ARPES/STM study of the surface terminations and $5f$-electron character in ${\mathrm{URu}}_2{\mathrm{Si}}_2$

Hidden order in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ has remained a mystery that is now entering its fourth decade. The importance of resolving the nature of the hidden order has stimulated extensive research. Here we present a detailed characterization of different surface terminations in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ by angle-resolved photoemission spectroscopy, in conjunction with scanning tunneling spectroscopy and dynamical mean-field theory calculations that may unveil a piece of this puzzle. The U-terminated surface is characterized by an electronlike band around the $\overline{X}$ point, while a holelike band characterizes the Si-terminated surface. We also investigate the temperature evolution of the electronic structure around the $\overline{X}$ point from 11 up to 70 K, and do not observe any abrupt change of the electronic structure around the coherence temperature (55 K). The $f$ spectral weight gradually weakens upon increasing temperature; still some $f$ spectral weight can be found above this temperature. Our results suggest that surface terminations in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ are an important issue to be taken into account in future work.

Figure 1

(a) Crystal structure of ${\mathrm{URu}}_2{\mathrm{Si}}_2$. Possible cleaving planes are marked in gray. (b) LEED patterns of the cleaved surface measured at 82 K. (c) Temperature dependence of the electrical resistivity. (d) Dc-magnetic susceptibility $\chi$($T$) measured in the magnetic field of 0.1 T parallel to the $c$ axis. (e) Temperature dependence of the specific heat. (f) Brillouin zone of the bulk ${\mathrm{URu}}_2{\mathrm{Si}}_2$, and the projected (001) surface Brillouin zone are marked in blue

Figure 2

ARPES characterization of different surface terminations in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ at 82 K. (a) ARPES data of the U-terminated surface. (b) ARPES data of the Si-terminated surface. The data were taken along the $\overline{\mathrm{\Gamma }}-\overline{X}$ direction at 82 K. For the meaning of the symbols, see the main text.

Figure 3

Band structure of the U- and Si-terminated surfaces measured at 82 K. (a) Calculated band structure of the U-terminated surface. (b) Photoemission intensity map of the U-terminated surface at $E_F$ integrated over a window of ($E_F-10$ meV, $E_F+10$ meV). (c) Low-energy band structure around the $\overline{\mathrm{\Gamma }}$ point along cut 1. (d) Momentum distribution curves (MDCs) around the $\overline{X}$ point along cut 1 near the Fermi level. (e) Low-energy band structure around the $\overline{\mathrm{\Gamma }}$ point along cut 2. (f)–(j) Same as (a)–(e), but for the Si-terminated surface.

Figure 4

STM topography and spectroscopy on ${\mathrm{URu}}_2{\mathrm{Si}}_2$ at 4.5 K. (a),(b) Constant current topographic image (20 mV, 60 pA) over a (a) $300\times 300{\mathrm{nm}}^2$ and (b) $50\times 50{\mathrm{nm}}^2$ area of the U-dominated surfaces. (c) The relative heights between U- and Si-terminated surfaces in (b). (d) Averaged electronic density of states (DOS) of the U-terminated surface. (e),(f) Constant current topographic image (20 mV, 60 pA) over a (e) $300\times 300{\mathrm{nm}}^2$ and (f) $40\times 40{\mathrm{nm}}^2$ area of the Si-dominated surfaces. (g) The relative heights between the U and Si surfaces in (f). (h) Averaged electronic density of states (DOS) of the Si-terminated surface. (i) The relative heights between the U-terminated surfaces in (a). (j) Schematic diagram illustrating the height of different layers in ${\mathrm{URu}}_2{\mathrm{Si}}_2$.

Figure 5

(a) Temperature dependence of the band structure around the $\overline{X}$ point. (b) Spectra in (a) after dividing by the Fermi-Dirac function convolved with a Gaussian function representing the instrumental resolution to remove the thermal-broadening contribution. (c) Temperature dependence of the EDCs around the $\overline{X}$ point in (a). (d) Temperature dependence of the EDCs around the $\overline{X}$ point in (b).