This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

https://iopscience.iop.org/article/10.1088/1361-6633/aa6ac7/pdf

Topological superconductors: a review

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

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Nature in London

Millimeter-sized ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ single crystals are grown out of a Bi-Te flux and characterized using magnetic, transport, scanning tunneling microscopy, and spectroscopy measurements. The magnetic structure of ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ below ${T}_{N}$ is determined by powder and single-crystal neutron diffraction measurements. Below ${T}_{N}$ = 24 K, ${\mathrm{Mn}}^{2+}$ moments order ferromagnetically in the $ab$ plane but antiferromagnetically along the crystallographic $c$ axis. The ordered moment is 4.04(13)${\ensuremath{\mu}}_{B}$/Mn at 10 K and aligned along the crystallographic $c$ axis in an A-type antiferromagnetic order. Below ${T}_{N}$, the electrical resistivity drops upon cooling or when going across the metamagnetic transition in increasing magnetic fields. A critical scattering effect is observed in the vicinity of ${T}_{N}$ in the temperature dependence of thermal conductivity, indicating strong spin-lattice coupling in this compound. However, no anomaly is observed in the temperature dependence of thermopower around ${T}_{N}$. Fine tuning of the magnetism and/or electronic band structure is needed for the proposed topological properties of this compound. The growth protocol reported in this work might be applied to grow high-quality crystals where the electronic band structure and magnetism can be finely tuned by chemical substitutions.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1395&context=ameslab_manuscripts

Crystal growth and magnetic structure of MnBi 2 Te 4

Material defects remain as the main bottleneck to the progress of topological insulators (TIs). In particular, efforts to achieve thin TI samples with dominant surface transport have always led to increased defects and degraded mobilities, thus making it difficult to probe the quantum regime of the topological surface states. Here, by utilizing a novel buffer layer scheme composed of an In2Se3/(Bi0.5In0.5)2Se3 heterostructure, we introduce a quantum generation of Bi2Se3 films with an order of magnitude enhanced mobilities than before. This scheme has led to the first observation of the quantum Hall effect in Bi2Se3.

Record Surface State Mobility and Quantum Hall Effect in Topological Insulator Thin Films via Interface Engineering.

/pdf/record-surface-state-mobility-and-quantum-hall-effect-in-2zw0wnew8u.pdf

Record surface state mobility and quantum Hall effect in topological insulator thin films via interface engineering

Combining high resolution scanning tunneling microscopy and first principles calculations, we identified the major native defects, in particular the Se vacancies and Se interstitial defects, that are responsible for the bulk conduction and nanoscale potential fluctuations in single crystals of archetypal topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. Here it is established that the defect concentrations in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ are far above the thermodynamic limit, and that the growth kinetics dominate the observed defect concentrations. Furthermore, through careful control of the synthesis, our tunneling spectroscopy suggests that our best samples are approaching the intrinsic limit with the Fermi level inside the band gap without introducing extrinsic dopants.

Toward the Intrinsic Limit of the Topological Insulator Bi 2 Se 3

In quasi-two-dimensional electron systems of layered transition metal dichalcogenides (TMDs) there is still controversy about the nature of the transitions to charge-density wave (CDW) phases, i.e., whether they are described by a Peierls-type mechanism or by a lattice-driven model. By performing scanning tunneling microscopy experiments on canonical TMD-CDW systems, we image the electronic modulation and the lattice distortion separately in 2H-TaS2, TaSe2, and NbSe2. Across the three materials, we found dominant lattice contributions instead of the electronic modulation expected from Peierls transitions, in contrast to the CDW states, which show the hallmark of contrast inversion between filled and empty states. Our results imply that periodic lattice distortion plays a vital role in the formation of CDW phases in TMDs and illustrate the importance of taking into account the more complicated lattice degrees of freedom when studying correlated electron systems.

Microscopic evidence for strong periodic lattice distortion in two-dimensional charge-density wave systems

We present scanning tunneling microscopy and spectroscopy experiments on the novel ${J}_{\mathrm{eff}}=1/2$ Mott insulator ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$. Local density of states (LDOS) measurements show an intrinsic insulating gap of 620 meV that is asymmetric about the Fermi level and is larger than previously reported values. The size of this gap suggests that ${\mathrm{Sr}}_{2}\mathrm{Ir}{\mathrm{O}}_{4}$ is likely a Mott rather than Slater insulator. In addition, we found a small number of native defects which create in-gap spectral weight. Atomically resolved LDOS measurements on and off the defects show that this energy gap is quite fragile. Together the extended nature of the 5$d$ electrons and poor screening of defects help explain the elusive nature of this gap.

/pdf/local-density-of-states-study-of-a-spin-orbit-coupling-3sxsdsqsbm.pdf

Jixia Dai

Papers

Record Surface State Mobility and Quantum Hall Effect in Topological Insulator Thin Films via Interface Engineering.

Record surface state mobility and quantum Hall effect in topological insulator thin films via interface engineering

Toward the Intrinsic Limit of the Topological Insulator Bi 2 Se 3

Microscopic evidence for strong periodic lattice distortion in two-dimensional charge-density wave systems

Local Density of States Study of a Spin-Orbit-Coupling Induced Mott Insulator Sr 2 IrO 4