Disorder‐Induced Quantum Griffiths Singularity Revealed in an Artificial 2D Superconducting System

Abstract Disorder‐induced Griffiths singularity of quantum phase transition (QPT) is a crucial issue in 2D superconductors (2DSC). In a superconducting system, the strength of disorder is found to be associated with the vortex pinning energy, which is closely related to the quantum Griffiths singularity; however, a direct study to elucidate the role of vortex pinning energy on the quantum Griffiths singularity in 2DSC remains to be undertaken. Here, an artificial 2DSC system is designed by randomly depositing superconducting nanoislands on 2Delectron gas (2DEG). Quantum Griffiths singularity is present in a graphene/Pb‐islands‐array hybrid, where the superconducting behavior transits to weakly localized metallic behavior induced by the vertical magnetic field and exhibits critical behavior with a diverging dynamical critical exponent approaching zero temperature. Compared to the study of graphene/Sn‐islands‐array hybrid where the sharp QPT is observed, the vortex pinning energy acquired from the Arrhenius plot analysis is greater in graphene/Pb‐islands‐array hybrid, which may contribute to the presence of the quantum Griffiths singularity. This work may provide a comprehensive interpretation of the QPT in 2DSC.


Device fabrication
Monolayer single-crystalline graphene was synthesized on the hydrogen-terminated intrinsic Ge (110) surfaces via an atmospheric pressure chemical vapour deposition (CVD). The chamber was first evacuated to high vacuum and then aerated by a mixture gas of Ar and H 2 to atmospheric pressure. Afterwards, the chamber was heated to 916 o C and kept at that temperature during the growth progress with a mixture gas of CH 4 , Ar, and H 2 for 300 min. Finally, the chamber was quickly cooled to room temperature under the protection of H 2 and Ar.
The Hall bar device was fabricated as follows: firstly, 10 nm Ti/100 nm Au electrode pattern was deposited utilizing a Hall bar stencil mask 1. Then, the graphene except the channel region was etched by oxygen plasma aligned with the stencil mask 2. Finally, 20-nm-thick Pb was deposited by electron beam evaporation very slowly to the channel region of the Hall bar device using the designed stencil mask 3.

Transport measurements.
The temperature and magnetic field dependent resistance was measured by a physical property measurement system (PPMS-9T, Quantum Design). Ultralow temperature was reached in an He 3 -He 4 dilution refrigerator (Quantum Design) equipped with a heat capacity cable/RF filter box to eliminate stray RF currents.

The estimation of coherence length.
The superconducting coherence length is estimated by the standard linearized Ginzburg-Landau (GL) theory, [1] i.e., (0) is the zero-temperature GL in-plane coherence length and ∅ 0 = 2.07 × 10 −15 Wb is the magnetic flux quantum. 2,⊥ is defined as the 90% resistance of the normal state just above the onset. From the slope of the linear fitting, we can derive that the zero-temperature GL in-plane coherence length for graphene/Pb-islands-array hybrid and graphene/Sn-islands-array hybrid are ~37 nm and ~41 nm. The data near T c diverges from the linear fit because the 2D superconductivity corresponding to the second superconducting transition region emerges.

Arrhenius plot analysis and TAFF region.
The Arrhenius plot is often used to study the thermally activated flux flow ( Raman spectra shows a sharp 2D peak and G peak at 2680 cm -1 , 1580 cm -1 separately.
The high ratio of 2D/G being ~1.7 and the absence of D peak near 1300 cm -1 indicate that the single-crystalline monolayer graphene is obtained.

Figure S16
Extracted upper critical magnetic fields 2,⊥ defined as the 90% resistance of the normal state as a function of temperature. The pink dots extracted from graphene/Pb-islands-array hybrid in the main text and the blue dots extracted from graphene/Sn-islands-array hybrid [2] . The dash curves are fit using 2D Ginzburg-Landau equation expressed as 2,⊥ = ∅ 0 2 (0) 2 (1 − ), where (0) is the zero-temperature GL in-plane coherence length and ∅ 0 is the magnetic flux quantum.
16 Figure S17. The comparison of the surface topographies. SEM images of graphene/Pb-islands-array hybrid (a) and graphene/Sn-islands-array hybrid (b) (image selected from ref.
2). In graphene/Pb-islands-array hybrid, there are considerable amounts of tiny scattering islands with only few nanometers surrounding the core islands, which rarely exist in graphene/Sn-islands-array hybrid. Figure S18. Phase diagram of graphene/Sn-islands-array hybrid (data collected from ref. 2). The superconducting dome exhibits a sharp transition at zero temperature as circled by the red line, which is quite different from our obversation in graphene/Pb-islands-array hybrid with quantum Griffiths singularity.