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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

We calculate the double resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes, and two-phonons ones. Phonon and electronic dispersions reproduce calculations based on density functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kind of idealized defects. For an excitation energy of $\epsilon_L=2.4$ eV, the agreement with measurements is very good and calculations reproduce: the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the D, $D'$, 2D and $2D'$ lines; the line shapes; the presence of small intensity lines in the 1800, 2000 cm$^{-1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. According to the present findings, the intensity ratio between the $2D'$ and 2D lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and $D'$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal.

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Theory of double-resonant Raman spectra in graphene: intensity and line shape of defect-induced and two-phonon bands

A topological superconductor A promising path toward topological quantum computing involves exotic quasiparticles called the Majorana bound states (MBSs). MBSs have been observed in heterostructures that require careful nanofabrication, but the complexity of such systems makes further progress tricky. Zhang et al. identified a topological superconductor in which MBSs may be observed in a simpler way by looking into the cores of vortices induced by an external magnetic field. Using angle-resolved photoemission, the researchers found that the surface of the iron superconductor FeTe0.55Se0.45 satisfies the required conditions for topological superconductivity. Science, this issue p. 182 Angle-resolved photoemission spectroscopy indicates that FeTe0.55Se0.45 harbors Dirac-cone–type spin-helical surface states. Topological superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topological quantum computer. Most of the proposed topological superconductors are realized in difficult-to-fabricate heterostructures at very low temperatures. By using high-resolution spin-resolved and angle-resolved photoelectron spectroscopy, we find that the iron-based superconductor FeTe1–xSex (x = 0.45; superconducting transition temperature Tc = 14.5 kelvin) hosts Dirac-cone–type spin-helical surface states at the Fermi level; the surface states exhibit an s-wave superconducting gap below Tc. Our study shows that the surface states of FeTe0.55Se0.45 are topologically superconducting, providing a simple and possibly high-temperature platform for realizing Majorana states.

Observation of topological superconductivity on the surface of iron-based superconductor

A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat mini-band that arises a `magic' twist angle. However, the nature of the Mott insulator, origin of superconductivity and an effective low energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks U(1) valley symmetry, and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hunds coupling. We also identify symmetry related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight binding description. First, although the charge density is concentrated on the triangular lattice sites of the moir$\\text{e }$ pattern, the Wannier states of the tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat band necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat mini-band are derived, which highlight the importance of further neighbor hopping and interactions. We discuss consequences of this picture for superconducting states obtained on doping the valley ordered Mott insulator. We show how important features of the experimental phenomenology may be explained and suggest a number of further experiments for the future. We also describe a model for correlated states in trilayer graphene heterostructures and contrast it with the bilayer case.

Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene

We study theoretically the coupling of electric charge and spin polarization in an equilibrium and nonequilibrium electric transport across a two-dimensional Josephson configuration comprised of disordered surface channels of a three-dimensional topological insulator. In the equilibrium state of the system, we predict the Edelstein effect, which is much more pronounced than its counterpart in conventional spin-orbit coupled materials. Employing a quasiclassical Keldysh technique, we demonstrate that the ground state of the system can be shifted experimentally into arbitrary macroscopic superconducting phase differences other than the standard ``0'' or ``$\ensuremath{\pi}$,'' constituting a ${\ensuremath{\phi}}_{0}$ junction, solely by modulating a quasiparticle flow injection into the junction. We propose a feasible experiment in which the quasiparticles are injected into the topological insulator surface by means of a normal electrode and voltage gradient so that oppositely oriented stationary spin densities can be developed along the interfaces and allow for direct use of the spin-momentum locking nature of Dirac fermions in the surface channels. The ${\ensuremath{\phi}}_{0}$ state is proportional to the voltage difference applied between the injector electrode and superconducting terminals that calibrates the injection rate of particles and, therefore, the ${\ensuremath{\phi}}_{0}$ shift.

