---
title: Granular Aluminium (grAl) Superconductors
url: https://www.emergentmind.com/topics/granular-aluminium-gral
type: topic
---

# Granular Aluminium (grAl) Superconductors

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 [2008.02860] [1407.7467] [2508.03873].

## 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 [2008.02860]. 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 [2508.03873].

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 [2008.02860]. 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 \(60\!-\!73\,\mathrm{nm}\) [2508.03873].

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 [1802.01859]. 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 [1911.02312]. As resistivity increases, the critical temperature first rises above that of pure Al and then decreases. For room-temperature growth, the maximum \(T_c\) is reported as \(2.3\,\mathrm{K}\); for lower-temperature growth around \(100\,\mathrm{K}\), the maximum is \(3.2\)–\(3.25\,\mathrm{K}\) [2008.02860]. Transport work also reports a \(T_c\) peak around \(3.2\,\mathrm{K}\) for liquid-nitrogen-temperature deposition and \(2.2\,\mathrm{K}\) for room-temperature deposition in the resistivity range \(100\)–\(300\,\mu\Omega\,\mathrm{cm}\) [1407.7467].

Two distinct resistivity scales recur in the literature. In STM studies, the “Mott resistivity” is \(\rho_\mathrm{M} \approx 400\,\mu\Omega\,\mathrm{cm}\), near the peak of the superconducting dome; above \(\rho_\mathrm{M}\), local charging effects, in-gap states, and additional low-energy excitations appear on individual grains, while similar films become insulating only later, around \(\rho \approx 10\,\mathrm{m}\Omega\,\mathrm{cm}\) [1911.02312]. By contrast, transport and \(\mu\)SR work identify the metal–insulator transition near \(\rho \approx 50{,}000\,\mu\Omega\,\mathrm{cm}\), where the low-temperature resistivity changes from logarithmic to exponential temperature dependence [1407.7467]. Taken together, these papers distinguish an earlier microscopic crossover toward decoupling from the later macroscopic metal–insulator transition.

The transport/\(\mu\)SR interpretation emphasizes correlations. Free spins are directly observed, with an inferred concentration of about \(350\,\mathrm{ppm}\), and the negative magneto-resistance grows by several orders of magnitude with increasing resistivity, following \(\Delta\rho \propto \rho^{1.38}\) [1407.7467]. Combining this with Hall-effect scaling yields \(m^* \propto \rho^{0.44}\) and an effective Fermi energy \(E_F^* \propto \rho^{-0.7}\); the central claim is that the metal–insulator transition occurs when \(E_F^*\) becomes comparable to the grain charging energy \(U \approx 85\,\mathrm{meV}\), so that the transition is best understood as a granular Mott transition rather than a purely Anderson-localization problem [1407.7467]. A related comparative argument states that grAl approaches a correlation-driven, Mott-like transition, whereas atomically disordered materials such as \(\mathrm{NbN_x}\) approach a disorder-driven Anderson transition with more abundant sub-gap states [2008.02860].

## 3. Superconducting electrodynamics and kinetic inductance

The superconducting utility of grAl derives from its large kinetic inductance. In the dirty limit,
\[
L_{k/\square}=\mu_0\frac{\lambda^2}{t}
\]
and, using the practical dirty-limit relation,
\[
L_{k/\square}=\frac{\hbar \rho_n}{\pi \Delta\, t}=\frac{\hbar R_\square}{\pi \Delta},
\]
with the weak-coupling BCS relation \(2\Delta=3.53\,k_B T_c\) [2008.02860]. A related low-temperature form used for sputtered aluminium-oxide wires is
\[
L_{\mathrm{kin},\square}=0.18\,\frac{\hbar R_{n,\square}}{k_B T_c}.
\]
This resistance-based scaling makes room-temperature sheet resistance a practical design knob for microwave inductance [1408.4347].

