Observation of two fine structures related to the hidden order in the spectral functions of URu${}_2$Si${}_2$

We studied the spectral functions of URu${}_2$Si${}_2$ in the hidden-order state by means of ultrahigh-resolution angle-resolved photoemission spectroscopy. High signal-to-noise ratio data uncover the existence of two anomalous fine structures, namely a “splitting” in the previously reported narrow dispersive band, and a small, dispersionless “satellite” structure. These structures can be explained by neither ordinary bands nor the development of a hybridization of two states; thus our observation should evoke the consideration of complicated many-body effects. As a possible origin, we suggest the existence of electron-mode coupling in the ordered state.

Figure 1

ARPES data of high signal-to-noise ratio measured below the hidden-order transition temperature. (a) Angle-integrated spectra at 7 K obtained from the integration along the $\Gamma$-M direction. (b) Energy-distribution curves (EDCs) near the Fermi level taken for the $\Gamma$-M (or [100]) direction at 7 K. (c) Enlarged picture showing the detail of spectral features in (b). (d) EDCs taken for the $\Gamma$-X direction (or [110]) at 5 K. (d') Enlarged view of the spectra in (d). (e) EDCs taken for the $\Gamma$-X direction (or [110]) at 8 K. (e') Enlarged view of the spectra in (e). Note that EDCs corresponding to $k_{\parallel }$ $=$ 0, 0.03, 0.06, and 0.1 Å${}^{-1}$ are drawn as blue bold lines, and broken lines are guides for the eye.

Figure 2

Polarization dependence of ARPES spectra measured along the $\Gamma$-M direction at 7 K. (a) ARPES intensity maps for circular (circ.), horizontal (hor.), and vertical (ver.) polarizations; see Ref. 30 for the experimental geometry. Note that the location of the hole pocket is indicated by a red dotted line. (b) EDC cuts at $k_{\parallel }$ $=$ 0 Å${}^{-1}$ taken from (a), and spectra are normalized to the intensity at $E_{\mathrm{B}}$ $=$ 5.3 meV. (c) The intensity of the spectra in (b) taken at $E_{\mathrm{B}}$ $=$ 3.1 meV. Note that error bars in (c) are estimated from the intensity at $\pm 0.25$ meV from $E_{\mathrm{B}}$ $=$ 3.1 meV.

Figure 3

Temperature dependence of angle-integrated spectra and their second derivatives. (a) Photoemission spectrum integrated over angles along the $\Gamma$-M (or [100]) direction. (b) The second-derivative spectra corresponding to (a). (c) The bottom panel indicates the energy positions of the main peak and the satellite plotted against temperatures for the $\Gamma$-M direction, and the top panel shows the difference in the energy positions between the main and the satellite. (d) Angle-integrated spectra obtained by the integration along the $\Gamma$-X (or [110]) direction. (e) The second-derivative spectra corresponding to (d). (f) The bottom panel indicates the energy positions plotted against temperature for the $\Gamma$-X direction, and the top panel shows the difference. Note that the intensity of the second-derivative spectra is multiplied by $-1$, and error bars in (c) and (f) are taken to be the step size of the spectra.