Observation of Chiral Heat Transport in the Quantum Hall Regime

Heat transport in the quantum Hall regime is investigated using micron-scale heaters and thermometers positioned along the edge of a millimeter-scale two dimensional electron system (2DES). The heaters rely on localized current injection into the 2DES, while the thermometers are based on the thermoelectric effect. In the $\nu =1$ integer quantized Hall state, a thermoelectric signal appears at an edge thermometer only when it is “downstream,” in the sense of electronic edge transport, from the heater. When the distance between the heater and the thermometer is increased, the thermoelectric signal is reduced, showing that the electrons cool as they propagate along the edge.

Figure 1

(a) Schematic diagram, not to scale, of device layout. Numbered squares represent Ohmic contacts; C1, C2, and C3 represent constrictions in the 2DES. (b) $V_f$ (dotted line) and $V_{2f}$ (solid line) vs magnetic field $B$ at $T=0.1\mathrm{K}$ in the $\nu =1$ QHE for the measurement circuit indicated. Edge state chirality is clockwise as shown.

Figure 2

(a) $V_{2f}$ vs two-terminal resistance $R_{\mathrm{sd}}$ of heater circuit at $T=0.1\mathrm{K}$ for fixed $I_{\mathrm{ex}}=15\mathrm{nA}$. (b) $V_{2f}$ vs heater power $P_h$ at $T=0.1$ and 0.6 K. Closed dots: varying $R_h$ at fixed $I_{\mathrm{ex}}$. Open dots: varying $I_{\mathrm{ex}}$ at fixed $R_h$. (c) Solid trace: $V_{2f}$ vs gate voltage $V_g$ applied to constriction C3. Dotted trace: $G_{\mathrm{C}3}$ vs $V_g$. All data are at $B=4.25\mathrm{T}$.

Figure 3

Chirality of thermal transport at $\nu =1$ at $T=0.1\mathrm{K}$. (a) and (d): $V_{2f}$ (solid line) and $V_f$ (dotted line) observed downstream from heater constriction, C2. (b) and (c) $V_{2f}$ and $V_f$ observed upstream from heater. Edge state chirality and magnetic field directions are indicated.

Figure 4

$V_{2f}$ signal at $\nu =1$ observed with a $40\mu \mathrm{m}$ separation between heater (here C1) and detector C3 vs the conductance $G_{\mathrm{C}2}$ of constriction C2 which lies midway between them. Data normalized by the $V_{2f}$ signal observed with a $20\mu \mathrm{m}$ heater-detector separation. $T=0.1\mathrm{K}$.