Direct Observation of Geometrical Phase Transitions in Mesoscopic Superconductors by Scanning Tunneling Microscopy

Using scanning tunneling microscopy, we mapped the distribution of the local density of states in a single crystal superconductor heterostructure with an array of submicron normal metal islands. We observe the coexistence of strongly interacting multiquanta vortex lattice with interstitial Abrikosov vortices. The newly formed composite magnetic flux structure undergoes a series of phase transitions between different topological configuration states. The vortex configuration states are strongly dependent on the number of flux quanta and the nanoscale confinement architecture of the mesoscopic superconductor. Here, we present images of vortex phase transitions due to confinement effects when the number of magnetic flux quanta in the system changes. The vortex dynamics in these systems could serve as a model for behavior of confined many-body systems when the number of particles changes.

Figure 1

(a),(b) Scanning electron micrographs (colorized) of the patterned ${\mathrm{NbSe}}_2$ single crystal, and (c),(d) scanning tunneling topography and spectroscopy. (a) Top view of the periodic structure containing a square array of $130\times 130$ islands. The yellow area contains the electroplated gold, and the blue area represents the patterned ${\mathrm{NbSe}}_2$ single crystal. (b) 45° view of the sample’s cross section after performing a cross-sectional cut using FIB. (c) Scanning tunneling microscopy of the patterned ${\mathrm{NbSe}}_2$ single crystal ($2\times 1.4\mu {\mathrm{m}}^2$) at 4.2 K. The red arrow indicates the locations where the tunneling spectroscopy curves shown in (d) were acquired. The scanning tunneling spectroscopy was performed using a $0.2\mathrm{G}\Omega$ junction at 20 mV bias voltage in zero applied magnetic field at 4.2 K. For clarity purposes, the curves are offset vertically by 0.15 a.u. as the tip approached the elliptical island.

Figure 2

Current image tunneling spectroscopy images and schematics of the vortex configurations in a square array of normal metal elliptical holes at matching magnetic fields of (a) $H=0$, (b) $H=5H_0$, (c) $H=8H_0$, and (d) $H=9H_0$, where $H_0$ is the matching field of 8.28 mT. Scanning tunneling spectroscopy images were taken at the ${\mathrm{NbSe}}_2$ superconducting peak energy $E_g=+2.0\mathrm{meV}$ on an area $1.4\times 2.0\mu {\mathrm{m}}^2$ at 4.2 K. Color scale represents regions with enhanced superconductivity (red) and suppressed superconducting order parameter (blue). Yellow ellipses in the schematic images represent the nonsuperconducting elliptical holes containing multiquanta vortices. Blue dots represent single-quanta Abrikosov vortices. The two sublattices form regular configurations at matching fields.

Figure 3

Images of vortex geometrical transitions in the periodic array of pinning centers using current image tunneling spectroscopy (left panels) and corresponding schematic distributions (right panels) on an area of $1.25\times 1.25\mu {\mathrm{m}}^2$ at 4.2 K. The applied magnetic field varies from (a) 82.5 mT, (b) 120 mT to (c) 212.5 mT.