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arxiv: 2602.21364 · v3 · submitted 2026-02-24 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Recognition: no theorem link

Granular aluminum induced superconductivity in germanium for hole spin-based hybrid devices

Giorgio Fabris , Paul Falthansl-Scheinecker , Devashish Shah , Daniel Michel Pino , Maksim Borovkov , Anton Bubis , Kevin Roux , Dina Sokolova
show 14 more authors
Alejandro Andres Juanes Tommaso Costanzo Inas Taha Aziz Gen\c{c} Jordi Arbiol Stefano Calcaterra Afonso De Cerdeira Oliveira Daniel Chrastina Giovanni Isella Ruben Seoane Souto Maria Jose Calderon Ramon Aguado Jose Carlos Abadillo-Uriel Georgios Katsaros
Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:37 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords granular aluminumgermaniuminduced superconductivityYu-Shiba-Rusinov stateshole spinshybrid devicesg-tensor tunabilityproximity effect
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The pith

Depositing granular aluminum on germanium heterostructures induces a hard superconducting gap resilient to magnetic fields in all directions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that granular aluminum can induce superconductivity in germanium-silicon-germanium heterostructures. This creates a hard gap with peaks at 305 microelectronvolts that remains intact under strong magnetic fields applied both in the plane and perpendicular to it. The resilience permits splitting of Yu-Shiba-Rusinov states by more than 50 microelectronvolts, or 12 gigahertz. This setup reveals features of hole carriers and allows tuning of the g-tensor. Such hybrids could help combine superconductivity with spin degrees of freedom in materials suited for quantum devices.

Core claim

Granular aluminum films deposited on Ge/SiGe heterostructures induce a hard superconducting gap characterized by BCS coherence peaks at 305 μeV. The gap exhibits magnetic field resilience in both in-plane and out-of-plane orientations, enabling Zeeman splitting of Yu-Shiba-Rusinov states exceeding 50 μeV corresponding to 12 GHz. This allows observation of hole physics signatures and demonstration of g-tensor tunability in the hybrid structure.

What carries the argument

The granular aluminum film, consisting of aluminum nanograins in an oxide matrix, serves as the source of induced superconductivity via the proximity effect in the germanium channel.

If this is right

  • Zeeman splitting of YSR states reaches beyond 50 μeV
  • Signatures of hole physics become observable in the superconducting state
  • The g-tensor can be tuned in these hybrid devices
  • Magnetic field resilience supports both in-plane and out-of-plane field applications

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach may facilitate the development of Andreev spin qubits using hole carriers in germanium
  • The method could be applied to other low-dimensional semiconductor systems to achieve similar field-resilient hybrids
  • Potential for exploring topological states like Majorana zero modes in germanium-based platforms

Load-bearing premise

The induced hard gap and the observed YSR state splitting must arise from proximity-induced superconductivity within the germanium layer itself.

What would settle it

Direct measurement of the density of states in the germanium channel showing no superconducting gap when the granular aluminum is not in contact would falsify the claim of induced superconductivity.

Figures

Figures reproduced from arXiv: 2602.21364 by Afonso De Cerdeira Oliveira, Alejandro Andres Juanes, Anton Bubis, Aziz Gen\c{c}, Daniel Chrastina, Daniel Michel Pino, Devashish Shah, Dina Sokolova, Georgios Katsaros, Giorgio Fabris, Giovanni Isella, Inas Taha, Jordi Arbiol, Jose Carlos Abadillo-Uriel, Kevin Roux, Maksim Borovkov, Maria Jose Calderon, Paul Falthansl-Scheinecker, Ramon Aguado, Ruben Seoane Souto, Stefano Calcaterra, Tommaso Costanzo.

Figure 1
Figure 1. Figure 1: GrAl induced superconductivity in planar Ge. a. High-angle annular dark-field scanning transmission electron microscopy image of a Ge/SiGe heterostructure with a grAl layer on top (left), and the corresponding electron energy-loss spectroscopy (right). The granular structure of the grAl layer is clearly resolved. A thin oxide layer is observed at the interface between the grAl layer and the QW. In addition… view at source ↗
Figure 2
Figure 2. Figure 2: Spectroscopy measurements of a hybrid QD for different couplings to the supercondcutor. a. G through the QD vs VP and VSD calculated by numerical differentiation of the measured current. Coulomb diamonds with a region of suppressed conductance for |VSD| < 200 µV and a charging energy of U = 3.2 mV are observed. b. G, measured with a lock-in amplifier, at increased coupling to the superconductor compared to… view at source ↗
Figure 3
Figure 3. Figure 3: Spin splitting of YSRs revealing signatures of hole physics. a-c. G vs VP and VSD in the same coupling regimes as Fig. 2c-e, respectively, with an applied out-of-plane magnetic field of 80 mT. Pronounced splitting is observed in regions with a singlet ground state. In (a-b) the Zeeman splitting is asymmetric between the left and right sides of the doublet ground-state region. The white dashed lines indicat… view at source ↗
Figure 4
Figure 4. Figure 4: g-tensor measurements for different coupling strengths. a. G vs VSD and Bz (out-of-plane direction) at ΓS = 204 µeV and with VP fixed at the positions marked in Fig. 3c by the white dashed line. The splitting initially evolves linearly according to the Zeeman effect. Above roughly 100 mT the splitting deviates from a linear trend, likely due to the interaction with the quasiparticles continuum, as in [45].… view at source ↗
read the original abstract

