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Engineering composite materials and devices with desired topological properties is accelerating the development of topological physics and its applications. Approaches of realizing novel topological hybrids, including in-situ epitaxy growth, planar/layered superlattices, and assembled (artificial) atom/dot arrays, etc., endow the topological systems with a substantial degree of control and tunability. Here, we propose a framework for realizing a field-programmable topological array (FPTA) that enables the implementation of dynamically reconfigurable topological platforms. FPTA allows for the independent, simultaneous, and local programmability of the various platform properties, such as the electromagnetic field, the spin-orbit field, and the superconducting order parameter. To demonstrate the effectiveness of the FPTA in rendering the system topologically-nontrivial and implementing non-Abelian manipulations, we simulate their operation in various case-studies. Our framework provides a playground for unearthing novel topological phases using components of high feasibility and sets the guidelines for run-time dynamic reconfiguration which is crucial for high-performance topological electronic circuits and quantum computing., Comment: 15 pages,6 figures

We present a novel route to realizing topological superconductivity using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. In the destructive Little-Parks regime, reentrant regions of superconductivity are associated with integer number of phase windings in the shell. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state around one applied flux quantum, {\Phi}_0 = h/2e, corresponding to 2{\pi} phase winding. Theoretical analysis indicates that in the presence of radial spin-orbit coupling in the semiconductor, the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Realistic modeling shows a topological phase persisting over a wide range of parameters, and reproduces experimental tunneling conductance data. Further measurements of Coulomb blockade peak spacing around one flux quantum in full-shell nanowire islands shows exponentially decreasing deviation from 1e periodicity with device length, consistent with Majorana modes at the ends of the nanowire., Comment: NBI QDEV CMT 2020. Supersedes previous separate theory (arXiv:1809.05512) and experiment (arXiv:1809.05513) versions

We demonstrate a novel means of creating Majorana zero modes using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core, unifying approaches based on proximitized nanowires and vortices in topological superconductors. In the destructive Little-Parks regime, reentrant regions of superconductivity are associated with integer number of phase windings in the shell. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state for flux around {\Phi}_0 = h/2e, corresponding to 2{\pi} phase winding. Coulomb peak spacing in full-shell islands around one applied flux shows exponentially decreasing deviation from 1e periodicity with device length, consistent with the picture of Majorana modes located at the ends of the wire.

The interplay between superconductivity and the Kondo effect has stimulated significant interest in condensed matter physics. They compete when their critical temperatures are close and can give rise to a quantum phase transition that can mimic Majorana zero modes. Here, we have fabricated and measured Al-InSb nanowire quantum dot-Al devices. In the Kondo regime, a supercurrent- induced zero-bias conductance peak emerges. This zero-bias peak shows an anomalous negative magnetoresistance (NMR) at weak magnetic fields. We attribute this anomalous NMR to quasi- particle trapping at vortices in the superconductor leads as a weak magnetic field is applied. The trapping effect lowers the quasiparticle-caused dissipation and thus enhances the Josephson current. This work connects the vortex physics and the supercurrent tunneling in Kondo regimes and can help further understand the physics of Josephson quantum dot system., Comment: 11 pages, 10 figures, Supplemental Materials

We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications., Comment: NBI QDEV 2018

Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a well-developed Majorana mode., Comment: As published version

We use the effective g-factor of subgap states, g*, in hybrid InAs nanowires with an epitaxial Al shell to investigate how the superconducting density of states is distributed between the semiconductor core and the metallic shell. We find a step-like reduction of g* and improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and g* exceeding the g-factor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zero-bias conductance peak.

Hybrid nanowires combining semiconductor and superconductor materials appear well suited for the creation, detection, and control of Majorana bound states (MBSs). We demonstrate the emergence of MBSs from coalescing Andreev bound states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot at the end of the nanowire as a spectrometer. Electrostatic gating tuned the nanowire density to a regime of one or a few ABSs. In an applied axial magnetic field, a topological phase emerges in which ABSs move to zero energy and remain there, forming MBSs. We observed hybridization of the MBS with the end-dot bound state, which is in agreement with a numerical model. The ABS/MBS spectra provide parameters that are useful for understanding topological superconductivity in this system., Comment: Article and Supplementary Material

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 figures

We explore the signatures of Majorana fermions in a nanowire based topological superconductor-quantum dot-topological superconductor hybrid device by charge transport measurements. The device is made from an epitaxially grown InSb nanowire with two superconductor Nb contacts on a Si/SiO$_2$ substrate. At low temperatures, a quantum dot is formed in the segment of the InSb nanowire between the two Nb contacts and the two Nb contacted segments of the InSb nanowire show superconductivity due to the proximity effect. At zero magnetic field, well defined Coulomb diamonds and the Kondo effect are observed in the charge stability diagram measurements in the Coulomb blockade regime of the quantum dot. Under the application of a finite, sufficiently strong magnetic field, a zero-bias conductance peak structure is observed in the same Coulomb blockade regime. It is found that the zero-bias conductance peak is present in many consecutive Coulomb diamonds, irrespective of the even-odd parity of the quasi-particle occupation number in the quantum dot. In addition, we find that the zero-bias conductance peak is in most cases accompanied by two differential conductance peaks, forming a triple-peak structure, and the separation between the two side peaks in bias voltage shows oscillations closely correlated to the background Coulomb conductance oscillations of the device. The observed zero-bias conductance peak and the associated triple-peak structure are in line with the signatures of Majorana fermion physics in a nanowire based topological superconductor-quantum dot-topological superconductor system, in which the two Majorana bound states adjacent to the quantum dot are hybridized into a pair of quasi-particle states with finite energies and the other two Majorana bound states remain as the zero-energy modes located at the two ends of the entire InSb nanowire., Comment: 6 pages, 4 figures

We present transport measurements in superconductor-nanowire devices with a gated constriction forming a quantum point contact. Zero-bias features in tunneling spectroscopy appear at finite magnetic fields, and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above ~ 0.5 T enhance conductance in the low-conductance (tunneling) regime but suppress conductance in the high-conductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as alternatives, including Kondo effect and analogs of 0.7 structure in a disordered nanowire., Comment: Supplemental Material here: https://dl.dropbox.com/u/1742676/Churchill_Supplemental.pdf

We report on the observation of excitation of Majorana fermions in a Nb-InSb nanowire quantum dot-Nb hybrid system. The InSb nanowire quantum dot is formed between the two Nb contacts by weak Schottky barriers and is thus in the regime of strong couplings to the contacts. Due to the proximity effect, the InSb nanowire segments covered by superconductor Nb contacts turn to superconductors with a superconducting energy gap $\Delta^*$. Under an applied magnetic field larger than a critical value for which the Zeeman energy in the InSb nanowire is $E_z\sim \Delta^*$, the entire InSb nanowire is found to be in a nontrivial topological superconductor phase, supporting a pair of Majorana fermions, and Cooper pairs can transport between the superconductor Nb contacts via the Majorana fermion states. This transport process will be suppressed when the applied magnetic field becomes larger than a second critical value at which the transition to a trivial topological superconductor phase occurs in the system. This physical scenario has been observed in our experiment. We have found that the measured zero-bias conductance for our hybrid device shows a conductance plateau in a range of the applied magnetic field in quasi-particle Coulomb blockade regions., Comment: 7 pages, 4 figures, supplementary materials of 3 pages and 1 figure