Mode-selected heat flow through a one-dimensional waveguide network
  Cross-correlated measurements of thermal noise are performed to determine the electron temperature in nanopatterned channels of a GaAs/AlGaAs heterostructure at 4.2 K. Two-dimensional (2D) electron reservoirs are connected via an extended one-dimensional (1D) electron waveguide network. Hot electrons are produced using a current $I_{\text{h}}$ in a source 2D reservoir, are transmitted through the ballistic 1D waveguide and relax in a drain 2D reservoir. We find that the electron temperature increase ${\Delta}T_{\text{e}}$ in the drain is proportional to the square of the heating current $I_{\text{h}}$, as expected from Joule's law. No temperature increase is observed in the drain when the 1D waveguide does not transmit electrons. Therefore, we conclude that electron-phonon interaction is negligible for heat transport between 2D reservoirs at temperatures below 4.2 K. Furthermore, mode control of the 1D electron waveguide by application of a top-gate voltage reveals that ${\Delta}T_{\text{e}}$ is not proportional to the number of populated subbands $N$, as previously observed in single 1D conductors. This can be explained with the splitting of the heat flow in the 1D waveguide network. 
Christian Riha, Philipp Miechowski, Sven S. Buchholz, Olivio Chiatti,   Andreas D. Wieck, Dirk Reuter and Saskia F. Fischer
cond-mat.mes-hall