There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

A possible sighting of Majorana states Nearly 80 years ago, the Italian physicist Ettore Majorana proposed the existence of an unusual type of particle that is its own antiparticle, the so-called Majorana fermion. The search for a free Majorana fermion has so far been unsuccessful, but bound Majorana-like collective excitations may exist in certain exotic superconductors. Nadj-Perge et al. created such a topological superconductor by depositing iron atoms onto the surface of superconducting lead, forming atomic chains (see the Perspective by Lee). They then used a scanning tunneling microscope to observe enhanced conductance at the ends of these chains at zero energy, where theory predicts Majorana states should appear. Science, this issue p. 602; see also p. 547 Scanning tunneling microscopy is used to observe signatures of Majorana states at the ends of iron atom chains. [Also see Perspective by Lee] Majorana fermions are predicted to localize at the edge of a topological superconductor, a state of matter that can form when a ferromagnetic system is placed in proximity to a conventional superconductor with strong spin-orbit interaction. With the goal of realizing a one-dimensional topological superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the surface of superconducting lead (Pb). Using high-resolution spectroscopic imaging techniques, we show that the onset of superconductivity, which gaps the electronic density of states in the bulk of the Fe chains, is accompanied by the appearance of zero-energy end-states. This spatially resolved signature provides strong evidence, corroborated by other observations, for the formation of a topological phase and edge-bound Majorana fermions in our atomic chains.

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Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

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Λιόλιος Ξερολιβαδιώτης : ένας αγνοημένος Μακεδόνας αγωνιστής του '21 και λίγα για την ιστορία του Ξερολιβάδου/ Γιώργου Χ. Χιονίδη

The controlled creation, manipulation and detection of spin-polarized currents by purely electrical means remains a central challenge of spintronics. Efforts to meet this challenge by exploiting the coupling of the electron orbital motion to its spin, in particular Rashba spin-orbit coupling, have so far been unsuccessful. Recently, it has been shown theoretically that the confining potential of a small current-carrying wire with high intrinsic spin-orbit coupling leads to the accumulation of opposite spins at opposite edges of the wire, though not to a spin-polarized current. Here, we present experimental evidence that a quantum point contact -- a short wire -- made from a semiconductor with high intrinsic spin-orbit coupling can generate a completely spin-polarized current when its lateral confinement is made highly asymmetric. By avoiding the use of ferromagnetic contacts or external magnetic fields, such quantum point contacts may make feasible the development of a variety of semiconductor spintronic devices.

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All-Electric Quantum Point Contact Spin Polarizer

Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase measurements as the fingerprint of the topological transition are missing. By embedding two gate-tunable $\mathrm{Al}/\mathrm{InAs}$ Josephson junctions in a loop geometry, we measure a $\ensuremath{\pi}$ jump in the junction phase with an increasing in-plane magnetic field ${\mathbit{B}}_{\ensuremath{\parallel}}$. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in ${\mathbit{B}}_{\ensuremath{\parallel}}$. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana bound states.

Phase Signature of Topological Transition in Josephson Junctions.

In a standard Josephson junction the current is zero when the phase difference between superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin–orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect—the hallmark effect of superconducting spintronics—which can be characterized by the corresponding anomalous phase shift. Here we report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device. By gate controlling the density of InAs, we are able to tune the spin–orbit coupling in the Josephson junction. This gives us the ability to tune the anomalous phase, and opens new opportunities for superconducting spintronics, and new possibilities for realizing and characterizing topological superconductivity. The anomalous Josephson effect can be regarded as the hall-mark effect of superconducting spintronics. Here, the authors report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device.

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Gate controlled anomalous phase shift in Al/InAs Josephson junctions.

Establishment of phase-coherence and a non-dissipative (super)current between two weakly coupled superconductors, known as the Josephson effect, plays a foundational role in basic physics and applications to metrology, precision sensing, high-speed digital electronics, and quantum computing. The junction ranges from planar insulating oxides to single atoms, molecules, semiconductor nanowires, and generally to any finite-size coherent conductor. Recently, junctions of more than two superconducting terminals gained broad attention in the context of braiding of Majorana fermions in the solid state for fault-tolerant quantum computing, and accessing physics and topology in dimensions higher than three. Here we report the first observation of Josephson effect in 3- and 4-terminal junctions, fabricated in a top-down fashion from a semiconductor/superconductor (InAs/Al) epitaxial two-dimensional heterostructure. Due to interactions, the critical current of an N-terminal junction becomes the boundary of an (N-1)-dimensional manifold of simultaneously allowed supercurrents. The measured shapes of such manifolds are explained by the scattering theory of mesoscopic superconductivity, and they can be remarkably sensitive to the junction's symmetry class. Furthermore, we observed a notably high-order (up to 8) multiple Andreev reflections simultaneously across every terminals pair, which verifies the multi-terminal nature of normal scattering and a high interface quality in our devices. Given the previously shown gate-control of carrier density and evidence of spin-orbit scattering in InAs/Al heterostructures, and device compatibility with other 2D materials, the multi-terminal Josephson effect reported here can become a testbed for physics and applications of topological superconductivity.

The multi-terminal Josephson effect

Semiconductor-based Josephson junctions provide a platform for studying the proximity effect due to the possibility of tuning junction properties by gate voltage and large-scale fabrication of complex Josephson circuits. Recently, Josephson junctions using the InAs weak link with epitaxial aluminum contact have improved the product of normal resistance and critical current, IcRN, in addition to fabrication process reliability. Here, we study similar devices with epitaxial contact and find a large supercurrent and substantial product of IcRN in our junctions. However, we find a striking difference when we compare these samples with higher mobility samples in terms of the product of excess current and normal resistance, IexRN. The excess current is negligible in lower mobility devices, while it is substantial and independent of the gate voltage and junction length in high mobility samples. This indicates that even though both sample types have epitaxial contacts, only the high-mobility one has a high transparency interface. In the high mobility short junctions, we observe the values of IcRN/Δ ∼ 2.2 and IexRN/Δ ∼ 1.5 in semiconductor weak links.

Superconducting proximity effect in epitaxial Al-InAs heterostructures

Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4$\pi$ periodic current phase relation. The experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. Here, we report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is found to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4$\pi$ periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4$\pi$ Josephson junctions in relationship to topological superconductivity.

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Kaushini Wickramasinghe

Papers

Phase Signature of Topological Transition in Josephson Junctions.

Gate controlled anomalous phase shift in Al/InAs Josephson junctions.

The multi-terminal Josephson effect

Superconducting proximity effect in epitaxial Al-InAs heterostructures

Missing Shapiro steps in topologically trivial Josephson Junction on InAs quantum well