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The heavy fermion superconductor URu$_2$Si$_2$ is a candidate for chiral, time-reversal symmetry-breaking superconductivity with a nodal gap structure. Here, we microscopically visualized superconductivity and spatially inhomogeneous ferromagnetism in URu$_2$Si$_2$. We observed linear-$T$ superfluid density, consistent with d-wave pairing symmetries including chiral d-wave, but did not observe the spontaneous magnetization expected for chiral d-wave. Local vortex pinning potentials had either four- or two-fold rotational symmetries with various orientations at different locations. Taken together, these data support a nodal gap structure in URu$_2$Si$_2$ and suggest that chirality either is not present or does not lead to detectable spontaneous magnetization.
To investigate a mysterious superconducting state of URu_2Si_2 embedded in the so-called hidden order state, the lower critical field H_{c1} is precisely determined down to 55 mK for H || a and H || c. For this purpose, the positional dependence of t
At T$_0$ = 17.5 K an exotic phase emerges from a heavy fermion state in {ur}. The nature of this hidden order (HO) phase has so far evaded explanation. Formation of an unknown quasiparticle (QP) structure is believed to be responsible for the massive
We find that in ultraclean heavy-fermion superconductor URu$_2$Si$_2$ ($T_{c0}=1.45$ K) a distinct flux line lattice melting transition with outstanding characters occurs well below the mean-field upper critical fields. We show that a very small numb
In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu$_2$Si$_2$, fully-gappe
When a second-order magnetic phase transition is tuned to zero temperature by a non-thermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these `quantum critical superc