
• Transport Measurements: Four-probe differential resistance ($dV/dI$) measurements were conducted at 30 mK to probe the superconducting state of the Al shell. These measurements were performed on specific segments of the nanowires while sweeping the magnetic field magnitude and angle relative to the wire axis.

Key Results

1. Correlation between Magnetic Texture and Superconductivity:

   • Superconductivity in the Al shell was observed exclusively when the EuS layer was in a multi-domain state. This state occurred after zero-field cooling and within the coercive field window.
   • In the saturated single-domain state (achieved at high fields), superconductivity was completely suppressed due to the large effective Zeeman field.
   • The superconducting window in transport data (characterized by reduced resistance at low bias) tracked the coercive field region of the EuS hysteresis loop, disappearing once the magnetization saturated.

2. Magnetic Texture Dynamics:

   • Scanning SQUID imaging revealed that the EuS magnetic texture is position-dependent and reconfigurable.
   • Near the coercive field ($H_c \approx -3.5$ mT), a single, well-defined domain wall forms. This domain wall can be moved along the nanowire with a displacement rate of approximately 5.5 µm/mT using sub-mT changes in the external field.
   • The coercive field window and the saturation field shift to higher values and broaden as the angle of the applied magnetic field relative to the nanowire axis increases.

3. Mechanism Identification (DWS vs. MDAS):

   • The authors could not definitively distinguish between DWS and MDAS due to the spatial resolution limits of the SQUID ($\approx 1$ µm) compared to the nanowire segments used for transport ($\approx 700$ nm).
   • However, the data supports both scenarios:
     • In zero-field states dominated by micron-scale domains, resistance drops were modest, suggesting superconductivity is confined to small regions near domain walls (DWS).
     • In the coercive window, where extended near-zero magnetization regions and complex multi-domain textures appear, resistance drops were significantly larger, suggesting a larger fraction of the wire is superconducting, potentially involving both DWS and MDAS.
   • The observed hysteretic, non-periodic field dependence rules out alternative explanations like the Little-Parks effect.

Significance and Claims
The paper establishes that superconductivity in full-shell InAs/EuS/Al nanowires is not merely suppressed by ferromagnetism but is modulated by the magnetic texture of the ferromagnetic shell. The key finding is that superconductivity re-emerges specifically in multi-domain configurations where the Zeeman field is averaged out or locally cancelled.

The authors claim that this system offers a platform for spatially controllable superconductivity. Because the magnetic domain walls can be moved with micron-scale precision using small external fields, the associated superconducting regions (whether DWS or MDAS) are similarly movable. The paper suggests this capability could be useful for:

• Topological qubits and Andreev spin qubits (by enabling phase control without external fields).
• Superconducting logic and memory devices (utilizing the reconfigurable nature of the superconducting phase).
• Josephson transistors (specifically referencing theoretical proposals where mobile domain walls in Josephson weak links could control the superconducting diode effect).

The work provides experimental evidence linking the coercive field of EuS to the survival of superconductivity in the Al shell, offering a new degree of freedom for engineering quantum states in hybrid nanowire devices.