Granular Aluminium (grAl) Superconductors

• Granular aluminium (grAl) is a superconducting material composed of nanocrystalline Al grains separated by thin oxide barriers, allowing tunable intergrain coupling and resistivity.
• It exhibits high kinetic inductance and acts as an effective Josephson-junction network, making it ideal for quantum circuits such as qubits, resonators, and parametric amplifiers.
• Its unique microstructure enables exploration of metal–insulator transitions, charging effects, and glassy nonequilibrium dynamics, underlining its significance in superconducting research.

Granular aluminium (grAl) is a superconducting aluminium film in which nanocrystalline or nano-scale Al grains are separated by thin aluminum-oxide barriers or embedded in an amorphous $\mathrm{AlO_x}$ matrix. Across a broad resistivity range, it is described as a granular superconductor, an effective Josephson-junction network, a high-kinetic-inductance material, and, in transport work near the metal–insulator transition, a correlated granular electron system. These properties underlie its use in high-impedance resonators, superinductors, qubits, parametric amplifiers, kinetic inductance detectors, and semiconductor–superconductor hybrids, while also linking it to localized spins, charging effects, in-gap states, and glassy nonequilibrium transport (Moshe et al., 2020, Bachar et al., 2014, Ramos et al., 5 Aug 2025).

1. Material definition and microstructure

Granular aluminium is produced by depositing Al in oxygen so that the film does not remain a uniform clean metal. In the formulation used across the literature, it consists of crystalline Al grains separated by thin aluminum-oxide barriers, or of nanometer-scale aluminum grains embedded in an amorphous oxide matrix (Moshe et al., 2020). Oxygen partial pressure and deposition rate tune the intergrain coupling and thus the normal-state resistivity; in sputtered films, the oxygen flow together with deposition rate sets the film resistivity and therefore the superconducting disorder, and measured sheet resistance is more reliable than nominal oxygen percentage because reproducibility versus nominal oxygen percentage is imperfect (Ramos et al., 5 Aug 2025).

The microstructure depends on growth conditions. Room-temperature growth gives typical grain size $\sim 3\,\mathrm{nm}$, whereas lower-temperature growth around $100\,\mathrm{K}$ yields smaller grains, $\sim 2\,\mathrm{nm}$, with a narrower size distribution (Moshe et al., 2020). In sputtered coplanar-resonator films, transmission electron microscopy indicates grain sizes ranging from about $3\,\mathrm{nm}$ to tens of nm, with average size $(6\pm1)\,\mathrm{nm}$, a columnar morphology along the growth direction, and smooth surfaces with rms roughness about $(1.2\pm0.3)\,\mathrm{nm}$, comparable to pure Al; film thicknesses are around $60\!-\!73\,\mathrm{nm}$ (Ramos et al., 5 Aug 2025).

This granular structure is central rather than incidental. Several device papers treat grAl as a three-dimensional network of effective Josephson junctions, and elongated strips are often modeled as effective one-dimensional junction arrays (Maleeva et al., 2018). A plausible implication is that grAl occupies an intermediate position between homogeneous dirty superconductors and lithographically defined Josephson-junction arrays: its disorder is structural and intergranular rather than purely atomic.

2. Disorder tuning, superconducting dome, and correlated-electron regimes

A defining feature of grAl is the tunability of its resistivity over a very wide range, from about $10$ to $10^5\,\mu\Omega\,\mathrm{cm}$ by changing oxygen pressure during deposition (Yang et al., 2019). As resistivity increases, the critical temperature first rises above that of pure Al and then decreases. For room-temperature growth, the maximum $\sim 3\,\mathrm{nm}$0 is reported as $\sim 3\,\mathrm{nm}$1; for lower-temperature growth around $\sim 3\,\mathrm{nm}$2, the maximum is $\sim 3\,\mathrm{nm}$3–$\sim 3\,\mathrm{nm}$4 (Moshe et al., 2020). Transport work also reports a $\sim 3\,\mathrm{nm}$5 peak around $\sim 3\,\mathrm{nm}$6 for liquid-nitrogen-temperature deposition and $\sim 3\,\mathrm{nm}$7 for room-temperature deposition in the resistivity range $\sim 3\,\mathrm{nm}$8–$\sim 3\,\mathrm{nm}$9 (Bachar et al., 2014).

Two distinct resistivity scales recur in the literature. In STM studies, the “Mott resistivity” is $100\,\mathrm{K}$0, near the peak of the superconducting dome; above $100\,\mathrm{K}$1, local charging effects, in-gap states, and additional low-energy excitations appear on individual grains, while similar films become insulating only later, around $100\,\mathrm{K}$2 (Yang et al., 2019). By contrast, transport and $100\,\mathrm{K}$3SR work identify the metal–insulator transition near $100\,\mathrm{K}$4, where the low-temperature resistivity changes from logarithmic to exponential temperature dependence (Bachar et al., 2014). Taken together, these papers distinguish an earlier microscopic crossover toward decoupling from the later macroscopic metal–insulator transition.