At the materials level, grAl can maintain a sharp superconducting transition at very high resistivity. One synthesis paper reports normal-state resistivity of order \(1\times 10^5\,\mu\Omega\cdot\mathrm{cm}\) and expected kinetic inductance of order \(10\,\mathrm{nH}/\square\), with superconductivity still present even when \(R_\square\) exceeds \(h/4e^2 \sim 6.5\,\mathrm{k}\Omega\) [2008.02860]. The same comparison argues that at approximately the same \(R_\square \approx 2000\,\Omega\), grAl resonators exhibit \(Q_i\sim10^5\), whereas \(\mathrm{NbN_x}\) resonators give only \(Q_i\sim10^3\) [2008.02860].

Microwave extraction shows that the resistance formula is not always numerically sufficient for actual coplanar structures. In quarter-wave coplanar resonators fabricated from \(57.5\!-\!73.1\,\mathrm{nm}\) films with \(R^\square\) from \(4.19\) to \(13.75\,\Omega/\square\), Mattis–Bardeen fits to temperature-dependent resonance shifts yield average kinetic-inductance fractions
\[
\bar{\alpha}_1(\mathrm{grAl\!-\!1})=0.201\pm0.001,\quad
\bar{\alpha}_1(\mathrm{grAl\!-\!2})=0.291\pm0.007,\quad
\bar{\alpha}_1(\mathrm{grAl\!-\!3})=0.356\pm0.008,
\]
with extracted effective sheet inductances up to \((6.9\pm0.3)\,\mathrm{pH}/\square\) and total resonator kinetic inductance up to \(1.070\,\mathrm{nH}\) for a \(5\!-\!6\,\mathrm{GHz}\) quarter-wave device [2508.03873]. That work explicitly notes an unresolved discrepancy between microwave-extracted \(L_k^\square\) and simple BCS resistance-based estimates, and therefore emphasizes direct microwave metrology rather than inference from nominal growth parameters alone [2508.03873].

## 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 \(10^{-2}\,\mathrm{Hz}\) to \(10^5\,\mathrm{Hz}\), within an order of magnitude from analytic calculations based on grAl microstructure, while \(Q_i\) remains in the \(10^5\) range [1802.01859]. 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 \(300\,\mu\mathrm{m}\) long grAl superinductor strip with estimated characteristic impedance \(Z \gtrsim 10\,\mathrm{k}\Omega\), first self-resonant mode at \(17.4\,\mathrm{GHz}\), total loop inductance \(225.6\,\mathrm{nH}\), and Ramsey coherence \(T_2^R\) up to \(30\,\mu\mathrm{s}\) [1809.10646]. A separate fluxonium variant replaces the conventional mesoscopic Al/AlO\(_x\)/Al junction with a lithographically defined grAl nano-junction; the resulting “gralmonium” has \(E_J/h = 23.4\,\mathrm{GHz}\), \(E_C/h = 15\,\mathrm{GHz}\), \(L_q = 285\,\mathrm{nH}\), average \(T_1=10\,\mu\mathrm{s}\), and Hahn echo \(T_2^\mathrm{echo}=9\,\mu\mathrm{s}\), while also showing spontaneous jumps of \(E_J\) on timescales from milliseconds to days [2202.01776].

grAl can also supply the nonlinear element of a transmon-like qubit. A \(10\times 200\times 500\,\mathrm{nm}^3\) grAl volume shunted by a thin-film aluminum capacitor yields an anharmonicity \(\alpha = 2\pi \times 4.48\,\mathrm{MHz}\), intrinsic linewidth \(\gamma = 2\pi \times 10\,\mathrm{kHz}\), and an intrinsic lifetime of \(16\,\mu\mathrm{s}\) [1911.02333]. 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 \(100\) times more compact than pure Al, with all-grAl devices reaching \(Q_i = 3.5 \times 10^6\) and hybrid grAl/Ta devices reaching \(Q_i = 4.5 \times 10^6\) [2411.12611]. 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 \(1\,\mathrm{T}\), with \(20\,\mathrm{dB}\) gain, a gain-bandwidth product of \(28\,\mathrm{MHz}\), and \(-110\,\mathrm{dBm}\) input saturation power [2403.10669].

