Zeeman Tunability of Andreev Bound States in van der Waals Tunnel Barriers.

Quantum dots proximity coupled to superconductors are attractive research platforms due to the intricate interplay between the single-electron nature of the dot and the many body nature of the superconducting state. These have been studied mostly using nanowires and carbon nanotubes, which allow a combination of tunability and proximity. Here we report a new type of quantum dot which allows proximity to a broad range of superconducting systems. The dots are realized as embedded defects within semiconducting tunnel barriers in van der Waals layers. By placing such layers on top of thin NbSe_{2}, we can probe the Andreev bound state spectra of such dots up to high in-plane magnetic fields without observing the effects of a diminishing superconducting gap. As tunnel junctions defined on NbSe_{2} have a hard gap, we can map the subgap spectra without a background related to the rest of the junction. We find that the proximitized defect states invariably have a singlet ground state, manifest in the Zeeman splitting of the subgap excitation. We also find, in some cases, bound states that converge to zero energy and remain there. We discuss the role of the spin-orbit term, present both in the barrier and the superconductor, in the realization of such topologically trivial zero-energy states.

Tunneling into the Vortex State of NbSe2 with van der Waals Junctions.

We have performed device-based tunneling spectroscopy of NbSe2 in the vortex state with a magnetic field applied both parallel and perpendicular to the a- b plane. Our devices consist of layered semiconductors placed on top of exfoliated NbSe2 using the van der Waals transfer technique. At zero field, the spectrum exhibits a hard gap, and the quasiparticle peak is split into low- and high-energy features. The two features, associated with the effective two-band nature of superconductivity in NbSe2, exhibit markedly distinct responses to the application of magnetic field, suggesting an order-of-magnitude difference in the spatial extent of the vortex cores of the two bands. At energies below the superconducting gap, the hard gap gives way to vortex-bound Caroli-de Gennes-Matricon states, allowing the detection of individual vortices as they enter and exit the junction. Analysis of the subgap spectra upon application of parallel magnetic field allows us to track the process of vortex surface formation and spatial rearrangement in the bulk.

Observation of the Unconventional Photon Blockade in the Microwave Domain.

We have observed the unconventional photon blockade effect for microwave photons using two coupled superconducting resonators. As opposed to the conventional blockade, only weakly nonlinear resonators are required. The blockade is revealed through measurements of the second order correlation function g^{(2)}(t) of the microwave field inside one of the two resonators. The lowest measured value of g^{(2)}(0) is 0.4 for a resonator population of approximately 10^{-2} photons. The time evolution of g^{(2)}(t) exhibits an oscillatory behavior, which is characteristic of the unconventional photon blockade.

Shiba Bound States across the Mobility Edge in Doped InAs Nanowires.

We present a study of Andreev quantum dots fabricated with small-diameter (30 nm) Si-doped InAs nanowires where the Fermi level can be tuned across a mobility edge separating localized states from delocalized states. The transition to the insulating phase is identified by a drop in the amplitude and width of the excited levels and is found to have remarkable consequences on the spectrum of superconducting subgap resonances. While at deeply localized levels only quasiparticle cotunneling is observed, for slightly delocalized levels Shiba bound states form and a parity-changing quantum phase transition is identified by a crossing of the bound states at zero energy. Finally, in the metallic regime, single Andreev resonances are observed.

Imaging the Quantum Capacitance of Strained MoS2 Monolayers by Electrostatic Force Microscopy.

We implemented radio frequency-assisted electrostatic force microscopy (RF-EFM) to investigate the electric field response of biaxially strained molybdenum disulfide (MoS2) monolayers (MLs) in the form of mesoscopic bubbles, produced via hydrogen (H)-ion irradiation of the bulk crystal. MoS2 ML, a semiconducting transition metal dichalcogenide, has recently attracted significant attention due to its promising optoelectronic properties, further tunable by strain. Here, we take advantage of the RF excitation to distinguish the intrinsic quantum capacitance of the strained ML from that due to atomic scale defects, presumably sulfur vacancies or H-passivated sulfur vacancies. In fact, at frequencies fRF larger than the inverse defect trapping time, the defect contribution to the total capacitance and to transport is negligible. Using RF-EFM at fRF = 300 MHz, we visualize simultaneously the bubble topography and its quantum capacitance. Our finite-frequency capacitance imaging technique is noninvasive and nanoscale and can contribute to the investigation of time- and spatial-dependent phenomena, such as the electron compressibility in quantum materials, which are difficult to measure by other methods.

Quantum bath engineering of a high impedance microwave mode through quasiparticle tunneling.

In microwave quantum optics, dissipation usually corresponds to quantum jumps, where photons are lost one by one. Here we demonstrate a new approach to dissipation engineering. By coupling a high impedance microwave resonator to a tunnel junction, we use the photoassisted tunneling of quasiparticles as a tunable dissipative process. We are able to adjust the minimum number of lost photons per tunneling event to be one, two or more, through a dc voltage. Consequently, different Fock states of the resonator experience different loss processes. Causality then implies that each state experiences a different energy (Lamb) shift, as confirmed experimentally. This photoassisted tunneling process is analogous to a photoelectric effect, which requires a quantum description of light to be quantitatively understood. This work opens up new possibilities for quantum state manipulation in superconducting circuits, which do not rely on the Josephson effect.

Tunable High Speed Atomic Rotor in Bi2Se3 Revealed by Current Noise.

The ability to manipulate individual atoms and molecules using a scanning tunneling microscope (STM) has been crucial for the development of a vast array of atomic-scale devices and structures ranging from nanoscale motors and switches to quantum corrals. Molecular motors in particular have attracted considerable attention in view of their potential for assembly into complex nanoscale machines. Whereas the manipulated atoms or molecules are usually on top of a substrate, motors embedded in a lattice can be very beneficial for bottom-up construction, and may additionally be used to probe the influence of the lattice on the electronic properties of the host material. Here, we present the discovery of controlled manipulation of a rotor in Fe doped Bi2Se3. We find that the current into the rotor, which can be finely tuned with the voltage, drives omni-directional switching between three equivalent orientations, each of which can be frozen in at small bias voltage. Using current fluctuation measurements at 1 MHz and model simulations, we estimate that switching rates of hundreds of kHz for sub-nanoampere currents are achieved.

Spin-Orbit induced phase-shift in Bi2Se3 Josephson junctions.

The transmission of Cooper pairs between two weakly coupled superconductors produces a superfluid current and a phase difference; the celebrated Josephson effect. Because of time-reversal and parity symmetries, there is no Josephson current without a phase difference between two superconductors. Reciprocally, when those two symmetries are broken, an anomalous supercurrent can exist in the absence of phase bias or, equivalently, an anomalous phase shift φ0 can exist in the absence of a superfluid current. We report on the observation of an anomalous phase shift φ0 in hybrid Josephson junctions fabricated with the topological insulator Bi2Se3 submitted to an in-plane magnetic field. This anomalous phase shift φ0 is observed directly through measurements of the current-phase relationship in a Josephson interferometer. This result provides a direct measurement of the spin-orbit coupling strength and open new possibilities for phase-controlled Josephson devices made from materials with strong spin-orbit coupling.