Heat Conduction and Energy Relaxation in an InAs Nanowire Approaching the Clean One-Dimensional Limit

Abstract

We investigate heat conduction and energy relaxation in an InAs semiconductor nanowire using a hybrid semiconductor-superconductor architecture. Local electronic temperatures are measured with an in-situ grown quantum dot thermometer, while controlled Joule heating is applied at different locations along the wire to probe temperature gradients at sub-kelvin temperatures. With a onedimensional heat transport model, we calculate an electron-phonon heat flow that scales as Q_{e-ph} \propto T^2.6, which is in close agreement with the T^3 dependence predicted for a clean one-dimensional electron gas coupled to a phonon bath. We further estimate a characteristic length l_{eq} = 370 nm, beyond this length scale, phonon-mediated heat transport dominates over heat conduction in our nanowire. Our results provide a quantitative measure of energy relaxation mechanisms in a onedimensional semiconductor and provide a framework for studying heat flow in low-dimensional nanostructures.

Figures (4)

• Figure 1: (a) Scanning electron micrograph of the semiconductor-superconductor hybrid device showing the NW-QD with the superconducting contacts and measurement setup. The QD is located 1.3 $\mu$m away from the tip. The contacts are positioned 250 nm apart, which allows for localized Joule heating by passing current between different pairs of contacts. (b) The measured current through the QD as a function of bias voltage $V_{b1}$ and side-gate voltage $V_G$, showing the standard Coulomb diamonds, and (c) Current-bias voltage characteristics of the S-Sm-S contacts. (d) A zoomed-in image of the Coulomb peak, measured with 25 fW heating power applied to the 1-2 lead, and (e) the current and differential conductance data as a function of gate voltages at $V_{b1} = 0.$ The solid lines are fits to Eq. (\ref{['Land']}).
• Figure 2: Measured source ($T_s$) and drain ($T_d$) temperatures as a function of the heating power applied to the nanowire segments between leads 1–2, 2–3, and 3–4. The source electrode is on the heated side. Solid lines represent fits obtained using the one-dimensional heat-flow model of Eq. (\ref{['heatCond']}) with $\Sigma = 2\times10^9$ W/m$^3$K$^{2.6}$. The dashed curves are added as guides to the eye. The green dashed line marks the transition from the supercurrent regime to the Joule-heating regime in the S–Sm–S heaters.
• Figure 3: (a) Schematic of a one-dimensional NW with cross-sectional area A, which consists of an elementary length dx, and the temperature at position x is denoted by T(x). (b) The heat balance for an elementary volume showing the heating power injected as the sum of heat dissipation via electron-phonon interaction and heat conduction to the neighboring elements.
• Figure 4: (a) The amount of heat flowing through the QD as a function of the input heat to the NW, calculated from the measured drain temperature $T_d$. (b) Calculated temperature profile along the full length of the NW for an applied heating power of $P_H$ = 50 fW. The red bar indicates the heating power density $p$ injected into the NW with leads 3 and 4.