The transport/$100\,\mathrm{K}$5SR interpretation emphasizes correlations. Free spins are directly observed, with an inferred concentration of about $100\,\mathrm{K}$6, and the negative magneto-resistance grows by several orders of magnitude with increasing resistivity, following $100\,\mathrm{K}$7 (Bachar et al., 2014). Combining this with Hall-effect scaling yields $100\,\mathrm{K}$8 and an effective Fermi energy $100\,\mathrm{K}$9; the central claim is that the metal–insulator transition occurs when $\sim 2\,\mathrm{nm}$0 becomes comparable to the grain charging energy $\sim 2\,\mathrm{nm}$1, so that the transition is best understood as a granular Mott transition rather than a purely Anderson-localization problem (Bachar et al., 2014). A related comparative argument states that grAl approaches a correlation-driven, Mott-like transition, whereas atomically disordered materials such as $\sim 2\,\mathrm{nm}$2 approach a disorder-driven Anderson transition with more abundant sub-gap states (Moshe et al., 2020).

3. Superconducting electrodynamics and kinetic inductance

The superconducting utility of grAl derives from its large kinetic inductance. In the dirty limit,

$\sim 2\,\mathrm{nm}$3

and, using the practical dirty-limit relation,

$\sim 2\,\mathrm{nm}$4

with the weak-coupling BCS relation $\sim 2\,\mathrm{nm}$5 (Moshe et al., 2020). A related low-temperature form used for sputtered aluminium-oxide wires is

$\sim 2\,\mathrm{nm}$6

This resistance-based scaling makes room-temperature sheet resistance a practical design knob for microwave inductance (Rotzinger et al., 2014).

At the materials level, grAl can maintain a sharp superconducting transition at very high resistivity. One synthesis paper reports normal-state resistivity of order $\sim 2\,\mathrm{nm}$7 and expected kinetic inductance of order $\sim 2\,\mathrm{nm}$8, with superconductivity still present even when $\sim 2\,\mathrm{nm}$9 exceeds $3\,\mathrm{nm}$0 (Moshe et al., 2020). The same comparison argues that at approximately the same $3\,\mathrm{nm}$1, grAl resonators exhibit $3\,\mathrm{nm}$2, whereas $3\,\mathrm{nm}$3 resonators give only $3\,\mathrm{nm}$4 (Moshe et al., 2020).

Microwave extraction shows that the resistance formula is not always numerically sufficient for actual coplanar structures. In quarter-wave coplanar resonators fabricated from $3\,\mathrm{nm}$5 films with $3\,\mathrm{nm}$6 from $3\,\mathrm{nm}$7 to $3\,\mathrm{nm}$8, Mattis–Bardeen fits to temperature-dependent resonance shifts yield average kinetic-inductance fractions

$3\,\mathrm{nm}$9

with extracted effective sheet inductances up to $(6\pm1)\,\mathrm{nm}$0 and total resonator kinetic inductance up to $(6\pm1)\,\mathrm{nm}$1 for a $(6\pm1)\,\mathrm{nm}$2 quarter-wave device (Ramos et al., 5 Aug 2025). That work explicitly notes an unresolved discrepancy between microwave-extracted $(6\pm1)\,\mathrm{nm}$3 and simple BCS resistance-based estimates, and therefore emphasizes direct microwave metrology rather than inference from nominal growth parameters alone (Ramos et al., 5 Aug 2025).

4. Microwave circuits, nonlinear elements, and hybrid platforms

grAl has become a circuit material because it combines large inductance, useful nonlinearity, and fabrication compatibility with Al-based processing. In resonator experiments spanning low GHz frequencies up to the spectral gap, measured self-Kerr coefficients range from $(6\pm1)\,\mathrm{nm}$4 to $(6\pm1)\,\mathrm{nm}$5, within an order of magnitude from analytic calculations based on grAl microstructure, while $(6\pm1)\,\mathrm{nm}$6 remains in the $(6\pm1)\,\mathrm{nm}$7 range (Maleeva et al., 2018). This distributed Josephson-medium description is central to its role in high-impedance circuit quantum electrodynamics.

