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abstract: Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed matter physics. In this Review, we survey the current status of this rapidly developing field, focusing on proposals for the realization of topological superconductivity in semiconductor superconductor heterostructures. We examine materials science progress in growing InAs and InSb semiconductor nanowires and characterizing these systems. We then discuss the observation of robust signatures of Majorana zero modes in recent experiments, paying particular attention to zero bias tunnelling conduction measurements and Coulomb blockade experiments. We also outline several next generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana based topological quantum computation.Realizing topological superconductivity and Majorana zero modes in the laboratory is a major goal in condensed matter physics. In this Review, the rapidly developing field is surveyed, with a focus on the realization of topological superconductivity in semiconductor superconductor heterostructures.
author_names: R M Lutchyn

Erik P A M Bakkers

L P Kouwenhoven

Peter Krogstrup

Charles M Marcus

Yuval Oreg
title: Majorana zero modes in superconductor semiconductor heterostructures
venue: Nature Reviews Materials
year: 2018

abstract: 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.
author_names: P Zhang

Koichiro Yaji

Takahiro Hashimoto

Yuichi Ota

Takeshi Kondo

Kozo Okazaki

Zhijun Wang

Jinsheng Wen

Genda Gu

Hong Ding

Shik Shin
title: Observation of topological superconductivity on the surface of an iron based superconductor
venue: Science
year: 2018

abstract: An iron home for Majoranas The surface of the iron based superconductor FeTe0.55Se0.45 has been identified as a potential topological superconductor and is expected to host exotic quasiparticles called the Majorana bound states (MBSs) Wang et al. looked for signatures of MBSs in this material by using scanning tunneling spectroscopy on the vortex cores formed by the application of a magnetic field. In addition to conventional states, they observed the characteristic zero bias peaks associated with MBSs and were able to distinguish between the two, owing to the favorable ratios of energy scales in the system. Science, this issue p. 333 Scanning tunneling spectroscopy reveals signatures of Majorana bound states on the surface of FeTe1 xSex. The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non Abelian statistics for robust quantum computation. Two dimensional superconducting topological materials have been predicted to host MBSs as zero energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron based superconductor FeTe0.55Se0.45, we observed a sharp zero bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.
author_names: Dongfei Wang

Lingyuan Kong

Peng Fan

Hui Chen

Shiyu Zhu

Wenyao Liu

Lu Cao

Yujie Sun

Shixuan Du

John A Schneeloch

Ruidan Zhong

Genda Gu

Liang Fu

Hong Ding

Hongjun Gao
title: Evidence for Majorana bound states in an iron based superconductor
venue: Science
year: 2018

abstract: A propagating Majorana mode Although Majorana fermions remain elusive as elementary particles, their solid state analogs have been observed in hybrid semiconductor superconductor nanowires. In a nanowire setting, the Majorana states are localized at the ends of the wire. He et al. built a two dimensional heterostructure in which a one dimensional Majorana mode is predicted to run along the sample edge (see the Perspective by Pribiag) The heterostructure consisted of a quantum anomalous Hall insulator (QAHI) bar contacted by a superconductor. The authors used an external magnetic field as a "knob" to tune into a regime where a Majorana mode was propagating along the edge of the QAHI bar covered by the superconductor. A signature of this propagation half quantized conductance was then observed in transport experiments. Science, this issue p. 294; see also p. 252 Transport experiments showing half integer quantized conductance indicate a propagating Majorana edge mode. Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantum computing.
author_names: Qing Lin He

Lei Pan

Alex Stern

Edward C Burks

Xiaoyu Che

Gen Yin

Jing Wang

Biao Lian

Quan Zhou

Eun Sang Choi

Koichi Murata

Xufeng Kou

Zhijie Chen

Tianxiao Nie

Qiming Shao

Yabin Fan

Shou-Cheng Zhang

Kai Liu

Jing Xia

Kang L Wang
title: Chiral Majorana fermion modes in a quantum anomalous Hall insulator superconductor structure
venue: Science
year: 2017

