Limit Cycle and Anomalous Capacitance in the Kondo Insulator ${\mathrm{SmB}}_6$

We report a frequency coding limit cycle and anomalous capacitance in the Kondo insulator ${\mathrm{SmB}}_6$ at low temperatures where the insulating gap becomes fully opened. The limit cycle appears to be associated with local activity and autocatalytic temporal pattern formation, as occurs in biological systems. The measured anomalous capacitance may indicate surface and bulk separation, suggesting the formation of a surface conducting state. The biological analogy suggests lossless information transport and complex information coding, and the surface state with a superconductor would provide a possible venue for quantum computing resources without decoherence.

Figure 1

Temperature dependency of resistance of ${\mathrm{SmB}}_6$ single crystal. The left inset shows a low temperature resistance versus temperature plot, and the right inset shows current versus voltage plots at various temperatures. The lower inset shows the crystal structure of ${\mathrm{SmB}}_6$.

Figure 2

Self-sustained oscillation of ${\mathrm{SmB}}_6$. (a) Frequency coding of action potential in nerve system. Information is encoded in the frequency change with stimulus voltage. (b) Frequency coding by stimulus current in ${\mathrm{SmB}}_6$ after insulating gap is developed; curves have been offset for clarity. (c) $dV/dI$ plot at 2 K. In Fig. 2b, the oscillation is confined to the NDR regime. (d) The measurement setup. (e) The oscillation is due to bifurcation from a stable focus to a limit cycle, the polarity change of $\lambda$ originates at the minimum capacitance necessary to trigger the oscillation. (f) Temperature dependence of oscillation; curves have been offset for clarity (g) Fast Fourier transforms of the oscillations.

Figure 3

Frequency dependence of Lissajous plots. (a) 1 Hz plot where continued cycling overlaps the initial trace and shows hysteresis from virtual thermal impedance. (b)–(e) Evolution of hysteresis plots with temperature and eventual saturation at final state. (f)–(h) The final states have the same resistive impedance. Above 10 kHz, hysteresis becomes conspicuous in Ohmic regime, the yellow lines showing Lissajous curves for the $1\Omega$ resistor at 10 and 20 kHz.

Figure 4

Time evolution of 10 kHz Lissajous plots. (a): the first five cycles are in a metastable state. (b)–(f): the resistance drop and the zero point hysteresis pinching by heating. (g): The resistance and time constant drop with the number of cycles due to heating. Above 4.2 K sample temperature, the capacitance disappears, the inset showing the topologically equivalent $RC$ circuit with possible $RC$ contributions, blue representing conducting layer and red high dielectric insulating regimes. (h): low current Lissajous plot in Ohmic regime.