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[Paper] Local observation of linear-T superfluid density and anomalous vortex dynamics in URu$_2$Si$_2$

日本語/**English**

Our study of local observation of linear-T superfluid density and anomalous vortex dynamics in URu$_2$Si$_2$ was published in Physical Review B, letter section.

(a),(b) Schematic image of scanning isolated vortex field and its dynamics, where the pinning potential is (a) anisotropic or (b) isotropic, by using a scanning SQUID microscope. (c) Locally observed linear-T superfluid density in URu$_2$Si$_2$. Reprinted figure from PRB **103**, L220503 (2021). Copyright 2021, by the American Physical Society.

Chiral superconductivity is an intriguing quantum phenomenon where unconventional superconductors spontaneously develop an angular momentum breaking time-reversal symmetry. It is a non-trivial topological state, which may have spontaneous topological modes at surface or defects, such as chiral edge currents or Majorana zero modes. The observation of the time reversal symmetry breaking or Majorana zero modes have been reported in some superconductors. However no one still reported a decisive evidence for chiral superconductivity.

The heavy fermion superconductor URu$_2$Si$_2$ is a candidate for chiral, time-reversal symmetry-breaking superconductivity with a nodal gap structure. URu$_2$Si$_2$ has been extensively studied to reveal the unconventional superconducting state coexisting the novel hidden order state for a long time. However, the signatures of chirality and nodes appear in some crystals but not in others, raising questions about the true nature of the superconducting state.

Here,
in order to measure spontaneous magnetism, the superfluid density and local
pinning potentials, we imaged the zero-field magnetic flux, the low-field
diamagnetic response, and the dynamics of isolated vortices in URu$_2$Si$_2$ with micron-scale spatial resolution, using scanning superconducting quantum
interference device microscopy. We observed superconductivity and spatially
inhomogeneous ferromagnetism. At non-ferromagnetic area, we observed linear-*T*
superfluid density, consistent with *d*-wave pairing symmetries including
chiral *d*-wave forms, but no spontaneous magnetization expected for
chiral superconductivity. Local vortex pinning potentials had either four- or twofold rotational symmetries with various orientations at different locations. Local superfluid density measurements have shown the linear-*T*
dependence at low temperature, suggesting the *d*-wave pairing symmetries
in URu$_2$Si$_2$. 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.

Title: Local observation of linear-*T* superfluid density and anomalous vortex dynamics in URu$_2$Si$_2$

Authors: **Y. Iguchi**, I. P. Zhang, E. D. Bauer, F. Ronning, J. R. Kirtley, K. A. Moler

Journal: Phys. Rev. B **103**, L220503 (2021).