abstract: Majoranas Arrive When a negatively charged electron meets a positron its positively charged antiparticle they annihilate each other in a flash of gamma rays. A Majorana fermion, on the other hand, is a neutral particle, which is its own antiparticle. No sightings of a Majorana have been reported in the elementary particle world, but recently they have been proposed to exist in solid state systems and suggested to be of interest as a quantum computing platform. Mourik et al. (p. 1003, published online 12 April; see the cover; see the Perspective by Brouwer) set up a semiconductor nanowire contacted on each end by a normal and a superconducting electrode that revealed evidence of Majorana fermions. Theoretically predicted particles that double as their own antiparticles emerge in a superconductor coupled indium antimonide nanowire. Majorana fermions are particles identical to their own antiparticles. They have been theoretically predicted to exist in topological superconductors. Here, we report electrical measurements on indium antimonide nanowires contacted with one normal (gold) and one superconducting (niobium titanium nitride) electrode. Gate voltages vary electron density and define a tunnel barrier between normal and superconducting contacts. In the presence of magnetic fields on the order of 100 millitesla, we observe bound, midgap states at zero bias voltage. These bound states remain fixed to zero bias, even when magnetic fields and gate voltages are changed over considerable ranges. Our observations support the hypothesis of Majorana fermions in nanowires coupled to superconductors.
author_names: Vincent Mourik

Kun Zuo

Sergey M Frolov

Sebastien R Plissard

Erik P A M Bakkers

L P Kouwenhoven
title: Signatures of Majorana Fermions in Hybrid Superconductor Semiconductor Nanowire Devices
venue: Science
year: 2012

abstract: 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.
author_names: Stevan Nadj-Perge

Ilya Drozdov

Jian Li

Hua Chen

Sangjun Jeon

Jungpil Seo

Allan H MacDonald

Bogdan Andrei Bernevig

Ali Yazdani
title: Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor
venue: Science
year: 2014

abstract: Recently, theory has predicted a Majorana zero mode (MZM) to induce spin selective Andreev reflection (SSAR) a novel magnetic property which can be used to detect the MZM. Here, spin polarized scanning tunneling microscopy or spectroscopy has been applied to probe SSAR of MZMs in a topological superconductor of the Bi_{2}Te_{3}/NbSe_{2} heterostructure. The zero bias peak of the tunneling differential conductance at the vortex center is observed substantially higher when the tip polarization and the external magnetic field are parallel rather than antiparallel to each other. This spin dependent tunneling effect provides direct evidence of MZM and reveals its magnetic property in addition to the zero energy modes. Our work will stimulate MZM research on these novel physical properties and, hence, is a step towards experimental study of their statistics and application in quantum computing.
author_names: Hao-Hua Sun

Kaiwen Zhang

Lunhui Hu

Chuan Li

Guan-Yong Wang

Hai-Yang Ma

Zhu-An Xu

Chun-lei Gao

Dandan Guan

Yao-Yi Li

Canhua Liu

Dong Qian

Yi Zhou

Liang Fu

Shao-Chun Li

Fu-chun Zhang

Jin-Feng Jia
title: Majorana Zero Mode Detected with Spin Selective Andreev Reflection in the Vortex of a Topological Superconductor.
venue: Physical review letters
year: 2016

abstract: New data, backed up by simulations, support the existence of Majorana fermions in the one dimensional topological superconductor that is induced by placing an aluminium superconductor close to an indium arsenide nanowire.
author_names: Anindya Sundar Das

Yuval Ronen

Yonatan Most

Yuval Oreg

Moty Heiblum

H Shtrikman
title: Zero bias peaks and splitting in an Al InAs nanowire topological superconductor as a signature of Majorana fermions
year: 2012

abstract: Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role in determining the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductor metal core shell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and the design of devices for specialized applications such as topological and gate controlled superconducting electronics. Our materials of choice, InAs/Al grown with epitaxially matched single plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and seems to solve the soft gap problem in superconducting hybrid structures.
author_names: Peter Krogstrup

N L B Ziino

W Chang

S M Albrecht

Morten Hannibal Madsen

Erik V Johnson

Jesper Nygard

Charles M Marcus

Thomas Sand Jespersen
title: Epitaxy of semiconductor superconductor nanowires.
venue: Nature materials
year: 2015

abstract: The fractional alternating current Josephson effect produces a series of steps in the current voltage characteristics of a superconducting junction driven at radiofrequencies. This unusual phenomenon is now observed in a semiconductor superconductor nanowire. What is more, a doubling in step size when a strong magnetic field is applied could be a possible signature of Majorana fermions, particles that are their own antiparticle.
author_names: Leonid P Rokhinson

Xinyu Liu

Jacek K Furdyna
title: The fractional a.c. Josephson effect in a semiconductor superconductor nanowire as a signature of Majorana particles
year: 2012