As a superinductor material, grAl has been implemented in fluxonium. One design uses a $(6\pm1)\,\mathrm{nm}$8 long grAl superinductor strip with estimated characteristic impedance $(6\pm1)\,\mathrm{nm}$9, first self-resonant mode at $(1.2\pm0.3)\,\mathrm{nm}$0, total loop inductance $(1.2\pm0.3)\,\mathrm{nm}$1, and Ramsey coherence $(1.2\pm0.3)\,\mathrm{nm}$2 up to $(1.2\pm0.3)\,\mathrm{nm}$3 (Grünhaupt et al., 2018). A separate fluxonium variant replaces the conventional mesoscopic Al/AlO$(1.2\pm0.3)\,\mathrm{nm}$4/Al junction with a lithographically defined grAl nano-junction; the resulting “gralmonium” has $(1.2\pm0.3)\,\mathrm{nm}$5, $(1.2\pm0.3)\,\mathrm{nm}$6, $(1.2\pm0.3)\,\mathrm{nm}$7, average $(1.2\pm0.3)\,\mathrm{nm}$8, and Hahn echo $(1.2\pm0.3)\,\mathrm{nm}$9, while also showing spontaneous jumps of $60\!-\!73\,\mathrm{nm}$0 on timescales from milliseconds to days (Rieger et al., 2022).

grAl can also supply the nonlinear element of a transmon-like qubit. A $60\!-\!73\,\mathrm{nm}$1 grAl volume shunted by a thin-film aluminum capacitor yields an anharmonicity $60\!-\!73\,\mathrm{nm}$2, intrinsic linewidth $60\!-\!73\,\mathrm{nm}$3, and an intrinsic lifetime of $60\!-\!73\,\mathrm{nm}$4 (Winkel et al., 2019). This establishes that the intrinsic grAl nonlinearity is sufficient for qubit operation.

For passive elements, low-loss lumped inductors made from grAl reach a few nH of inductance in footprints up to $60\!-\!73\,\mathrm{nm}$5 times more compact than pure Al, with all-grAl devices reaching $60\!-\!73\,\mathrm{nm}$6 and hybrid grAl/Ta devices reaching $60\!-\!73\,\mathrm{nm}$7 (Gupta et al., 2024). For active microwave electronics, a non-degenerate grAl parametric amplifier built from two coupled grAl resonators is resilient to in-plane magnetic field up to $60\!-\!73\,\mathrm{nm}$8, with $60\!-\!73\,\mathrm{nm}$9 gain, a gain-bandwidth product of $10$0, and $10$1 input saturation power (Zapata et al., 2024).

The hybrid-device role of grAl extends beyond all-superconducting circuits. Deposited on Ge/SiGe heterostructures, grAl induces a hard superconducting gap with BCS peaks at $10$2, remains resilient for both in-plane and out-of-plane magnetic fields, and allows Zeeman splitting of Yu–Shiba–Rusinov states beyond $10$3 ($10$4), together with $10$5-tensor tunability (Fabris et al., 24 Feb 2026). This suggests that grAl is useful not only as a high-impedance circuit material but also as a parent superconductor for spin-based hybrid devices.

5. Microwave loss, quasiparticles, TLS, and magnetic-field response

Microwave loss in grAl is not governed by a single mechanism across all regimes. In coplanar resonators made from sputtered films with modest sheet resistance, the low-temperature internal quality factor increases with microwave power in a way consistent with TLS saturation. Fits give an average TLS contribution $10$6, $10$7 close to $10$8, TLS saturation power below one photon, and a non-TLS loss floor corresponding to quality factor limited to roughly $10$9 (Ramos et al., 5 Aug 2025). That work does not find a clear systematic trend of TLS loss with kinetic inductance fraction or oxidation level, although it stresses that TLS are intrinsic to the growth process because oxygen is incorporated during deposition (Ramos et al., 5 Aug 2025).

At lower resistivity, grAl can reach much higher $10^5\,\mu\Omega\,\mathrm{cm}$0, but a compactness–coherence trade-off emerges. In lumped-element inductors with sheet inductances from $10^5\,\mu\Omega\,\mathrm{cm}$1 to $10^5\,\mu\Omega\,\mathrm{cm}$2, the measured internal quality factors systematically decrease with increasing room-temperature resistivity for all devices, while the lowest-resistivity films reach $10^5\,\mu\Omega\,\mathrm{cm}$3 for all-grAl devices and $10^5\,\mu\Omega\,\mathrm{cm}$4 for hybrid grAl/Ta devices (Gupta et al., 2024). The loss analysis in that work suggests that the surface loss factor of low-resistivity grAl is similar to that of pure Al, whereas the increasing losses with resistivity could be explained by increasing conductor loss in the grAl film (Gupta et al., 2024).

