We measure transport through a Ga [Al]As heterostructure at temperatures between 32 mK and 30 K. Increasing the temperature enhances the electron-electron scattering rate and viscous effects in the two-dimensional electron gas arise. To probe this regime we measure so-called vicinity voltages and use a voltage-biased scanning tip to induce a movable local perturbation. We find that the scanning gate images differentiate reliably between the different regimes of electron transport. Our data are in good agreement with recent theories for interacting electron liquids in the ballistic and viscous regimes stimulated by measurements in graphene. However, the range of temperatures and densities where viscous effects are observable in Ga [Al]As are very distinct from the graphene material system. arXiv:1807.03177v3 [cond-mat.mes-hall]

We experimentally determine the energy spectrum of a quantum point contact realized by a suitable gate geometry in bilayer graphene. Using finite bias spectroscopy we measure the energy scales arising from the lateral confinement as well as the Zeeman splitting and find a spin g-factor gs ∼ 2. The valley g-factor is highly tunable by vertical electric fields, gv ∼ 40 − 120. The results are quantitatively explained by a calculation considering topological magnetic moment and its dependence on confinement and the vertical displacement field. arXiv:1911.05968v1 [cond-mat.mes-hall]

Crystal fields occur due to a potential difference between chemically different atomic species. In Van-der-Waals heterostructures such fields are naturally present perpendicular to the planes. It has been realized recently that twisted graphene multilayers provide powerful playgrounds to engineer electronic properties by the number of layers, the twist angle, applied electric biases, electronic interactions and elastic relaxations, but crystal fields have not received the attention they deserve.Here we show that the bandstructure of large-angle twisted double bilayer graphene is strongly modified by crystal fields. In particular, we experimentally demonstrate that twisted double bilayer graphene, encapsulated between hBN layers, exhibits an intrinsic bandgap. By the application of an external field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer E b = 0.13 V/nm ≈ −Et = 0.12 V/nm. We show both by means of first principles calculations and low energy models that crystal fields open a band gap in the groundstate. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of twisted double bilayer graphene, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers. arXiv:1910.10524v2 [cond-mat.mes-hall] 4 Nov 2019 a c FIG. 1. a) Two twisted, AB-stacked bilayer graphene (BG) sheets. The electrostatic potential of the outer layers is different from the potential in the inner layers. This leads to crystal fields Et = −E b pointing in opposite direction in the top and bottom BG. In the experiment, the two bilayer systems are encapsulated in hBN which reduces the strength of the crystal fields compared to vacuum. b) The TDBG band structure consists of Brillouin-zones of the top and bottom BG rotated with respect to each other. For large twist angles θ, the bands of the top and bottom layer intersect at energies large compared to the Fermi energies of the individual layers. Therefore, at typical Fermi energies, the individual BG band structures remain intact.The crystal fields open a single-particle gap in both layers. c) In such a structure we observe a gap at zero density and zero external field in a resistance versus density trace R(ntot). We show traces for two devices, device 1 is further discussed in the main text and further measurements of device 2 and device 3 are shown in the Supplemental Material.

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin–orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin–orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin–orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin–orbit interaction.

We demonstrate an experimental method for measuring quantum state degeneracies in bound state energy spectra. The technique is based on the general principle of detailed balance, and the ability to perform precise and efficient measurements of energy-dependent tunnelling-in and -out rates from a reservoir. The method is realized using a GaAs/AlGaAs quantum dot allowing for the detection of time-resolved single-electron tunnelling with a precision enhanced by a feedback-control. It is thoroughly tested by tuning orbital and spin-degeneracies with electric and magnetic fields. The technique also lends itself for studying the connection between the ground state degeneracy and the lifetime of the excited states.Degeneracies play an important role in quantum statistics [1]. They often arise from symmetries of the underlying system [2,3] and govern the theoretical description of macroscopic quantum phenomena such as superconductivity [4] and the quantum Hall effect [5], but also play an important role for atomic spectra [6]. Theoretical concepts of topological protection are based on ground-state degeneracies [7], and modern schemes to control qubits make use of tunable degeneracies [8]. While the concept is omnipresent in quantum theory, measuring the degeneracy of an energy level in a quantum system seems to be less developed. A familiar way to experimentally demonstrate the existence of a degeneracy consists in breaking underlying symmetries, thereby lifting the degeneracy as in the Zeeman-[9-12], or the Stark-effects. Alternative techniques use selective excitations such as left-or rightcircularly polarized light to distinguish degenerate excitations [13].We demonstrate an experimental method of measuring the degeneracy of discrete energy levels alternative to the techniques mentioned above. The method is based on a general relation derived from detailed balance, and makes use of tunnelling spectroscopy and our ability to detect individual tunnelling events in real time [14]. We overcome previous accuracy limitations of this technique [15] by implementing a feedback-control. A single few-electron quantum dot in GaAs serves as the system of choice to test our experimental method. In this system, ground and excited states are well studied [9,[16][17][18][19][20][21][22][23][24] and the presence of degeneracies is established from symmetry-breaking measurement techniques [9,11,16,19,20,[25][26][27][28][29]. Our method reliably traces these degeneracies with great accuracy. Furthermore, the system combined with our measurement method allows us to controllably alter the degeneracy of energy levels. The method of degeneracy detection is very general and can be directly transferred to other systems where states are accessible by tunnelling.Our samples are made from a GaAs/AlGaAs heterostructure hosting a two-dimensional electron gas 90 nm below the surface. As shown in Fig. 1(a) we form a quantum dot by applying negative voltages to the metallic top-gate fingers thereby depleting the electron gas below. The quantum dot i...