Ultra-low electron temperatures in nanostructured samples

Nanostructured samples, be it semiconducting or metallic ones, have received considerable experimental and theoretical attention due to the manifold of possibilities to investigate fundamental physics. Not only are they viable candidates for realizations of qubits, the key ingredient of quantum computation, but the surrounding solid makes it a testing ground for many-body physics. Novel quantum mechanical effects, such as topological phases and electron-mediated ferromagnetic nuclear spin ordering, are predicted to emerge in such systems. Low temperatures are crucial for these many-body effects as the energies scales involved are typically very small. State of the art electron transport experiments reach an electron temperature of roughly 10 mK. In order to reach sub-millikelvin electron temperatures, we develop a novel type of refrigerator aimed at cooling nanostructured samples, where nuclear demagnetization refrigerators are integrated into every measurement lead, directly cooling the electrons therein. Hence circumventing the limitation of electron-phonon coupling which is drastically suppressed at the lowest temperatures due to its T^5 dependence.
We implement various kinds of electron thermometers to measure the electron temperature in typical samples. In metallic Coulomb blockade thermometers (CBTs), we observe a deviation from the electron-phonon cooling mechanism, indicating that we succeed in cooling samples through the conduction electrons. Further, we investigate a quantum dot in a typical GaAs device. The quantum dot thermometer is operated in deep Coulomb blockade and probes the Fermi edge of the surrounding electron reservoir both through direct transport and a proximal charge sensing device. After considerable tuning effort an electron temperature of 10~mK is extracted. Our experiments show that the temperature reading is very susceptible to the electrostatic environment, emphasizing the importance of the surrounding solid and demonstrating the difficulty to implement a temperature sensor at the lowest temperatures. More importantly the low electron temperatures open the possibility for very sensitive measurements of back-action effects of the charge sensor or the charge stability of the material.
After optimizing the chip socket and improving the filtering in the system, an electron temperature of 5.2 mK $\pm$ 0.3 mK in a CBT is measured after demagnetization. By measuring the temperature dependent I-V curves of a normal metal/insulator/superconductor (NIS) tunnel junction, we implement yet another thermometer, which we employ as both primary and secondary thermometer. On top of that, we demonstrate with the help of reentrant features in the fractional quantum Hall regime, cooling of electrons in a high mobility GaAs two-dimensional electron gas (2DEG) below the base temperature of our dilution refrigerator.
Using our low electron temperatures, we investigate high mobility GaAs 2DEG devices in large magnetic fields. In our samples the typical signature of the quantum Hall effect is dramatically altered, resulting in a quantized longitudinal resistance. We can show that this quantization, which occurs only at the lowest temperatures, is due to a large electron density gradient in the 2DEG. As we show subsequently for the $\nu$=5/2 fractional quantum Hall state, the electron density gradient heavily influences the extraction of the energy gap between the ground and excited state. Being a candidate for one of the above mentioned topologically non-trivial ground states, our findings could have important consequences for the fabrication of $\nu=5/2$ fractional quantum Hall state samples.
Additionally, we measure the electrical resistance anisotropy in both natural graphite and highly ordered pyrolytic graphite (HOPG), comparing macroscopic samples, with exfoliated, nanofabricated specimens of nanometer thickness. In nanoscale samples, independent on the graphite type, we find a very large c-axis resistivity $\rho_c$ -- much larger than expected from simple band theory -- and non-monotonic temperature dependence. This is similar to macroscopic HOPG, but in stark contrast to macroscopic natural graphite. A recent model of disorder-induced delocalization is consistent with our transport data. Furthermore, Micro-Raman spectroscopy reveals clearly reduced disorder in exfoliated samples and HOPG, as expected within the model.