Magnetoelectrics in disordered topological insulator Josephson junctions

We study superconductivity in a Weyl semimetal with a tilted dispersion around two Weyl points of opposite chirality. In the absence of any tilt, the state with zero momentum pairing between two Fermi sheets enclosing each Weyl point has four point nodes in the superconducting gap function. Moreover, the surface of the superconductor hosts Fermi arc states and Majorana flat bands. We show that a quantum phase transition occurs at a critical value of the tilt, at which two gap nodes disappear by merging at the center of the first Brillouin zone, or by escaping at its edges, depending on the direction of the tilt. The region in the momentum space that the Majorana flat band occupies is found to increase as the tilt parameter is made larger. Additionally, the superconducting critical temperature and electronic specific heat can be enhanced in the vicinity of the quantum phase transition due to the singularity in the electronic density of states.

Superconductivity in type-II Weyl semimetals

We theoretically study the electromagnetic response of type-I and type-II centrosymmetric Weyl metals We derive an anisotropic permittivity tensor with off-diagonal elements to describe such gyrotropic media Our findings reveal that for appropriate Weyl cones tilts, the real part of the transverse component of the permittivity can exhibit an $\ensuremath{\epsilon}$-near-zero response The tilt parameter can also control the amount of loss in the medium, ranging from lossless to dissipative when transitioning from type-I to type-II Similarly, by tuning either the frequency of the electromagnetic field or the chemical potential in the system, an $\ensuremath{\epsilon}$-near-zero response can appear as the permittivity of the Weyl semimetal transitions between positive and negative values Employing the obtained permittivity tensor, we consider a setup where the Weyl semimetal is deposited on a perfect conductive substrate and study the refection and absorption characteristics of this nano-layered configuration We show that by choosing the proper geometrical and material parameters, devices can be created that perfectly absorb electromagnetic energy over a wide angular range of incident electromagnetic waves

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Epsilon-near-zero response and tunable perfect absorption in Weyl semimetals

We develop a theory for strain control of Majorana zero energy modes and the Josephson effect in black phosphorus (BP) devices proximity coupled to a superconductor. Employing realistic values for the band parameters subject to strain, we show that the strain closes the intrinsic band gap of BP; however, the proximity effect from the superconductor reopens it and creates Dirac and Weyl nodes. Our results illustrate that Majorana zero energy flat bands connect the nodes within the band-inverted regime in which their associated density of states is localized at the edges of the device. In a ferromagnetically mediated Josephson configuration, the exchange field induces superharmonics in the supercurrent phase relation in addition to a ${\ensuremath{\varphi}}_{0}$ phase shift, corresponding to a spontaneous supercurrent, and strain offers an efficient tool to control these phenomena. We analyze the experimental implications of our findings and show that they can pave the way for creating a rich platform for studying two-dimensional Dirac and Weyl superconductivity.

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Strain-engineered Majorana zero energy modes and φ 0 Josephson state in black phosphorus

Employing a Keldysh-Eilenberger technique, we theoretically study the generation of a spontaneous supercurrent and the appearance of the ${\ensuremath{\varphi}}_{0}$ phase shift parallel to uniformly in-plane magnetized superconducting interfaces made of the surface states of a three-dimensional topological insulator. We consider two weakly coupled uniformly magnetized superconducting surfaces where a macroscopic phase difference between the $s$-wave superconductors can be controlled externally. We find that, depending on the magnetization strength and orientation on each side, a spontaneous supercurrent due to the ${\ensuremath{\varphi}}_{0}$ states flows parallel to the interface at the nanojunction location. Our calculations demonstrate that nonsinusoidal phase relations of current components with opposite directions result in maximal spontaneous supercurrent at phase differences close to $\ensuremath{\pi}$. We also study the Andreev subgap channels at the interface and show that the spin-momentum locking phenomenon in the surface states can be uncovered through density of states studies. We finally discuss realistic experimental implications of our findings.

Mohammad Alidoust

Papers

Magnetoelectrics in disordered topological insulator Josephson junctions

Superconductivity in type-II Weyl semimetals

Epsilon-near-zero response and tunable perfect absorption in Weyl semimetals

Strain-engineered Majorana zero energy modes and φ 0 Josephson state in black phosphorus

Spontaneous supercurrent and φ 0 phase shift parallel to magnetized topological insulator interfaces