Absence of Cyclotron Resonance in the Anomalous Metallic Phase in ${\mathrm{InO}}_x$

It is observed that many thin superconducting films with not too high disorder level (generally $R_N/\square <2000\mathrm{\Omega }$) placed in magnetic field show an anomalous metallic phase where the resistance is low but still finite as temperature goes to zero. Here we report in weakly disordered amorphous ${\mathrm{InO}}_x$ thin films that this anomalous metal phase possesses no cyclotron resonance and hence non-Drude electrodynamics. The absence of a finite frequency resonant mode can be associated with a vanishing downstream component of the vortex current parallel to the supercurrent and an emergent particle-hole symmetry of this metal, which establishes its non-Fermi-liquid character.

Figure 1

(a) Temperature dependence of the dc sheet resistance under different magnetic fields. (b),(c) Complex sheet conductance at base temperature on a log-log scale. (b) Real part $G_1$. $G_1$ ($H=0\mathrm{T}$) is not plotted, but can be found in Fig. 2. (c) The corresponding imaginary part.

Figure 2

Complex conductance fits for (a) 0 T, (b) 0.8 T, (c) 1.5 T, (d) 2.5 T, (e) 4 T, and (f) 6 T. Panels (a)–(c) are on log-log scales while panels (d),(e) only have the vertical axis on log scale to show dc data. The black triangle represents the comeasured dc data. Models used in the fitting are described in the text.

Figure 3

Spectral weight from fits in the units of kelvin for the delta function and Drude terms. Blue and red correspond to the superfluid (delta function) and the slowly decaying component, respectively. The sum of the total spectral weight is in black. The spectral weight for component 2 at 0.05 T is not plotted because the real part of conductance falls below sensitivity. See Fig. S6 in SM [43] for details.