Close to the superconductor–insulator transition, non-equilibrium quasiparticles become the dominant microwave-loss mechanism. Resonators fabricated from grAl with room-temperature resistivity $10^5\,\mu\Omega\,\mathrm{cm}$5, sheet resistance $10^5\,\mu\Omega\,\mathrm{cm}$6, thickness $10^5\,\mu\Omega\,\mathrm{cm}$7, and kinetic inductance fraction close to unity show $10^5\,\mu\Omega\,\mathrm{cm}$8 on the order of $10^5\,\mu\Omega\,\mathrm{cm}$9 in the single-photon regime, with excess quasiparticle density $\sim 3\,\mathrm{nm}$00, quasiparticle bursts every $\sim 3\,\mathrm{nm}$01, and relaxation times in the range of $\sim 3\,\mathrm{nm}$02 (Grünhaupt et al., 2018). These relaxation times are several orders of magnitude longer than in aluminum films or Josephson-junction superinductances.

Magnetic-field response is strongly anisotropic but can be unusually robust for in-plane fields. grAl resonators with kinetic sheet inductance $\sim 3\,\mathrm{nm}$03 retain single-photon $\sim 3\,\mathrm{nm}$04 in in-plane magnetic fields up to $\sim 3\,\mathrm{nm}$05, with measurements extending to $\sim 3\,\mathrm{nm}$06 (Borisov et al., 2020). Small perpendicular fields around $\sim 3\,\mathrm{nm}$07 can enhance $\sim 3\,\mathrm{nm}$08 by approximately $\sim 3\,\mathrm{nm}$09, possibly because fluxons act as quasiparticle traps, whereas larger perpendicular fields drive the resonator into an irreversible plastic regime dominated by trapped and mobile vortices (Borisov et al., 2020). The same experiments reveal a reproducible ESR-related dip with $\sim 3\,\mathrm{nm}$10, consistent with a spin-$\sim 3\,\mathrm{nm}$11 impurity ensemble, possibly in oxide regions between grains (Borisov et al., 2020).

6. Localized states, spins, charging, and insulating-glass phenomenology

Scanning tunneling spectroscopy shows that grAl is not a uniformly disordered superconductor. Near $\sim 3\,\mathrm{nm}$12, individual grains have an enhanced superconducting gap $\sim 3\,\mathrm{nm}$13; above $\sim 3\,\mathrm{nm}$14, grains still show $\sim 3\,\mathrm{nm}$15, but spectroscopy also reveals charging thresholds, Coulomb-blockade-like peaks, in-gap states at $\sim 3\,\mathrm{nm}$16 and $\sim 3\,\mathrm{nm}$17, and a secondary gap of approximately $\sim 3\,\mathrm{nm}$18 with additional low-energy peaks (Yang et al., 2019). The preferred interpretation is that localized spins in the oxide barrier create Yu–Shiba–Rusinov-like in-gap states on nearby superconducting grains when grains are sufficiently decoupled, while the additional peaks may indicate bosonic excitations of the superconducting order parameter, although that assignment remains unresolved (Yang et al., 2019).

Independent $\sim 3\,\mathrm{nm}$19SR work directly demonstrates free spins in grAl, with a concentration of about $\sim 3\,\mathrm{nm}$20 in a relatively metallic sample and an inferred interface spin density of about $\sim 3\,\mathrm{nm}$21 for $\sim 3\,\mathrm{nm}$22 grains if the spins are associated with Al/Al$\sim 3\,\mathrm{nm}$23O$\sim 3\,\mathrm{nm}$24 interfaces (Bachar et al., 2014). This provides a microscopic basis for spin-flip scattering, magneto-resistance anomalies, and, plausibly, some of the in-gap states and microwave loss channels seen in more resistive films.

On the insulating side, grAl also exhibits electron-glass-like transport. Thin insulating granular Al films show a symmetrical field effect, a conductance dip centered at the equilibration gate voltage, memory, and very slow conductance relaxations; in one representative sample at $\sim 3\,\mathrm{nm}$25, $\sim 3\,\mathrm{nm}$26 and the dip full width at half maximum corresponds to $\sim 3\,\mathrm{nm}$27 (Grenet, 2012). Subsequent work demonstrates aging and $\sim 3\,\mathrm{nm}$28 scaling, and then “true aging,” meaning that the anomalous field-effect relaxation depends on the time elapsed since cooling: the longer this time, the longer it takes for the system to react to a gate-voltage change (Delahaye et al., 2012, Delahaye et al., 2012). These observations place grAl among disordered insulators that display slow nonequilibrium electronic dynamics in addition to superconductivity and high-kinetic-inductance behavior.

Taken together, these results portray grAl as a material system in which superconductivity, granularity, charging energy, localized spins, intergrain tunneling, high kinetic inductance, and nonequilibrium glassy dynamics coexist on experimentally relevant scales. This breadth explains both its utility in quantum devices and the persistent need for direct microwave, spectroscopic, and transport characterization in each processing regime.