🔬 mesoscale physics

Understanding the superconducting proximity effect in semiconductors through quantum oscillations

This paper demonstrates that Shubnikov-de Haas oscillations, analyzed with a method that accounts for superconducting shunting, can successfully characterize the normal-state electronic parameters of buried semiconductor quantum wells beneath various superconducting films, revealing that while interface subbands form, the intrinsic properties of the underlying well remain largely unchanged and its quantum lifetime is preserved or enhanced.

Original authors: Milo Coombs, Teun A. J. van Schijndel, Yu Wu, Jason T. Dong, Yilmaz Gul, Julian Choi, Christopher J. Palmstrøm, Greg P. Mazur

Published 2026-09-02

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CC BY 4.0

Original authors: Milo Coombs, Teun A. J. van Schijndel, Yu Wu, Jason T. Dong, Yilmaz Gul, Julian Choi, Christopher J. Palmstrøm, Greg P. Mazur

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quest to build the next generation of quantum computers, scientists are trying to fuse two very different materials: a superconductor, which conducts electricity with zero resistance, and a semiconductor, which can be switched on and off to process information. When these two are pressed together, they are expected to create a new, exotic state of matter that could host the fragile quantum bits, or qubits, needed for powerful computing. However, a major hurdle has always been that the superconductor acts like a short circuit, hiding the semiconductor's true properties from view. Because the metal layer carries most of the electrical current, researchers have been unable to measure the semiconductor's density, mass, or magnetic response directly while it is still covered by the superconductor. Instead, they have had to guess these values by measuring separate, uncovered samples, a method that often fails because the presence of the metal changes the semiconductor's behavior in subtle but critical ways.

A team of researchers at the University of California, Santa Barbara, and colleagues has now solved this problem by looking at the semiconductor through a different window. They studied a thin layer of indium arsenide, a type of semiconductor, buried beneath films of six different metals, including aluminum, tin, and tantalum. By applying a strong magnetic field and measuring how the electrical resistance changed, they were able to detect faint, rhythmic fluctuations known as quantum oscillations. These oscillations act like a fingerprint, revealing the specific properties of the electrons trapped inside the semiconductor layer, even though the metal film sits directly on top of them. The researchers developed a new way to analyze these signals that accounts for the metal's interference, allowing them to extract the true density, mass, and magnetic sensitivity of the buried semiconductor without ever removing the superconductor.

The study revealed that every metal film creates a new, distinct layer of electrons right at the boundary where the metal meets the semiconductor. This "interface subband" is a separate state of matter that did not exist before the metal was added. The researchers found that these new layers fall into two distinct categories based on the type of metal used. Metals like aluminum and tin create a very dense layer of electrons, while metals like tantalum, niobium, and vanadium create a less dense layer. Surprisingly, the strength of the metal's own magnetic properties or its work function, which usually dictates how it interacts with other materials, could not predict which category a metal would fall into. Instead, the behavior seemed to depend on the specific chemical character of the metal's electrons, with some metals having a "sp" character and others having a "d" character, leading to these two separate classes of interaction.

Perhaps most importantly, the researchers discovered that the buried semiconductor layer itself remained remarkably unchanged by the presence of the metal. The mass of the electrons and their magnetic response, known as the g-factor, stayed exactly the same as they were in the uncovered samples, varying by no more than ten percent. This finding rules out the idea that the metal fundamentally alters the basic nature of the semiconductor's electrons. Furthermore, the metal films did not degrade the quality of the semiconductor; in fact, for the aluminum and tin films, the electrons in the buried layer moved even more freely than they did in the uncovered samples. This suggests that the metal layer actually helps to screen out electrical noise from the environment, making the semiconductor cleaner and more stable.

By measuring how long these electrons could maintain their quantum state before scattering, the team was able to calculate how strongly the semiconductor was coupled to the metal. They found that the buried layer was only weakly connected to the metal, while the new interface layer was much more strongly connected. This distinction is crucial for designing future quantum devices, as it means scientists can tune the interaction between the two materials without destroying the delicate properties of the semiconductor. The study provides the first direct measurements of these normal-state parameters in a hybrid system, offering a solid foundation for building more reliable and predictable quantum computers. By proving that the semiconductor retains its identity beneath the superconductor, the work removes a layer of uncertainty that has long plagued the field, allowing engineers to move forward with confidence in their designs.

Technical Summary: Understanding the superconducting proximity effect in semiconductors through quantum oscillations

Problem Statement
Superconductor–semiconductor hybrids are central to the development of topological superconductivity and hybrid quantum devices. However, characterizing the semiconductor parameters (carrier density, effective mass, g-factor, mobility) within these intact hybrids is notoriously difficult. The superconducting metal film shunts electrical transport, rendering conventional semiconductor characterization methods (such as Hall bar measurements on etched structures) ineffective or physically distinct from the actual coupled system. Removing the metal alters electrostatic boundary conditions, and etching modifies the surface accumulation layer. Consequently, parameters used in theoretical models are often inferred from uncapped "sister" wafers or device spectroscopy, leaving the actual state of the coupled semiconductor to speculation. Tunnelling spectroscopy can measure the induced gap and subgap g-factor but cannot directly measure the underlying normal-state density, mass, or g-factor that these values renormalize.

