Observation of multiple-gap structure in hidden order state of URu${}_{2}$Si${}_{2}$ from optical conductivity

Observation of multiple-gap structure in hidden order state of URu $_{2}$ Si $_{2}$ from optical conductivity

Jesse S. Hall, Urmas Nagel, Taaniel Uleksin, Toomas Rõõm, Travis Williams, Graeme Luke, and Thomas Timusk

Phys. Rev. B 86, 035132 – Published 20 July 2012

Abstract

We have measured the far-infrared reflectance of the heavy-fermion compound URu $_{2}$ Si $_{2}$ through the phase transition at $T_{HO} = 17.5$ K dubbed “hidden order” with light polarized along both the $a$ and $c$ axes of the tetragonal structure. The optical conductivity allows the formation of the hidden order gap to be investigated in detail. We find that both the conductivity and the gap structure are anisotropic, and that the c-axis conductivity shows evidence for a double gap structure, with $Δ_{1, c} = 2.7$ meV and $Δ_{2, c} = 1.8$ meV, respectively, at 4 K, while the gap seen in the $a$ -axis conductivity has a value of $Δ_{a} = 3.2$ meV at 4 K. The opening of the gaps does not follow the behavior expected from mean-field theory in the vicinity of the transition.

Received 26 March 2012

DOI:https://doi.org/10.1103/PhysRevB.86.035132

Authors & Affiliations

Jesse S. Hall¹, Urmas Nagel², Taaniel Uleksin², Toomas Rõõm², Travis Williams¹, Graeme Luke^1,3, and Thomas Timusk^1,3

¹Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada
²National Institute of Chemical Physics and Biophysics, Akadeemia tee 23, 12618 Tallinn, Estonia
³The Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada

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Vol. 86, Iss. 3 — 15 July 2012

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Images

Figure 1
Relative reflectance of the sample for light polarized along the $a$ (top) and $c$ (bottom) axes. The reflected spectrum $R (T)$ is measured at 20 K and then at one of the temperatures indicated, and the ratio $R (T) / R (20 K)$ is constructed by dividing the reflectance at the temperature of interest by the reflectance at the reference temperature. The sample is held stationary during the measurements so there is little noise.Reuse & Permissions
Figure 2
Absolute reflectance measured in the $a b$ plane from the far infrared to the ultraviolet. The shoulderlike features at 380 and 1200 meV correspond to interband transitions. The partial hybridization gap appears in the 25 K spectrum as a drop in the reflectance between 15 and 30 meV. The hidden order gap opening causes a strong absorption centered around 5 meV, visible in the 25 K spectrum.Reuse & Permissions
Figure 3
(a) Absolute reflectance in the $a$ axis at 25 K, with the polynomial fit (red line) to smooth out geometrical artifacts introduced during motion of the sample. The same procedure was used for the $c$ axis (not shown). (b) Refined reflectance along the $a$ axis, obtained by multiplying the measured reflectance ratios $R (T) / R (25 K)$ by the fit to the absolute reflectance at 25 K. (c) Refined reflectance along the $c$ axis. At the lowest temperatures, additional structure appears within the absorption around the minimum near 5 meV.Reuse & Permissions
Figure 4
Real part of the optical conductivity of the $a$ (top) and $c$ (bottom) axes for selected temperatures above and below the hidden order transition at 17.5 K. The arrow in the lower panel shows the position of the second gap at lower temperatures. The dashed lines at low frequency indicate the Drude peak that has been extrapolated to agree with dc conductivity measurements.Reuse & Permissions
Figure 5
Fits of a Dynes $s$ -wave model for the density of states to the optical conductivity for the $a$ (top) and $c$ (bottom) axes for selected temperatures in the hidden order state. The dashed lines at low energy indicate the Drude model extrapolation, the solid lines are the measured conductivity, and the circles indicate the conductivity calculated on the basis of the $s$ -wave model. Above the cutoff energy exact agreement is not expected since the details of the band structure are not taken into account in the fitting process.Reuse & Permissions
Figure 6
The gap value as a function of temperature for the $a$ -axis (top) and the larger $c$ -axis gap (bottom). Solid lines are guides to the eye to show the trend of the gap values. Insets show the behavior expected from a mean-field BCS model from which the data deviates at temperatures close to the transition; at lower temperatures the behavior is closer to mean-field theory. The smaller $c$ -axis gap is nearly constant to within our sensitivity and is not shown. Error bars are determined from the largest change of gap value that can be made to agree with the data if the other parameters in the model are varied.Reuse & Permissions

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