Introduction

Abstract

One of the most fundamental issues in the research of condensed matter physics is the phase transition phenomenon characterized by the spontaneous symmetry breaking. The heavy-fermion superconductor $\mathrm{URu}_{2}\mathrm{Si}_{2}$ exhibits the so-called “hidden-order” phase transition at $T_{0} = 17.5\,\mathrm{K}$, whose order parameter remains to be clarified despite the past quarter-century study. Here, through the precise magnetic torque measurement, we show that an in-plane magnetic anisotropy with broken four-fold rotational symmetry in tetragonal crystal structure of $\mathrm{URu}_{2}\mathrm{Si}_{2}$ emerges below $T_{0}$. In addition, we study the superconducting transition at $T_c = 1.4\,\mathrm{K}$, which occurs within the hidden-order phase. The local magnetization measurement precisely determines the lower critical field, which strongly depends on the superconducting gap symmetry. We also show the magnetotransport study on the superconducting phase of $\mathrm{URu}_{2}\mathrm{Si}_{2}$, providing an essential clue to understand the quasiparticle dynamics in the periodic vortex lattice. In this chapter, we will briefly overview the content of this book.