Methodology
The authors directly measure the semiconductor beneath the superconductor using Shubnikov–de Haas (SdH) quantum oscillations in a buried InAs quantum well (10 nm) capped by an In $_{0.75}$ Ga $_{0.25}$ As barrier (7 nm) and various superconducting films (Al, Sn, V, Nb, Ta, Re).

Sample Preparation: Films were deposited at 7 K to suppress interdiffusion, followed by an in-situ oxidation of a nominal 2.5 nm Al protection layer to prevent parallel superconducting conduction in the cap.
Measurement: Four-terminal magnetotransport was performed on unpatterned material in magnetic fields up to 14 T and temperatures of 1.8–20 K.
Analysis Strategy: In a shunted system, the measured resistance oscillations arise solely from the semiconductor's oscillatory conductivity, while the metal provides a smooth background. The authors developed a specific analysis to account for the "shunt filter" effect. Unlike standard Dingle analysis, which fails for shunted wells because the shunt modifies the amplitude envelope, the authors fit the oscillation amplitude using a model that incorporates the Drude prefactor of the semiconductor's transport mobility ( $\mu_t$ ) and the smooth sheet resistance of the stack. This allows for the extraction of the quantum lifetime ( $\tau_q$ ) and mobility intervals without assuming a specific transport mobility.

Key Results

Interface Subbands: Every metal film induces a new interface subband localized near the metal/InGaAs boundary. The occupation of this subband falls into two distinct classes based on the metal type:
- Refractory metals (Ta, Nb, V, Re): Lower frequency oscillations corresponding to densities of $(5.3–6.5) \times 10^{11}$ cm $^{-2}$ .
- sp-metals (Al, Sn): Higher frequency oscillations corresponding to densities of $(1.2–1.3) \times 10^{12}$ cm $^{-2}$ (approximately five times the density of the buried well).
- The occupation energy does not correlate with the metal work function, suggesting strong pinning at two distinct levels determined by the interface chemistry (e.g., orbital character of the metal states).
Invariance of Buried Well Parameters: Despite the presence of the metal, the fundamental parameters of the buried InAs quantum well remain unchanged:
- Effective Mass ( $m^*$ ): Remains $0.040–0.044 m_e$ (within 10% of the uncapped value) for all metals.
- g-factor: The product $|g_{eff}|m^*$ is invariant, yielding a common $|g_{eff}| = 4.9 \pm 0.2$ for the buried well under all films.
- Quantum Lifetime: No film shortens the quantum lifetime of the buried well compared to uncapped references. Notably, Al and Sn films lengthen the quantum lifetime, likely due to the dense interface subband screening remote charge disorder.
Coupling Bounds: Using the measured quantum lifetimes, the authors place upper bounds on the hybridization rate ( $\Gamma$ ) between the semiconductor states and the metal:
- For interface subbands, $\Gamma$ is bounded to $2–4$ meV (3–10 times the parent superconducting gap $\Delta_0$ ).
- For the buried well, the coupling is significantly weaker. For Al, $\Gamma \le 0.18$ meV; for Ta and Re, $\Gamma \le 0.5–0.6$ meV.
- These bounds imply that the quasiparticle weight $Z$ (renormalization factor) is at least $0.1–0.2$ , meaning the semiconductor retains significant character even when coupled.

Significance and Claims
The paper claims to supply the "normal-state parameters that tunnelling spectroscopy renormalizes but cannot measure." By combining quantum oscillation spectroscopy with tunnelling data, the full low-energy Hamiltonian of the hybrid can be constrained.

Direct Measurement: The study demonstrates that semiconductor parameters can be measured directly in the intact hybrid, avoiding the uncertainties of inferring properties from etched or uncapped structures.
Device Implications: The results indicate that the as-grown stack carries two subbands, which sets the depletion requirements for reaching the odd-channel regime in Majorana constructions. Furthermore, because the superconducting film does not inherently broaden the well (disorder remains unchanged or improves), the coupling strength and level width can be tuned separately.
Generalizability: The authors note that these findings apply specifically to In $_{0.75}$ Ga $_{0.25}$ As barrier stacks, the most widely used platform for InAs 2DEGs, and that the influence of a metal is a property of the complete metal-barrier-well stack, not just the metal itself.

The work provides a rigorous experimental foundation for modeling hybrid devices, moving beyond educated guesswork regarding the semiconductor's state beneath the superconductor.

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