Splitting the heat: the quantum limits of thermal energy flow

Device geometry. a) Scanning electron micrograph of an the sample. The 1D waveguides with a lithographic width of 170 nm form a half-ring connected to reservoirs A-F. A global top-gate is present. Heating of reservoirs A, B is generated by applying a current Ih, thermal noise measurements are performed at contacts E, F. The reservoirs C and D are left floating. b) Device potential for the ballistic transport model with labels A∗ and E∗ denoting the joined reservoirs A+B and E+F. Harmonic waveguide network with Gaussian scatterer (indicated by arrow). Mode spacing is ħω = 5 meV. © 2016 Kramer et al. Citation: AIP Advances 6, 065306 (2016); http://dx.doi.org/10.1063/1.4953812

With ever shrinking sizes of electronic transistors, the quantum mechanical nature of electrons becomes more visible. For instance two electrons with the same spin orientation and velocities cannot be at the same location (Pauli blocking). At low temperatures, electronic waves travel many mircometers completely coherently, only reflected by the geometric of the confinement. A tight confinement leads to larger separation of quantized energy levels and restricts the lateral spread of the electrons to specific eigenmodes of a nanowire.

The distribution of the electronic current into various is then given by the geometrical scattering properties of the device interior, which are conveniently computed using wave packets. The ballistic electrons entering a nanodevice carry along charge and thermal energy. The maximum amount of thermal energy Q per time which can be transported through a single channel between two reservoirs of different temperatures is limited to  Q ≤ π² k_B² (T₂²-T₁²)/(3h) [h denotes Planck’s and k_B Boltzmann’s constant]. This has implications for computing devices, since this restricts the cooling rate (Pendry 1982).

In a collaboration with the novel materials group at Humboldt University (Prof. S.F. Fischer, Dr. C. Riha, Dr. O. Chiatti, S. Buchholz) and using wafers produced in the lab of A. Wieck, D. Reuter (Bochum, Paderborn) C. Kreisbeck and I have compared theoretical expectations with experimental data for the thermal energy and charge currents in multi-terminal nanorings (AIP Advances 2016, open access). Our findings highlight the influence of the device geometry on both, charge and thermal energy transfer and demonstrate the usefulness of the time-dependent wave-packet algorithm to find eigenstates over a whole range of temperature.

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