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A growing number of two-dimensional superconductors are being discovered in the family of layered van der Waals (vdW) materials. Due to small sample volume, their characterization has been largely limited to electrical transport measurements. As a consequence, characterization of the diamagnetic response of the superfluid to an applied magnetic field, a defining property of any superconductor, has been lacking. Here, we use a local magnetic probe to directly measure the superfluid response of the tunable, gate-induced superconducting state in MoS$_2$. We find that the backgate changes the superconducting transition temperature non-monotonically whereas the superfluid stiffness at low temperature and the normal state conductivity monotonically increase with backgate voltage. In some devices, we find direct signatures in agreement with a Berezinskii-Kosterlitz-Thouless transition, whereas in others we find a broadened, shallow onset of the superfluid response. We show that the observed behavior is consistent with disorder playing an important role in determining the superconducting properties in superconducting MoS$_2$. Our work demonstrates that magnetic property measurements are within reach for vdW superconductors and reveals that the superfluid response significantly deviates from simple BCS-like behavior.

The valleys in hexagonal two-dimensional systems with broken inversion symmetry carry an intrinsic orbital magnetic moment. Despite this, such systems possess zero net magnetization unless additional symmetries are broken, since the contributions from both valleys cancel. A nonzero net magnetization can be induced through applying both uniaxial strain to break the rotational symmetry of the lattice and an in-plane electric field to break time-reversal symmetry owing to the resulting current. This creates a magnetoelectric effect whose strength is characterized by a magnetoelectric susceptibility, which describes the induced magnetization per unit applied in-plane electric field. Here, we predict the strength of this magnetoelectric susceptibility for Bernal-stacked bilayer graphene as a function of the magnitude and direction of strain, the chemical potential, and the interlayer electric field. We estimate that an orbital magnetization of ~5400 $\mu_{\text{B}}/\mu\text{m}^2$ can be achieved for 1% uniaxial strain and a 10 $\mu\text{A}$ bias current, which is almost three orders of magnitude larger than previously probed experimentally in strained monolayer MoS$_2$. We also identify regimes in which the magnetoelectric susceptibility not only switches sign upon reversal of the interlayer electric field but also in response to small changes in the carrier density. Taking advantage of this reversibility, we further show that it is experimentally feasible to probe the effect using scanning magnetometry., Comment: 12 pages, 8 figures

We report a scanning superconducting quantum interference device (SQUID) microscope in a cryogen-free dilution refrigerator with a base temperature at the sample stage of at least 30 mK. The microscope is rigidly mounted to the mixing chamber plate to optimize thermal anchoring of the sample. The microscope housing fits into the bore of a superconducting vector magnet, and our design accommodates a large number of wires connecting the sample and sensor. Through a combination of vibration isolation in the cryostat and a rigid microscope housing, we achieve relative vibrations between the SQUID and sample that allow us to image with micrometer resolution over a 150 $\mu$m range while the sample stage temperature remains at base temperature. To demonstrate the capabilities of our system, we show images acquired simultaneously of the static magnetic field, magnetic susceptibility, and magnetic fields produced by a current above a superconducting micrometer-scale device.

Solid-state magnetic field sensors are important to both modern electronics and fundamental materials science. Many types of these sensors maintain high sensitivity only in a limited range of temperature and background magnetic field, but Hall-effect sensors are in principle able to operate over a broad range of these conditions. Here, we fabricate and characterize micrometer-scale graphene Hall sensors demonstrating high magnetic field sensitivity from liquid-helium to room temperature and in background magnetic field up to several Tesla. By tuning the charge carrier density with an electrostatic gate, we optimize the magnetic field sensitivity for different working conditions. From measurements of the Hall coefficient and the Hall voltage noise at 1 kHz, we estimate an optimum magnetic field sensitivity of 80 nT Hz$^{-1/2}$ at 4.2 K, 700 nT Hz$^{-1/2}$ at room temperature, and 3 $\mu$T Hz$^{-1/2}$ in 3 T background magnetic field at 4.2 K. Our devices perform competitively with the best existing Hall sensor technologies at room temperature, outperform any Hall sensors reported in the literature at 4.2 K, and demonstrate high sensitivity for the first time in a few Tesla applied magnetic field.

We report a systematic study of thickness-dependent superconductivity and carrier transport properties in exfoliated layered 2H-NbS2. Hall-effect measurements reveal 2H-NbS2 in its normal state to be a p-type metal with hole mobility of 1-3 cm2/Vs. The superconducting transition temperature is found to decrease with thickness. We find that the suppression of superconductivity is due to disorder resulting from the incorporation of atmospheric oxygen and a reduced hole density. Cross-section transmission electron microscope (TEM) imaging reveals a chemical change of NbS2 in ambient conditions, resulting in the formation of amorphous oxide layers sandwiching crystalline layered NbS2. Though few-nm-thick 2H-NbS2 completely converts to amorphous oxide in ambient conditions, PMMA encapsulation prevents further chemical change and preserves superconductivity., Comment: 16 pages, 5 figures