Response of a mesoscopic superconducting disk to perpendicular magnetic fields is studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the disk are measured simultaneously. This allows us for the first experimental distinction between the giant vortex states and multivortex states. Moreover, we experimentally find magnetic field induced rearrangement and combination of vortices. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg-Landau theory.The appearance of vortices in various quantum systems, such as superconductors, superfluids and BoseEinstein condensates, is an intriguing phenomenon in nature. A conventional quantum vortex is singly quantized, having a core where the value of the order parameter decreases to zero, while its phase changes by 2π when encircling the core. Recently, an important breakthrough was established by the observation of doubly quantized vortex lines in superfluid 3 He-A[1]. For superconductors expectations are even more spectacular. In macroscopic type-II superconductors a triangular lattice of single flux quanta is formed, whereas two kinds of fundamentally new vortex states have theoretically been predicted in mesoscopic superconductors where the sample size approaches the size of Cooper-pairs [2,3,4,5]; (i) multivortex states (MVSs) with a unique spatial arrangement of singly quantized vortices, and (ii) multiply quantized or giant vortex states (GVSs) with a single core in the center [6,7].Although several experimental techniques have been developed for observing these novel states [7,8,9,10,11,12,13], none of them has been able to make a clear distinction between MVSs and GVSs. In this Letter, we present the first experimental evidence for the existence of GVSs and MVSs in a circular disk, and demonstrate magnetic-field induced MVS-GVS and MVS-MVS transitions. Our results are in good agreement with the theoretical prediction based on the nonlinear GinzburgLandau (G-L) theory.Here we used the multiple-small-tunnel-junction (MSTJ) method, in which several small tunnel junctions with high tunnel resistance are attached to a mesoscopic superconductor to simultaneously detect small changes in the local density of states (LDOS) under the junctions [14,15]. Since the LDOS depends on the local supercurrent density, the MSTJ method gives us information on the distribution of the supercurrent, which reflects the detailed vortex structure inside the disk. Figure 1 shows a schematic drawing and a scanning electron microscopy (SEM) image of the sample. Four normal-metal (Cu) leads are connected to the periphery of the superconducting Al disk through highly resistive small tunnel junctions, A, B, C, and D. The sample is designed to be symmetrical with respect to the central axis SS ′ . The angles AOD and BOC are 120 and 32 degrees, respectively. Although junctions A and D and junctions B and C ideally have the same area and tunnel resistance, small differences actu...

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A method for inducing nonuniform strain in graphene films is developed. Pillars made of a dielectric material (electron beam resist) are placed between graphene and the substrate, and graphene sections between pillars are attached to the substrate. The strength and spatial pattern of the strain can be controlled by the size and separation of the pillars. Application of strain is confirmed by Raman spectroscopy as well as from scanning electron microscopy (SEM) images. From SEM images, the maximum stretch of the graphene film reaches about 20%. This technique can be applied to the formation of band gaps in graphene.Comment: Appl. Phys. Express, in pres

We report low-temperature carrier transport properties of a series of nominally uncompensated neutron-transmutation-doped 70 Ge:Ga samples very close to the critical concentration Nc for the metal-insulator transition. The nine samples closest to Nc have Ga concentrations N in the range 0.99Nc < N < 1.01Nc. The electrical conductivity σ has been measured in the temperature range T = 0.02 − 1 K. On the metallic side of the transition the standard σ(T ) = a + bT q with q = 1/2 was observed for all the samples except for the two that are closest to Nc with N between Nc and 1.0015Nc. These samples clearly show q = 1/3.An extrapolation technique has been developed in order to obtain the zero-temperature conductivity σ(0) from σ(T ) with different dependence on T . Based on the analysis, ν ≈ 0.5 in the familiar form of σ(0) ∝ (N/Nc − 1) ν has been found. On the insulating side of the transition, variable range hopping resistivity ρ(T ) ∝ exp(T0/T ) p with p = 1/2 has been observed for all the samples having N < 0.991Nc. In this regime T0 ∝ (1 − N/Nc) α with α ≈ 1 as N → Nc. The values of T0 agree very well with theoretical estimates based on the modified Efros and Shklovskii relation kBT0 ≈ (2.8e 2 /4πǫ0κ0ξ0)(1 − N/Nc) α , where κ0 and ξ0 are the dielectric constant and the Bohr radius, respectively. The insulating samples very close to the transition (0.991Nc < N < Nc) exhibit quite a different behavior. In this range 1/p increases rapidly as N changes from 0.991Nc to Nc. The relevance of our findings to the collapsing of the Coulomb gap is discussed.

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