Far-Infrared Absorption Spectra of Thick Superconducting Films

Abstract

We have examined the absorption spectra of thick evaporated films of Pb, Sn, In, V, Ta, and Nb in the superconductive energy-gap region by a calorimetric detection technique. The intensity available from our far-infrared monochromator, together with the improved sensitivity of the detection system, made it possible to employ modulation techniques to obtain the derivatives of the absorption spectra of our samples. Multiple energy gaps were found for a Sn film and two thick Pb films, while a thinner Pb film and the other samples had single gaps. We suggest that these are the first far-infrared measurements to reveal multiple absorption edges in films. The energy gaps found for the two thick Pb films were (4.18±0.04)&r c and (4.46±0.04)&r c for one, and (4.28±0.04)£r c and (4.65:4=0.04) &r c for the other. For the Sn film, the gaps were (3.58=b0.02)&r c and (3.86=b0.04)j&r c . The gaps found for the other samples, in units of kT c , were: for the thin Pb film, 4.34±0.02; for In, 3.69±0.04; for V, 3.4±0.1; for Ta, 3.5d=0.2; and for Nb, 3.6db0.2. These values are more precise than the earlier far-infrared results; in addition, the anomalously low values of ~3k T c obtained in previous far-infrared experiments for the Ta and Nb gaps are not reproduced in this work. The observed absorption edges are steeper than those predicted by either the extreme local or extreme anomalous limits of skin-effect theory. The energy gap of a thick Pb sample was measured as a function of magnetic field, this being the first such measurement by far-infrared calorimetric techniques. The gap was found to decrease by approximately 7% in going from zero field to the critical field for the bulk material (H C b), in fair agreement with the Ginzburg-Landau theory. No gap was observed above H C b, in agreement with previous observations on the superconducting surface sheath.

Influence of scattering on optical response of superconductivity

“…By further decreasing ω below 2∆ 0 , due to the fast increase of σ 1n (ω) in Eq. ( 32), a significant upturn of σ 1s (ω), exhibiting ω −2 growth, is observed, in qualitative agreement with the experimental findings [9][10][11][12][13][14][15][16][17][18][19][20] .…”

“…Moreover, as mentioned in the introduction, the MB theory derived from anomalous-skin-effect region is excessively used in the literature 10,11,[13][14][15][16][17][18][19][20] to fit the experimental data in the normal-skin-effect region where the scattering effect dominates. Nevertheless, as shown by the dotted curve in Fig.…”

“…1, at low temperature, when ω < 2∆ 0 , σ 1s (ω) from MB theory derived at the anomalousskin-effect region, which comes from the quasiparticle contribution 21 , is too small in comparison with the finite experimental observation 10,11,[13][14][15][16][17][18][19][20] . Therefore, such an unphysical fit underestimates the upturn of σ 1s (ω) below 2∆ 0 particularly at low temperature, and hence, is incapable of capturing the experimental findings [10][11][12][13][14][15][16][17][18][19][20] . 32).…”

“…In the past few decades, the optical properties of the superconducting states have attracted much attention in both linear and nonlinear regimes. The linear response is focused on the behavior of the optical conductivity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] , which was first discussed by Mattis and Bardeen (MB) within the framework of the Kubo current-current correlation approach in the anomalous-skin-effect region 21,22 . In this region, the excited current at one space point, depends not only on the electric field at that point but also on the ones nearby.…”

Mapping the orbital structure of impurity bound states in a superconductor

“…2a. Contrary to single-crystal measurements24 the spectra on bare Pb films never showed the characteristic double gap structure, probably due to the small film thickness compared to the Pb coherence length scale25, which washes out the anisotropy of the Fermi Surface26. Cr atoms were deposited on the Pb(111) surface at a surface temperature of ∼15 K. The shown spectra were obtained using a lock-in amplifier, with modulation V rms =10 μV at 938.5 Hz.…”