Session H1: Hidden Order in URu2Si2 Revealed by Advanced Spectroscopies

Chirality density wave of the "hidden order" phase in URu2Si2

Many novel electronic ground states have been found to emerge from the hybridization between localized~$d-~$or~$f-$electron states and conduction electron states in correlated electron materials. The heavy fermion compound URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$~exhibits the coexistence of two such ground states: so-called ``hidden order'' (HO) below T$_{\mathrm{HO}}=$17.5 K and superconductivity below T$_{\mathrm{c}}$~$=$1.5 K. Despite 30 years of research the symmetry of the order parameter associated with HO phase below 17.5 K has remained ambiguous. \\ \\Here we report results of polarization resolved Raman spectroscopy study aimed to specify the symmetry of the low energy excitations above and below the HO transition. These excitations involve transitions between interacting heavy uranium~\textit{5f}~orbitals, responsible for the broken symmetry in the HO phase. From the symmetry analysis of the collective mode, we determine that the HO parameter breaks local vertical and diagonal reflection symmetries at the uranium sites, resulting in crystal field states with distinct chiral properties, which order to a commensurate~\textit{chirality density wave}~ground state [1]. We further explore the competition between the HO phase and large moment antiferromagnetic (LMAFM) phase~[2],~and the connection between the HO chirality density wave and the unconventional superconductivity~which has recently been proposed to be of a chiral~$d$-wave type [3].\\ \\1.~H.H.~Kung, R.E. Baumbach, E.D. Bauer, V.K. Thorsmolle, W.L. Zhang, K. Haule, J.A. Mydosh, and G. Blumberg. Chirality density wave of the 'hidden order' phase in URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$. Science,~\textbf{347}, 1339 (2015). \newline 2. K. Haule and G. Kotliar. ~Complex Landau-Ginzburg theory of the hidden order in URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$.~Eur. Phys. Lett.~\textbf{89}, 57006 (2010). \newline 3.~T. Yamashita et al.~Colossal thermomagnetic response in the exotic superconductor URu$_{\mathrm{2}}$Si$_{\mathrm{2}}$.\textbf{~}Nature Phys.~\textbf{11}, 17 (2014).   

Magneto-optical measurements as tests for time-reversal symmetry breaking in the hidden order and superconducting phases of URu$_2$Si$_2$

It is now experimentally well established that the superconducting (SC) phase of URu$_2$Si$_2$ with $T_c$ =1.5K emerges from the hidden order (HO) phase with $T_{HO}$ = 17.5K. Thus, it is of great interest to discern the different symmetries of both phases. In particular, recent theoretical proposals for time-reversal symmetry breaking (TRSB) order parameters of either phases pose the question of whether the HO one drives the SC one, or TRSB appears in the SC phase independently. In this talk we report high resolution polar Kerr effect (PKE) measurements as a function of temperature for several high-quality single crystals of URu$_2$Si$_2$. We find an onset of PKE below the superconducting transition that is consistent with a TRS-breaking order parameter. This effect appears to be independent of an additional, possibly extrinsic, PKE generated in the hidden order phase, and contains structure below Tc suggestive of additional physics within the superconducting state.   

Colossal thermomagnetic response in chiral $d$-wave superconductor URu$_2$Si$_2$

The heavy-fermion compound URu$_2$Si$_2$ exhibits unconventional superconductivity at $T_c$ = 1.45 K deep inside the so-called hidden order phase. An intriguing aspect is that this system has been suggested to be a candidate of a chiral $d$-wave superconductor [1], and possible Weyl-type topological superconducting states have been discussed recently. Here we report on the observation of a highly unusual Nernst signal due to the superconducting fluctuations above $T_c$. The Nernst coefficient is anomalously enhanced (by a factor of $\sim 10^6$) as compared with the theoretically expected value of the Gaussian fluctuations. This colossal Nernst effect intimately reflects the highly unusual superconducting state of URu$_2$Si$_2$. The results invoke possible chiral or Berry-phase fluctuations associated with the broken time-reversal symmetry of the superconducting order parameter [2]. [1]Y. Kasahara et al. Phys. Rev. Lett. 99, 116402 (2007). [2]T. Yamashita et al. Nature Phys. 11, 17 (2015).   

Evidence for preservation of crystallographic four-fold rotational symmetry in hidden order of URu$_{2}$Si$_{2}$

Recent experimental studies have suggested that the four-fold rotational symmetry around the tetragonal c axis is broken in the hidden-ordered state of URu$_{2}$Si$_{2}$ below 17.5 K [1-5]. Those experimental findings give strong constraints on the theoretical arguments, and have provoked discussions on the electric/magnetic ``nematic'' ordering. However, the detected signals that suggest the broken symmetry are extremely weak in magnitude, and thus it is very important to test the reproducibility of the observations. Among the reported experiments, the orthorhombic distortion detected by X-ray diffraction is particularly important, because it may prove the broken rotational symmetry to be a thermodynamic phenomenon. We have performed synchrotron X-ray backscattering measurements of a high-quality single crystal with RRR $>$ 350 with the highest spatial resolution ever achieved. We will present the most reliable evidence for the preservation of crystallographic four-fold rotational symmetry in the hidden-order state. We will also present the tests for reproducibility of magnetic torque measurements, and discuss the intrinsic nature of URu$_{2}$Si$_{2}$. [1] R. Okazaki et al., Science 331, 439 (2011). [2] S. Tonegawa et al., Phys. Rev. Lett. 109, 036401 (2012). [3] S. Kambe et al., Phys. Rev. Lett. 110, 246406 (2013). [4] S. Tonegawa et al., Nat. Commun. 5, 4188 (2014). [5] S. C. Riggs et al., Nat. Commun. 6, 6425 (2015).   

The Optical Phase Diagram of URu$_2$Si$_2$: Effects of Anisotropy, Charge Coherence and Fermi Surface Gapping

URu$_2$Si$_2$ is a heavy fermion with a Kondo temperature of 370 K. Hybridization between heavy $f$ electrons with conduction electrons creates a crossover to a Kondo liquid state having coherent transport properties below 70 K. At 17.5 K, a second-order mean-field transition creates an electronically ordered state, which clear origin remains unknown. The formation of an unconventional superconducting phase below 1.5 K completes the thermal phase diagram. The charged nature of this phase diagram, makes it a fertile ground for optical investigations. Here I discuss the optical properties of the hidden order, the Kondo coherent and the Kondo phases. On the $ab$-plane, an incoherent conductor exists at room temperature. Upon crossing into the Kondo coherent state, a sharp Drude peak develops and narrows quickly upon further cooling. Along the $c$-axis the Drude peak is present at all temperatures and is mostly insensitive to the formation of the coherent Kondo state. When entering the hidden order phase, a 6.5 meV gap opens. It follows a mean-field temperature dependence in the $ab$-plane but remains constant along the $c$-axis where it fills-up rather than close. In parallel, phonons are very sensitive to the Kondo coherence and couple strongly to the electronic continuum. The optical properties of URu$_2$Si$_2$ shows a strongly anisotropic behavior between the $ab$-plane and the $c$-axis.