Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks

Motivated by an important recent experiment [Deng et al., Science 354, 1557 (2016)], we theoretically consider the interplay between Andreev bound states(ABSs) and Majorana bound states(MBSs) in quantum dot-nanowire semiconductor systems with proximity-induced superconductivity(SC), spin-orbit coupling and Zeeman splitting. The dot induces ABSs in the SC nanowire which show complex behavior as a function of Zeeman splitting and chemical potential, and the specific question is whether two such ABSs can come together forming a topological MBS. We consider physical situations involving the dot being non-SC, SC, or partially SC. We find that the ABSs indeed tend to coalesce together producing near-zero-energy midgap states as Zeeman splitting and/or chemical potential are increased, but this mostly happens in the non-topological regime although there are situations where the ABSs could come together forming a topological MBS. The two scenarios(two ABSs forming a near-zero-energy non-topological ABS or a zero-energy topological MBS) are difficult to distinguish by tunneling conductance spectroscopy due to essentially the same signatures. Theoretically we distinguish them by knowing the critical Zeeman splitting for the topological quantum phase transition or by calculating the topological visibility. We find that the "sticking together" propensity of ABSs to produce a zero-energy midgap state is generic in class D systems, and by itself says nothing about the topological nature of the underlying SC nanowire. One must use caution in interpreting tunneling conductance measurements where the midgap sticking-together behavior of ABSs cannot be construed as definitive evidence for topological SC with non-Abelian MBSs. We also suggest some experimental techniques for distinguishing between trivial and topological ZBCPs.Comment: 32 pages, 29 figure

A geometric protocol for a robust Majorana magic gate

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves the missing, so called, $\pi/8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $\pi/8$ is substituted by any $\alpha$.Comment: 14 pages, 8 figures (including appendices), v3: simplified derivation, more explicit connection between topological protection and exponential convergenc

Systematic Comparison of HF CMOS Transconductors

Transconductors are commonly used as active elements in high-frequency (HF) filters, amplifiers, mixers, and oscillators. This paper reviews transconductor design by focusing on the V-I kernel that determines the key transconductor properties. Based on bandwidth considerations, simple V-I kernels with few or no internal nodes are preferred. In a systematic way, virtually all simple kernels published in literature are generated. This is done in two steps: 1) basic 3-terminal transconductors are covered and 2) then five different techniques to combine two of them in a composite V-I kernel. In order to compare transconductors in a fair way, a normalized signal-to-noise ratio (NSNR) is defined. The basic V-I kernels and the five classes of composite V-I kernels are then compared, leading to insight in the key mechanisms that affect NSNR. Symbolic equations are derived to estimate NSNR, while simulations with more advanced MOSFET models verify the results. The results show a strong tradeoff between NSNR and transconductance tuning range. Resistively generated MOSFETs render the best NSNR results and are robust for future technology developments

An Introduction to Breakdown Phenomena in Disordered Systems

The rupture of a medium under stress typifies breakdown phenomena. More generally, the latter encompass the dynamics of systems of many interacting elements governed by the interplay of a driving force with a pinning disorder, resulting in a macroscopic transition. A simple mean-field formalism incorporating these features is presented and applied to systems representative of fracture phenomena, social dilemmas, and magnets out of equilibrium. The similarities and differences in the corresponding mathematical structures are emphasized. The solutions are best obtained from a graphical method, from which very general conclusions may be drawn. In particular, the various classes of disorder distribution are treated without reference to a particular analytical or numerical form, and are found to lead to qualitatively different transitions. Finally, the notion of effective (or phenomenological) theory is introduced and illustrated for non-equilibrium disordered magnets.Comment: Pedagogical article published as part of a special issue on thermodynamics and statistical physics; 20 page

Periodic magnetoconductance fluctuations in triangular quantum dots in the absence of selective probing

We have studied the magnetoconductance of quantum dots with triangular symmetry and areas down to 0.2 square microns, made in a high mobility two-dimensional electron gas embedded in a GaAs-AlGaAs heterostructure. Semiclassical simulations show that the gross features in the measured magnetoconductance are caused by ballistic effects. Below 1 K we observe a strong periodic oscillation, which may be explained in terms of the Aharanov-Bohm flux quantization through the area of a single classical periodic orbit. From a numerical and analytical analysis of possible trajectories in hard- and soft-walled potentials, we identify this periodic orbit as the enscribed triangle. Contrary to other recent experiments, this orbit is not accessible by classical processes for the incoming collimated beam.Comment: RevTex 8 pages, including 5 postscript figure

Metodologia Per la Caratterizzazione di amplificatori a basso rumore per UMTS

In questo lavoro si presenta una metodologia di progettazione elettronica a livello di sistema, affrontando il problema della caratterizzazione dello spazio di progetto dell' amplificatore a basso rumore costituente il primo stadio di un front end a conversione diretta per UMTS realizzato in tecnologia CMOS con lunghezza di canale .18u. La metodologia è sviluppata al fine di valutare in modo quantititativo le specifiche ottime di sistema per il front-end stesso e si basa sul concetto di Piattaforma Analogica, che prevede la costruzione di un modello di prestazioni per il blocco analogico basato su campionamento statistico di indici di prestazioni del blocco stesso, misurati tramite simulazione di dimensionamenti dei componenti attivi e passivi soddisfacenti un set di equazioni specifico della topologia circuitale. Gli indici di prestazioni vengono successivamente ulizzati per parametrizzare modelli comportamentali utilizzati nelle fasi di ottimizzazione a livello di sistema. Modelli comportamentali atti a rappresentare i sistemi RF sono stati pertanto studiati per ottimizzare la scelta delle metriche di prestazioni. L'ottimizzazione dei set di equazioni atti a selezionare le configurazione di interesse per il campionamento ha al tempo stesso richiesto l'approfondimento dei modelli di dispositivi attivi validi in tutte le regioni di funzionamento, e lo studio dettagliato della progettazione degli amplificatori a basso rumore basati su degenerazione induttiva. Inoltre, il problema della modellizzazione a livello di sistema degli effetti della comunicazione tra LNA e Mixer è stato affrontato proponendo e analizzando diverse soluzioni. Il lavoro ha permesso di condurre un'ottimizzazione del front-end UMTS, giungendo a specifiche ottime a livello di sistema per l'amplificatore stesso