Probing the local temperature of a two-dimensional electron gas microdomain with a quantum dot: Measurement of electron-phonon interaction

We demonstrate local detection of the electron temperature in a two-dimensional microdomain using a quantum dot. Our method relies on the observation that a temperature bias across the dot changes the functional form of Coulomb-blockade peaks. We apply our results to the investigation of electron-energy relaxation at subkelvin temperatures, find that the energy flux from electrons into phonons is proportional to the fifth power of temperature, and give a measurement of the coupling constant.

Figure 1

(a) False-color scanning electron micrograph of the device and scheme of the measurement setup. Schottky gates (light gray) define a $16-\mu {\mathrm{m}}^2$-sized central electronic domain connected to outer regions of the 2DEG through a QD (bottom) and three QPCs (left, right, top). Crossed squares indicate Ohmic contacts to the 2DEG. (b)–(d) Characterization measurements: finite-bias stability plot of the QD (b), zero-bias conductance $G$ of QPC1 versus gate voltage $V_{\mathit{QPC}1}$ (c), and current-voltage characteristics of QPC1 for different values of the gate voltage $V_{\mathit{QPC}1}$ close to pinchoff (d). $G_0$ is the conductance quantum.

Figure 2

(a) Energy-level diagram for transport through a temperature-biased QD (all quantities are defined in the text). (b) Calculated zero-bias conductance $G(\epsilon )$ for different temperatures of the leads: $T_1=T_2=250$ mK (dotted line), $T_1=T_2=1\hspace{0.5em}\mathrm{K}$ (dashed line), $T_1=250$ mK and $T_2=1\hspace{0.5em}\mathrm{K}$ (full line).

Figure 3

. (a),(b) Conductance $G$ versus gate voltage $V_G$ for increasing values of the heating current $I_H$: 11.6 nA (squares), 20 nA (circles), 28.6 nA (triangles). The corresponding full lines are best fits of the derivative of Eq. (1) to each dataset. The hotter and colder temperature thereby estimated are, respectively, $T_1=426$ mK, $T_2=604$ mK; $T_1=446$ mK, $T_2=861$ mK; and $T_1=485$ mK, $T_2=1.15$ K. The data are plotted on both linear (a) and semilogarithmic (b) scale; in (a) traces have been offset vertically for clarity. (b) Extracted temperatures $T_1$ and $T_2$ as a function of $I_H$. The hotter $T_2$ pertains to the heated microdomain; the colder $T_1$ to the external portion of the 2DEG.

Figure 4

(a) Scheme of the main contributions to the steady-state power balance. (b),(c) Temperature $T_2$ versus injected power $P_H$ for different configurations of the device: $R_{\mathit{QPC}1,2,3}=$ 7.4 $\mathrm{k}\Omega$ (b), $R_{\mathit{QPC}1,2}=$ 20 $\mathrm{M}\Omega$, $R_{\mathit{QPC}3}=$ 1 $\mathrm{M}\Omega$ (c). For each case, the full lines are a fit of the expressions given in the text. (d) Joint bilogarithmic plot of (b) and (c).