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 \(305\,\mu\mathrm{eV}\), remains resilient for both in-plane and out-of-plane magnetic fields, and allows Zeeman splitting of Yu–Shiba–Rusinov states beyond \(50\,\mu\mathrm{eV}\) (\(12\,\mathrm{GHz}\)), together with \(g\)-tensor tunability [2602.21364]. 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 \(F\delta_{\mathrm{TLS}}\sim 1.5\times10^{-4}\), \(\beta\) close to \(1\), TLS saturation power below one photon, and a non-TLS loss floor corresponding to quality factor limited to roughly \(5\times10^4\) [2508.03873]. 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 [2508.03873].

At lower resistivity, grAl can reach much higher \(Q_i\), but a compactness–coherence trade-off emerges. In lumped-element inductors with sheet inductances from \(30\) to \(320\,\mathrm{pH/sq}\), the measured internal quality factors systematically decrease with increasing room-temperature resistivity for all devices, while the lowest-resistivity films reach \(Q_i = 3.5\times 10^6\) for all-grAl devices and \(Q_i = 4.5\times 10^6\) for hybrid grAl/Ta devices [2411.12611]. 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 [2411.12611].

Close to the superconductor–insulator transition, non-equilibrium quasiparticles become the dominant microwave-loss mechanism. Resonators fabricated from grAl with room-temperature resistivity \(4\times 10^3\,\mu\Omega\cdot\mathrm{cm}\), sheet resistance \(2\,\mathrm{k}\Omega/\square\), thickness \(20\,\mathrm{nm}\), and kinetic inductance fraction close to unity show \(Q_i\) on the order of \(10^5\) in the single-photon regime, with excess quasiparticle density \(x_{\mathrm{qp}} = 5\times 10^{-6}\), quasiparticle bursts every \(\sim 20\,\mathrm{s}\), and relaxation times in the range of \(1\,\mathrm{s}\) [1802.01858]. 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 \(1.2\!-\!1.5\,\mathrm{nH}/\square\) retain single-photon \(Q_i > 10^5\) in in-plane magnetic fields up to \(1\,\mathrm{T}\), with measurements extending to \(1.2\,\mathrm{T}\) [2006.05171]. Small perpendicular fields around \(0.6\,\mathrm{mT}\) can enhance \(Q_i\) by approximately \(15\%\), 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 [2006.05171]. The same experiments reveal a reproducible ESR-related dip with \(g \approx 2.01\), consistent with a spin-\(\tfrac12\) impurity ensemble, possibly in oxide regions between grains [2006.05171].

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

Scanning tunneling spectroscopy shows that grAl is not a uniformly disordered superconductor. Near \(\rho \approx 300\,\mu\Omega\,\mathrm{cm}\), individual grains have an enhanced superconducting gap \(\Delta = 292 \pm 26\,\mu\mathrm{eV}\); above \(\rho_\mathrm{M} \approx 400\,\mu\Omega\,\mathrm{cm}\), grains still show \(\Delta = 309 \pm 23\,\mu\mathrm{eV}\), but spectroscopy also reveals charging thresholds, Coulomb-blockade-like peaks, in-gap states at \(\pm 100\,\mu\mathrm{eV}\) and \(\pm 200\,\mu\mathrm{eV}\), and a secondary gap of approximately \(8\Delta\) with additional low-energy peaks [1911.02312]. 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 [1911.02312].

Independent \(\mu\)SR work directly demonstrates free spins in grAl, with a concentration of about \(350\,\mathrm{ppm}\) in a relatively metallic sample and an inferred interface spin density of about \(10^{16}\,\mathrm{m}^{-2}\) for \(2\,\mathrm{nm}\) grains if the spins are associated with Al/Al\(_2\)O\(_3\) interfaces [1407.7467]. 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 \(4\,\mathrm{K}\), \(\delta G/G \sim 2\%\) and the dip full width at half maximum corresponds to \(\Delta Q \sim 5 \times 10^{11}\,e/\mathrm{cm}^2\) [1206.4978]. Subsequent work demonstrates aging and \(t/t_w\) 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 [1207.1564] [1206.4989]. 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.

Source: https://www.emergentmind.com/topics/granular-aluminium-gral