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.

/pdf/observation-of-majorana-fermions-in-ferromagnetic-atomic-5451hode2h.pdf

Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor

Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.

High-Temperature Majorana Corner States.

We review theoretical and experimental highlights in transport in two-dimensional materials focussing on key developments over the last five years. Topological insulators are finding applications in magnetic devices, while Hall transport in doped samples and the general issue of topological protection remain controversial. In transition metal dichalcogenides valley-dependent electrical and optical phenomena continue to stimulate state-of-the-art experiments. In Weyl semimetals the properties of Fermi arcs are being actively investigated. A new field, expected to grow in the near future, focuses on the non-linear electrical and optical responses of topological materials, where fundamental questions are once more being asked about the intertwining roles of the Berry curvature and disorder scattering. In topological superconductors the quest for chiral superconductivity, Majorana fermions and topological quantum computing is continuing apace.

https://iopscience.iop.org/article/10.1088/2053-1583/ab6ff7/pdf

Transport in two-dimensional topological materials: recent developments in experiment and theory

Although signatures of superconductivity in Dirac semimetals have been reported, for instance by applying pressure or using point contacts, our understanding of the topological aspects of Dirac semimetal superconductivity is still developing. Here, we utilize nanoscale phase-sensitive junction technology to induce superconductivity in the Dirac semimetal Bi1−xSbx. Our radiofrequency irradiation experiments then reveal a significant contribution of 4π-periodic Andreev bound states to the supercurrent in Nb–Bi0.97Sb0.03–Nb Josephson junctions. The conditions for a substantial 4π contribution to the supercurrent are favourable because of the Dirac cone’s very broad transmission resonances and a measurement frequency faster than the quasiparticle poisoning rate. In addition, we show that a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0 to π regimes. Our results open the technologically appealing avenue of employing the topological bulk properties of Dirac semimetals for topological superconductivity research and topological quantum computer development.

/pdf/4p-periodic-andreev-bound-states-in-a-dirac-semimetal-1a4pu8ympj.pdf

4π-periodic Andreev bound states in a Dirac semimetal

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. An anomalous phase shift in a topological insulator based Josephson junction is expected but never been observed. Here, Assouline et al. observe an anomalous phase shift in a Bi2Se3 based Josephson junction in presence of an in-plane magnetic field, opening opportunities for phase-controlled Josephson devices.

/pdf/spin-orbit-induced-phase-shift-in-bi-2-se-3-josephson-1dcmwxw7g0.pdf

Spin-Orbit induced phase-shift in Bi 2 Se 3 Josephson junctions

Electrons in a Dirac semimetals possess linear dispersion in all three spatial dimensions, and form part of a developing platform of novel quantum materials. Bi$_{1-x}$Sb$_x$ supports a three-dimensional Dirac cone at the Sb-induced band inversion point. Nanoscale phase-sensitive junction technology is used to induce superconductivity in this Dirac semimetal. Radio frequency irradiation experiments reveal a significant contribution of 4$\pi$-periodic Andreev bound states to the supercurrent in Nb-Bi$_{0.97}$Sb$_{0.03}$-Nb Josephson junctions. The conditions for a substantial $4\pi$ contribution to the supercurrent are favourable because of the Dirac cone's topological protection against backscattering, providing very broad transmission resonances. The large g-factor of the Zeeman effect from a magnetic field applied in the plane of the junction, allows tuning of the Josephson junctions from 0 to $\pi$ regimes.

$4\pi$ periodic Andreev bound states in a Dirac semimetal

One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction is $\ensuremath{\pi}$-junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman-effect-induced $0\text{\ensuremath{-}}\ensuremath{\pi}$ transitions in ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, three-dimensional Dirac semimetal-based Josephson junctions. The large in-plane $g$ factor allows tuning of the Josephson junctions from 0 to $\ensuremath{\pi}$ regimes. This is revealed by measuring a $\ensuremath{\pi}$ phase shift in the current-phase relation measured with an asymmetric superconducting quantum interference device (SQUID). Additionally, we directly measure a nonsinusoidal current-phase relation in the asymmetric SQUID, consistent with models for ballistic Josephson transport.

/pdf/zeeman-effect-induced-0-p-transitions-in-ballistic-dirac-mqwhahpo0u.pdf

Zeeman-Effect-Induced 0 − π Transitions in Ballistic Dirac Semimetal Josephson Junctions

The field of topological materials science has recently been focusing on three-dimensional Dirac semimetals, which exhibit robust Dirac phases in the bulk. However, the absence of characteristic surface states in accidental Dirac semimetals (DSMs) makes it difficult to experimentally verify claims about the topological nature using commonly used surface-sensitive techniques. The chiral magnetic effect (CME), which originates from the Weyl nodes, causes an $\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{B}$-dependent chiral charge polarization, which manifests itself as negative magnetoresistance. We exploit the extended lifetime of the chirally polarized charge and study the CME through both local and nonlocal measurements in Hall bar structures fabricated from single crystalline flakes of the DSM ${\mathrm{Bi}}_{0.97}{\mathrm{Sb}}_{0.03}$. From the nonlocal measurement results we find a chiral charge relaxation time, which is over one order of magnitude larger than the Drude transport lifetime, underlining the topological nature of ${\mathrm{Bi}}_{0.97}{\mathrm{Sb}}_{0.03}$.

/pdf/nonlocal-signatures-of-the-chiral-magnetic-effect-in-the-2poiqvhduw.pdf

Jorrit Cornelis de Boer

Papers

4π-periodic Andreev bound states in a Dirac semimetal

$4\pi$ periodic Andreev bound states in a Dirac semimetal

Zeeman-Effect-Induced 0 − π Transitions in Ballistic Dirac Semimetal Josephson Junctions

Nonlocal signatures of the chiral magnetic effect in the Dirac semimetal Bi0.97Sb0.03