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

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

Strongly correlated systems can give rise to spectacular phenomenology, from high-temperature superconductivity to the emergence of states of matter characterized by long-range quantum entanglement. Low-density flat-band systems play a vital role because the energy range of the band is so narrow that the Coulomb interactions dominate over kinetic energy, putting these materials in the strongly-correlated regime. Experimentally, when a band is narrow in both energy and momentum, its filling may be tuned in situ across the whole range, from empty to full. Recently, one particular flat-band system—that of van der Waals heterostructures, such as twisted bilayer graphene—has exhibited strongly correlated states and superconductivity, but it is still not clear to what extent the two are linked. Here, we review the status and prospects for flat-band engineering in van der Waals heterostructures and explore how both phenomena emerge from the moire flat bands. The identification of superconductivity and strong interactions in twisted bilayer 2D materials prompted many questions about the interplay of these phenomena. This Perspective presents the status of the field and the urgent issues for future study.

/pdf/superconductivity-and-strong-correlations-in-moire-flat-145zhjtoy2.pdf

Superconductivity and strong correlations in moiré flat bands

We describe experimental signatures of Majorana fermion edge states, which form at the interface between a superconductor and the surface of a topological insulator. If a lead couples to the Majorana fermions through electron tunneling, the Majorana fermions induce resonant Andreev reflections from the lead to the grounded superconductor. The linear tunneling conductance is 0 (2e(2)/h) if there is an even (odd) number of vortices in the superconductor. Similar resonance occurs for tunneling into the zero mode in the vortex core. We also study the current and noise of a two-lead device.

https://dspace.mit.edu/openaccess-disseminate/1721.1/52593

Majorana Fermion Induced Resonant Andreev Reflection

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

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.

The emergence of flat bands and correlated behaviors in "magic angle" twisted bilayer graphene (tBLG) has sparked tremendous interest, though its many aspects are under intense debate. Here we report observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of ~0.93°, which is smaller than the magic angle by 15%. At an electron concentration of ±5 electrons/moire unit cell, we observe a narrow resistance peak with an activation energy gap ~0.1 meV. This indicates additional correlated insulating state, and is consistent with theory predicting a high-energy flat band. At doping of ±12 electrons/moire unit cell we observe resistance peaks arising from the Dirac points in the spectrum. Our results reveal that the "magic" range of tBLG is in fact larger than what is previously expected, and provide a wealth of new information to help decipher the strongly correlated phenomena observed in tBLG.

https://advances.sciencemag.org/content/advances/5/9/eaaw9770.full.pdf

Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle

The emergence of flat bands and correlated behaviors in 'magic angle' twisted bilayer graphene (tBLG) has sparked tremendous interest, though many aspects of the system are under intense debate. Here we report observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of approximately 0.93, which is smaller than the magic angle by 15%. At an electron concentration of +/-5 electrons per moire unit cell, we observe a narrow resistance peak with an activation energy gap of approximately 0.1 meV, indicating the existence of an additional correlated insulating state. This is consistent with theory predicting the presence of a high-energy band with an energetically flat dispersion. At a doping of +/-12 electrons per moire unit cell we observe a resistance peak due to the presence of Dirac points in the spectrum. Our results reveal that the magic range of tBLG is in fact larger than what is previously expected, and provide a wealth of new information to help decipher the strongly correlated phenomena observed in tBLG.

Correlated Insulating and Superconducting States in Twisted Bilayer Graphene Below the Magic Angle

Small-twist-angle (<2°) bilayer graphene has received extraordinary attention recently due to its exciting physical properties1–11. Compared with monolayer graphene, the Brillouin zone folding in twisted bilayer graphene (TBG) leads to the formation of a superlattice bandgap and substantial modification to the density of states4,6,7,12,13. However, these emerging properties have rarely been leveraged to realize new optoelectronic devices. Here, we demonstrate the strong, gate-tunable photoresponse in the mid-infrared wavelength range of 5 to 12 μm. A maximum extrinsic photoresponsivity of 26 mA W−1 has been achieved at 12 μm when the Fermi level in 1.81° TBG was tuned to its superlattice bandgap. Moreover, the strong photoresponse critically depends on the formation of a superlattice bandgap, and it vanishes in the gapless case with an ultrasmall twist angle (<0.5°). Our demonstration reveals the promising optical properties of TBG and provides an alternative material platform for tunable mid-infrared optoelectronics. Owing to the superlattice-induced bandgap and superlattice-enhanced density of states, small-twist-angled (<2°) bilayer graphene exhibits a strong gate-tunable photoresponse in the mid-infrared regime of 5 to 12 μm, reaching an extrinsic peak responsivity of 26 mA W−1 at 12 μm.

Qiyue Wang

Papers

High-Temperature Majorana Corner States.

Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle

Correlated Insulating and Superconducting States in Twisted Bilayer Graphene Below the Magic Angle

Strong mid-infrared photoresponse in small-twist-angle bilayer graphene

High-Temperature Majorana Corner States