Study of 0-π\pi phase transition in hybrid superconductor-InSb nanowire quantum dot devices

Hybrid superconductor-semiconducting nanowire devices provide an ideal platform to investigating novel intragap bound states, such as the Andreev bound states (ABSs), Yu-Shiba-Rusinov (YSR) states, and the Majorana bound states. The competition between Kondo correlations and superconductivity in Josephson quantum dot (QD) devices results in two different ground states and the occurrence of a 0-$\pi$ quantum phase transition. Here we report on transport measurements on hybrid superconductor-InSb nanowire QD devices with different device geometries. We demonstrate a realization of continuous gate-tunable ABSs with both 0-type levels and $\pi$-type levels. This allow us to manipulate the transition between 0 and $\pi$ junction and explore charge transport and spectrum in the vicinity of the quantum phase transition regime. Furthermore, we find a coexistence of 0-type ABS and $\pi$-type ABS in the same charge state. By measuring temperature and magnetic field evolution of the ABSs, the different natures of the two sets of ABSs are verified, being consistent with the scenario of phase transition between the singlet and doublet ground state. Our study provides insights into Andreev transport properties of hybrid superconductor-QD devices and sheds light on the crossover behavior of the subgap spectrum in the vicinity of 0-$\pi$ transition

Conjugate Points and Shocks in Nonlinear Optimal Control

In this paper the authors use the method of characteristics to extend the Jacobi conjugate points theory to the Bolza problem arising in nonlinear optimal control. This yields necessary and sufficient optimality conditions for weak and strong local minima stated in terms of the existence of a solution to a corresponding matrix Riccati differential equation. The same approach allows to investigate as well smoothness of the value function

Optimality and Characteristics of Hamilton-Jacobi-Bellman Equations

In this paper the authors study the Bolza problem arising in nonlinear optimal control and investigate under what circumstances the necessary conditions for optimality of Pontryagin's type are also sufficient. This leads to the question when shocks do not occur in the method of characteristics applied to the associated Hamilton-Jacobi-Bellman equation. In this case the value function is its (unique) continuously differentiable solution and can be obtained from the canonical equations. In optimal control this corresponds to the case when the optimal trajectory of the Bolza problem is unique for every initial state and the optimal feedback is an upper semicontinuous set-valued map with convex, compact images

Correlation-induced conductance suppression at level degeneracy in a quantum dot

The large, level-dependent g-factors in an InSb nanowire quantum dot allow for the occurrence of a variety of level crossings in the dot. While we observe the standard conductance enhancement in the Coulomb blockade region for aligned levels with different spins due to the Kondo effect, a vanishing of the conductance is found at the alignment of levels with equal spins. This conductance suppression appears as a canyon cutting through the web of direct tunneling lines and an enclosed Coulomb blockade region. In the center of the Coulomb blockade region, we observe the predicted correlation-induced resonance, which now turns out to be part of a larger scenario. Our findings are supported by numerical and analytical calculations.Comment: 5 pages, 4 figure

Formation of Long Single Quantum Dots in High Quality InSb Nanowires Grown by Molecular Beam Epitaxy

We report on realization and transport spectroscopy study of single quantum dots (QDs) made from InSb nanowires grown by molecular beam epitaxy (MBE). The nanowires employed are 50-80 nm in diameter and the QDs are defined in the nanowires between the source and drain contacts on a Si/SiO$_2$ substrate. We show that highly tunable QD devices can be realized with the MBE-grown InSb nanowires and the gate-to-dot capacitance extracted in the many-electron regimes is scaled linearly with the longitudinal dot size, demonstrating that the devices are of single InSb nanowire QDs even with a longitudinal size of ~700 nm. In the few-electron regime, the quantum levels in the QDs are resolved and the Land\'e g-factors extracted for the quantum levels from the magnetotransport measurements are found to be strongly level-dependent and fluctuated in a range of 18-48. A spin-orbit coupling strength is extracted from the magnetic field evolutions of a ground state and its neighboring excited state in an InSb nanowire QD and is on the order of ~300 $\mu$eV. Our results establish that the MBE-grown InSb nanowires are of high crystal quality and are promising for the use in constructing novel quantum devices, such as entangled spin qubits, one-dimensional Wigner crystals and topological quantum computing devices.Comment: 19 pages, 5 figure

Conjugate times and regularity of the minimum time function with differential inclusions

