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

Magnetic cooling for microkelvin nanoelectronics on a cryofree platform

We present a parallel network of 16 demagnetization refrigerators mounted on a cryofree dilution refrigerator aimed to cool nanoelectronic devices to sub-millikelvin temperatures. To measure the refrigerator temperature, the thermal motion of electrons in a Ag wire -- thermalized by a spot-weld to one of the Cu nuclear refrigerators -- is inductively picked-up by a superconducting gradiometer and amplified by a SQUID mounted at 4 K. The noise thermometer as well as other thermometers are used to characterize the performance of the system, finding magnetic field independent heat-leaks of a few nW/mol, cold times of several days below 1 mK, and a lowest temperature of 150 microK of one of the nuclear stages in a final field of 80 mT, close to the intrinsic SQUID noise of about 100 microK. A simple thermal model of the system capturing the nuclear refrigerator, heat leaks, as well as thermal and Korringa links describes the main features very well, including rather high refrigerator efficiencies typically above 80%.Comment: 4 color figures, including supplementary inf

Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges

Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments.Comment: 7 page

Superconducting Gatemon Qubit based on a Proximitized Two-Dimensional Electron Gas

The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductor-semiconductor JJs for qubit control. Here, we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show 2DEG gatemons meet the requirements by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate

Field effect enhancement in buffered quantum nanowire networks

III-V semiconductor nanowires have shown great potential in various quantum transport experiments. However, realizing a scalable high-quality nanowire-based platform that could lead to quantum information applications has been challenging. Here, we study the potential of selective area growth by molecular beam epitaxy of InAs nanowire networks grown on GaAs-based buffer layers. The buffered geometry allows for substantial elastic strain relaxation and a strong enhancement of field effect mobility. We show that the networks possess strong spin-orbit interaction and long phase coherence lengths with a temperature dependence indicating ballistic transport. With these findings, and the compatibility of the growth method with hybrid epitaxy, we conclude that the material platform fulfills the requirements for a wide range of quantum experiments and applications

Selective-area chemical beam epitaxy of in-plane InAs one-dimensional channels grown on InP(001), InP(111)B, and InP(110) surfaces

We report on the selective-area chemical beam epitaxial growth of InAs in-plane, one-dimensional (1-D) channels using patterned SiO$_{2}$-coated InP(001), InP(111)B, and InP(110) substrates to establish a scalable platform for topological superconductor networks. Top-view scanning electron micrographs show excellent surface selectivity and dependence of major facet planes on the substrate orientations and ridge directions, and the ratios of the surface energies of the major facet planes were estimated. Detailed structural properties and defects in the InAs nanowires (NWs) were characterized by transmission electron microscopic analysis of cross-sections perpendicular to the NW ridge direction and along the NW ridge direction. Electrical transport properties of the InAs NWs were investigated using Hall bars, a field effect mobility device, a quantum dot, and an Aharonov-Bohm loop device, which reflect the strong spin-orbit interaction and phase-coherent transport characteristic in the selectively grown InAs systems. This study demonstrates that selective-area chemical beam epitaxy is a scalable approach to realize semiconductor 1-D channel networks with the excellent surface selectivity and this material system is suitable for quantum transport studies

Microwave sensing of Andreev bound states in a gate-defined superconducting quantum point contact

We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with adiabatic coupling to Andreev bound states. Near $\pi$ phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. We identify features consistent with the presence of single Andreev bound states and describe the Andreev-cavity interaction using a dispersive Jaynes-Cummings model. By fitting the weak Andreev-cavity coupling, we extract ~GHz decoherence consistent with charge noise and the transmission dispersion associated with a localized state

Field effect enhancement in buffered quantum nanowire networks

arXiv:1802.07808v2III-V semiconductor nanowires have shown great potential in various quantum transport experiments. However, realizing a scalable high-quality nanowire-based platform that could lead to quantum information applications has been challenging. Here, we study the potential of selective area growth by molecular beam epitaxy of InAs nanowire networks grown on GaAs-based buffer layers, where Sb is used as a surfactant. The buffered geometry allows for substantial elastic strain relaxation and a strong enhancement of field effect mobility. We show that the networks possess strong spin-orbit interaction and long phase-coherence lengths with a temperature dependence indicating ballistic transport. With these findings, and the compatibility of the growth method with hybrid epitaxy, we conclude that the material platform fulfills the requirements for a wide range of quantum experiments and applications.The project was supported by Microsoft Station Q, the European Research Council (ERC) under the grant agreement No.716655 (HEMs-DAM), the European Union Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 722176, the Danish National Science Research Foundation and the Villum Foundation. SMS acknowledges funding from >Programa Internacional de Becas >la Caixa>-Severo Ochoa>. JA and SMS also acknowledge funding from Generalitat de Catalunya 2017 SGR 327. ICN2 acknowledges support from the Severo Ochoa Programme (MINECO, Grant no. SEV-2013-0295) and is funded by the CERCA Programme / Generalitat de Catalunya