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Majorana zero modes (MZMs) are exotic excitations (in condensed matter systems) of fundamental scientific interest and hold great promise as the basis of fault-tolerant topological quantum computation. Though MZMs have been predicted in many platforms, their existence is still under debate. In this paper, we review the recent progress in engineering and detecting MZMs in semiconductor-superconductor heterostructures. We also briefly review the protocols for implementing topological quantum computation by hybrid semiconductor-superconductor nanowires. [ABSTRACT FROM AUTHOR]

With a series of recent breakthroughs, iron-based superconductors (FeSC) with a topological Dirac surface state are becoming a promising material platform for hosting Majorana zero modes, which we refer to as the iron-Majorana platform. This platform uniquely combines high-Tc superconductivity, a topological band structure, and electron correlations into a single material, successfully avoiding the difficulties of achieving intrinsic p-wave topological superconductors and superconductor/topological insulator heterojunction systems. The most important advantages of the iron-Majorana platform are its wide topological region and large quasiparticle gap, which provide strong topological protection for pure Majorana zero modes (MZMs). When the superconductor/topological insulator heterojunction systems, e.g., InAs/Al nanowire, have the controversies of being trivial Majorana-like states, the iron-Majorana platform, which possesses well-understood physics and clear experimental evidence of vortex MZMs, is more likely to be a true MZM. However, unlike the nanowire Majorana systems with clear theoretical proposals for braiding schemes, the iron-Majorana system has no concrete method for exchanging the vortex MZMs or constructing a topological qubit. In this article, we propose a roadmap of the future efforts required for more physical exploration and achieving the non-Abelian exchange statistics of MZMs based on the iron-Majorana platform. [ABSTRACT FROM AUTHOR]

A feasible strategy for realizing the Majorana fermions is searching for a simple compound with both bulk superconductivity and Dirac surface states. In this paper, we perform calculations of electronic band structure, the Fermi surface, and the surface states, and measure the resistivity, magnetization, and specific heat of a TlSb compound with a CsCl-type structure. The band structure calculations show that TlSb is a Dirac semimetal when spin-orbit coupling is considered. TlSb is first determined to be a type-II superconductor with Tc=4.38 K, Hc1(0) = 148 Oe, Hc2(0)=1.12 T, and κGL = 10.6. We also confirm that TlSb is a moderately coupled s-wave superconductor. Although we cannot determine the band near the Fermi level EF that is responsible for superconductivity, its coexistence with topological surface states implies that the TlSb compound may be a simple material platform to realize the fault-tolerant quantum computations. [ABSTRACT FROM AUTHOR]

Majorana fermion (MF), an exotic particle that is identical to its own antiparticle, was recently found in solid matter as a quasiparticle excitation, the Majorana zero mode (MZM), in the vortex of an artificial topological superconductor (TSC). This artificial TSC, first proposed by Fu and Kane in 2008, is a heterostructure made of a topological insulator BiTe and an s-wave superconductor NbSe. This paper will briefly review the experimental progresses based on the BiTe/NbSe heterostructure. All evidences are self-consistent and reveal that the MZM exists in the center of vortex. Those experimental results are also supported by theory. This finding is a milestone in the research of Majorana fermions in solid state physics and a starting point of MZM's application in topological quantum computation. [ABSTRACT FROM AUTHOR]

Topological superconductivity has drawn much attention recently, and most interests are focused on the Majorana bound states existing at the edges of one-dimensional topological superconductors. These Majorana bound states are ideal platform for studying non-Abelian statistics. Meanwhile, they are proposed to be useful in quantum computation. In this review, we introduce the basic concepts and models in this area. We begin from the Kitaev model, which is the most concise model for one-dimensional topological superconductivity. Then, we discuss how to realize this model with spin-orbit coupling in realistic materials. Finally, we show some simple methods to detect the Majorana bound states and study their novel properties with the help of adjacent quantum dots. [ABSTRACT FROM AUTHOR]