This paper studies the regularity of the minimum time function, $T(\cdot)$, for a control system with a general closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation which guarantees the propagation of the proximal subdifferential of $T$ along any optimal trajectory. Then, we obtain the local $C^2$ regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times

Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging

Coherent diffraction imaging (CDI) on Bragg reflections is a promising technique for the study of three-dimensional (3D) composition and strain fields in nanostructures, which can be recovered directly from the coherent diffraction data recorded on single objects. In this article we report results obtained for single homogeneous and heterogeneous nanowires with a diameter smaller than 100 nm, for which we used CDI to retrieve information about deformation and faults existing in these wires. The article also discusses the influence of stacking faults, which can create artefacts during the reconstruction of the nanowire shape and deformation.Comment: 18 pages, 6 figures Submitted to New Journal of Physic

A candidate gene study of tardive dyskinesia in the CATIE schizophrenia trial

Tardive dyskinesia (TD) is a movement disorder characterized by involuntary oro-facial, limb, and truncal movements. As a genetic basis for inter-individual variation is assumed, there have been a sizeable number of candidate gene studies. All subjects met diagnostic criteria for schizophrenia and were randomized to receive antipsychotic medications as participants in the Clinical Antipsychotic Trials of Intervention Effectiveness project (CATIE). TD was assessed via the Abnormal Involuntary Movement Scale at regular intervals. Probable TD was defined as meeting Schooler–Kane criteria at any scheduled CATIE visit (207/710 subjects, 29.2%). A total of 128 candidate genes were studied in 710 subjects—2,580 SNPs in 118 candidate genes selected from the literature (e.g., dopamine, serotonin, glutamate, and GABA pathways) and composite genotypes for 10 drug-metabolizing enzymes. No single marker or haplotype association reached statistical significance after adjustment for multiple comparisons. Thus, we found no support for either novel or prior associations from the literature

Detection of variable VHE gamma-ray emission from the extra-galactic gamma-ray binary LMC P3

Context. Recently, the high-energy (HE, 0.1-100 GeV) $\gamma$-ray emission from the object LMC P3 in the Large Magellanic Cloud (LMC) has been discovered to be modulated with a 10.3-day period, making it the first extra-galactic $\gamma$-ray binary. Aims. This work aims at the detection of very-high-energy (VHE, >100 GeV) $\gamma$-ray emission and the search for modulation of the VHE signal with the orbital period of the binary system. Methods. LMC P3 has been observed with the High Energy Stereoscopic System (H.E.S.S.); the acceptance-corrected exposure time is 100 h. The data set has been folded with the known orbital period of the system in order to test for variability of the emission. Energy spectra are obtained for the orbit-averaged data set, and for the orbital phase bin around the VHE maximum. Results. VHE $\gamma$-ray emission is detected with a statistical significance of 6.4 $\sigma$. The data clearly show variability which is phase-locked to the orbital period of the system. Periodicity cannot be deduced from the H.E.S.S. data set alone. The orbit-averaged luminosity in the $1-10$ TeV energy range is $(1.4 \pm 0.2) \times 10^{35}$ erg/s. A luminosity of $(5 \pm 1) \times 10^{35}$ erg/s is reached during 20% of the orbit. HE and VHE $\gamma$-ray emissions are anti-correlated. LMC P3 is the most luminous $\gamma$-ray binary known so far.Comment: 5 pages, 3 figures, 1 table, accepted for publication in A&

Atomic scale strain relaxation in axial semiconductor III-V nanowire heterostructures

Combination of mismatched materials in semiconductor nanowire heterostructures offers a freedom of bandstructure engineering that is impossible in standard planar epitaxy. Nevertheless, the presence of strain and structural defects directly control the optoelectronic properties of these nanomaterials. Understanding with atomic accuracy how mismatched heterostructures release or accommodate strain, therefore, is highly desirable. By using atomic resolution high angle annular dark field scanning transmission electron microscopy combined with geometrical phase analyses and computer simulations, we are able to establish the relaxation mechanisms (including both elastic and plastic deformations) to release the mismatch strain in axial nanowire heterostructures. Formation of misfit dislocations, diffusion of atomic species, polarity transfer, and induced structural transformations are studied with atomic resolution at the intermediate ternary interfaces. Two nanowire heterostructure systems with promising applications (InAs/InSb and GaAs/GaSb) have been selected as key examples