Axon-like active signal transmission

Abstract

Any electrical signal propagating in a metallic conductor loses amplitude due to the natural resistance of the metal. Compensating for such losses presently requires repeatedly breaking the conductor and interposing amplifiers that consume and regenerate the signal. This century-old primitive severely constrains the design and performance of modern interconnect-dense chips¹. Here we present a fundamentally different primitive based on semi-stable edge of chaos (EOC)^2,3, a long-theorized but experimentally elusive regime that underlies active (self-amplifying) transmission in biological axons^4,5. By electrically accessing the spin crossover in LaCoO₃, we isolate semi-stable EOC, characterized by small-signal negative resistance and amplification of perturbations^6,7. In a metallic line atop a medium biased at EOC, a signal input at one end exits the other end amplified, without passing through a separate amplifying component. While superficially resembling superconductivity, active transmission offers controllably amplified time-varying small-signal propagation at normal temperature and pressure, but requires an electrically energized EOC medium. Operando thermal mapping reveals the mechanism of amplification-bias energy of the EOC medium, instead of fully dissipating as heat, is partly used to amplify signals in the metallic line, thereby enabling spatially continuous active transmission, which could transform the design and performance of complex electronic chips.

Fig. 1. Bio-inspired active transmission.

a, Prevailing solution to on-chip signal transmission, in which the signal path is broken by repeaters or amplifiers (A), which re-amplify the decaying signal. b, The bio-inspired transmission primitive in which signal amplification occurs continuously throughout an unbroken signal path. c, Neurons operate in a region of non-monotonic responses between the ion flux and Na⁺ ion activation (Na⁺ act.) channels. Such a behaviour, similar to an NDR, is theoretically predicted to embody semi-stable EOC, which enables local amplification. d, Electronic version of a bio-inspired active-medium transmission, based on an active medium that exhibits NDR and EOC.

Fig. 2. Test structure, material and its quasistatic electrical behaviour.

a, Schematic of the test structure. The phase-shift and noise measurements were performed on components with electrode widths (in the x direction) of 100 µm, with a gap between the electrodes (in the y direction) of 6 µm. b, Temperature-dependent electrical conductivity of LaCoO₃ exhibiting a 10³ times nonlinear increase between 300 and 650 K. c, Measured quasistatic bias voltage (V_bias) as a function of applied bias current (I_bias), with no time-varying signals applied. The regions of NDR and PDR are marked. Source Data

Fig. 3. Dynamic measurements for circuit, phase shifts and noise amplification.

a, Schematic of the circuit of the dynamic measurements, which featured the simultaneous application of a d.c. bias current and a time-varying small-signal current (i(t)), as well as a measurement of the resulting d.c. voltage and the time-varying small-signal voltage (v(t)). Resistor R_s was used to set the a.c. small-signal amplitude, whereas R_L suppressed self-oscillations at all the d.c. biases of the device, M, under study (Methods). b, Time evolution of v(t) and i(t) at different d.c. current biases with the frequency of v(t) set to 100 Hz. The current biases correspond to PDR (1 mA), the cusp of the PDR–NDR transition (3 mA) and NDR (4 mA). The phase shifts Δϕ are marked, and v(t) and i(t) are scaled and plotted on the same ordinate to allow a visual comparison of their relative phases. The amplitude of v_a.c.(t) in all the measurements was fixed (Methods). c, Contour plot of Δϕ (corresponding to the colour) as a function of frequency and I_bias. Contour lines for Δϕ of –$\frac{\mathrm{\pi }}{2}$, 0, $\frac{\mathrm{\pi }}{2}$ and π are displayed. d, Contour plot of the PSD of the measured v(t) (corresponding to the colour) as a function of frequency and I_bias. The yellow band of increased PSD across all the frequencies is apparent at I_bias around 2.9–3.4 mA. All data were normalized to the data at 100 Hz. Data in c and d were obtained on the same device for which the quasistatic behaviour is displayed in Fig. 2c. Source Data

Fig. 4. Active transmission line.

a, Schematic of the active transmission line, and the applied and measured signals. The measurement displayed here was performed on a component with electrode length (in the x direction) of 1 mm, with a gap between the electrodes (in the y direction) of 12 µm. Output (v_out(t)) was measured at varying distances (d) from the input (v_in(t)) along the x direction on the signal-carrying line at varying frequencies (f). b, Normalized time evolution of v_in(t) and v_out(t) on injecting either of two different I_bias levels into the LaCoO₃ medium to poise it once in PDR (locally passive) and once in NDR (semi-stable EOC) regimes of the corresponding d.c. response of the structure (f = 100 Hz, d = 0.5 mm). For the NDR bias, it is apparent that |v_out(t)| > |v_in(t)|. Data have been normalized for ease of visualization such that v_in(t) at different biases have the same normalized magnitude and the ratio between v_out(t) and v_in(t) at a given bias is maintained. c, Gain (amplitude of v_out(t) divided by amplitude of v_in(t)) as a function of d (f = 100 Hz). d, Gain as a function of f (d = 0.5 mm). Error bars in c and d are smaller than most of the data markers. Estimation of error bars is described in the Methods. Source Data

Fig. 5. Analysing energy partitioning in semi-stable EOC.

a, Black-body thermal maps of the active region of a test structure (illustrated in Fig. 2a) biased at semi-stable EOC (I_bias = 3 mA), with three different temporal small signals superimposed on the same d.c. bias in semi-stable EOC. On careful review, it is apparent that the heat map corresponding to a signal of frequency 100 Hz exhibits lower temperatures than the other two (especially the centre pixel, which is indicated with an arrow). b, Cross-sections of the heat maps comparing the temperatures for d.c. bias with no signal (0 Hz) and with a 100 Hz input signal. Data markers correspond to experimental data and curves correspond to Gaussian fits. c, Change in local temperature corresponding to small signals of different frequencies relative to the local temperatures corresponding to d.c. bias, all of which are measured at the same d.c. bias in semi-stable EOC. The shaded region indicates lower temperatures or relative local cooling. The error bars in all the panels are described in the Methods. d, Mechanism of a part of the input d.c. energy being used for signal amplification when biased at semi-stable EOC. Source Data