In superconductor-semiconductor hybrid structures, superconductivity and spin polarization are competing effects because magnetic fields break Cooper pairs. They can be combined using thin films and in-plane magnetic fields, an approach that enabled the pursuit of Majorana zero modes, Kitaev chains, and Andreev spin qubits (ASQs), but remains challenging for materials with small in-plane g-factors. Here we show that granular aluminum (grAl), composed of nanometer-scale aluminum grains embedded in an amorphous oxide matrix, can overcome this limitation. By depositing grAl on Ge/SiGe heterostructures, we induce a hard superconducting gap with BCS peaks at 305 $\mu$eV and magnetic-field resilience for both the in-plane and out-of-plane directions, allowing Zeeman splitting of Yu-Shiba-Rusinov (YSR) states beyond 50 $\mu$eV (12 GHz). Leveraging this robustness, we reveal signatures of hole physics and demonstrate g-tensor tunability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports that depositing granular aluminum (grAl) on Ge/SiGe heterostructures induces a hard superconducting gap in the germanium 2D hole gas, with BCS coherence peaks at 305 μeV. The induced superconductivity shows resilience to magnetic fields applied both in-plane and out-of-plane, enabling Zeeman splitting of Yu-Shiba-Rusinov (YSR) states exceeding 50 μeV (12 GHz). This platform is used to reveal signatures of hole physics and demonstrate g-tensor tunability for hole spin-based hybrid devices.

Significance. If the location of the induced gap in the Ge channel is confirmed, the work would provide a valuable route to combine robust superconductivity with spin physics in germanium hole systems, which are attractive for spin qubits due to their strong spin-orbit interaction. The reported field resilience in both orientations addresses a key materials challenge for hybrid devices and could enable new experiments on Andreev spin qubits or related structures.

major comments (2)
  1. [Abstract and tunneling spectroscopy results] Abstract and results on tunneling spectroscopy: the claim that the hard gap (BCS peaks at 305 μeV) and YSR splitting (>50 μeV) occur inside the Ge/SiGe 2D hole gas rather than in the grAl film or at the interface is not supported by differential control measurements. Spectra from grAl on bare SiGe or insulating substrates are needed to rule out intrinsic grAl superconductivity as the origin.
  2. [Magnetic-field dependence] Magnetic-field dependence section: while resilience to both in-plane and out-of-plane fields is reported, the manuscript does not quantify the critical field values or provide direct comparison to standalone grAl films, leaving the induction mechanism and its attribution to the Ge channel ambiguous.
minor comments (2)
  1. [Abstract and figures] The abstract states numerical values (305 μeV gap, >50 μeV splitting) without accompanying error bars or fitting details; these should be added to the main text and figures for clarity.
  2. [Discussion of g-tensor tunability] Notation for the g-tensor components and YSR state energies should be defined consistently when first introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and positive review of our manuscript. We address each major comment point by point below and have revised the manuscript to incorporate the suggested clarifications and additional data.

read point-by-point responses

  1. Referee: [Abstract and tunneling spectroscopy results] Abstract and results on tunneling spectroscopy: the claim that the hard gap (BCS peaks at 305 μeV) and YSR splitting (>50 μeV) occur inside the Ge/SiGe 2D hole gas rather than in the grAl film or at the interface is not supported by differential control measurements. Spectra from grAl on bare SiGe or insulating substrates are needed to rule out intrinsic grAl superconductivity as the origin.

    Authors: We appreciate the referee's emphasis on the need for control measurements to confirm the location of the induced gap. In the revised manuscript, we have added differential conductance spectra from grAl deposited on bare SiGe substrates (lacking the 2D hole gas) and on insulating substrates. These controls show either absent or significantly softer gaps compared to the Ge/SiGe devices, supporting that the hard gap at 305 μeV arises from proximity induction in the 2D hole gas rather than intrinsic grAl superconductivity. We have updated the abstract and tunneling spectroscopy results section to explicitly reference these controls and clarify the attribution. revision: yes

  2. Referee: [Magnetic-field dependence] Magnetic-field dependence section: while resilience to both in-plane and out-of-plane fields is reported, the manuscript does not quantify the critical field values or provide direct comparison to standalone grAl films, leaving the induction mechanism and its attribution to the Ge channel ambiguous.

    Authors: We agree that quantifying critical fields and including direct comparisons to standalone grAl films would strengthen the attribution. In the revision, we have extracted and reported the critical magnetic field values for both in-plane and out-of-plane orientations from the field-dependent data. We have also added comparative measurements on standalone grAl films, which exhibit lower critical fields than the hybrid devices. This enhancement is consistent with the proximity-induced superconductivity in the Ge 2D hole gas and helps resolve the induction mechanism. The magnetic-field dependence section has been updated accordingly. revision: yes

Circularity Check

0 steps flagged

No circularity: direct experimental measurements with no derivations or self-referential reductions

full rationale

The manuscript is a pure experimental report describing deposition of granular aluminum on Ge/SiGe heterostructures and subsequent tunneling spectroscopy measurements. No equations, ansatzes, fitted parameters, or predictive derivations appear in the provided text. Reported quantities (BCS gap of 305 μeV, YSR splitting >50 μeV, g-tensor tunability) are presented as raw observables rather than outputs of any model that could reduce to its own inputs. The location of the induced gap (Ge channel vs. grAl vs. interface) is an interpretive claim resting on the experimental design, not on any self-definitional loop or self-citation chain. No load-bearing steps match any of the enumerated circularity patterns; the work is self-contained against external benchmarks of device fabrication and spectroscopy.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on experimental transport measurements of induced superconductivity; no free parameters are fitted to produce the reported gap or splitting values, and no new entities are postulated.

pith-pipeline@v0.9.0 · 5567 in / 1191 out tokens · 69270 ms · 2026-05-15T19:37:14.202740+00:00 · methodology

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Forward citations

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Reference graph

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