Interferometric and noise signatures of Majorana fermion edge states in transport experiments

Domain walls between superconducting and magnetic regions placed on top of a topological insulator support transport channels for Majorana fermions. We propose to study noise correlations in a Hanbury Brown-Twiss type interferometer and find three signatures of the Majorana nature of the channels. First, the average charge current in the outgoing leads vanishes. Furthermore, we predict an anomalously large shot noise in the output ports for a vanishing average current signal. Adding a quantum point contact to the setup, we find a surprising absence of partition noise which can be traced back to the Majorana nature of the carriers.     

Kondo correlations and Majorana bound states in a metal to quantum-dot to topological-superconductor junction

Electron transport through a normal-metal-quantum-dot-topological-superconductor junction is studied and reveals interlacing physics of Kondo correlations with two Majorana fermions bound states residing on the opposite ends of the topological superconductor. When the strength of the Majorana fermion coupling exceeds the temperature T, this combination of Kondo-Majorana fermion physics might be amenable for an experimental test: The usual peak of the temperature dependent zero bias conductance σ(V=0,T) splits and the conductance has a dip at T=0. The heights of the conductance side peaks decrease with magnetic field.     

Influence of <Emphasis Type="Italic">CP</Emphasis> and <Emphasis Type="Italic">CPT</Emphasis> on production and decay of Dirac and Majorana fermions

The consequences of CP and CPT invariance for production and subsequent decay of Dirac and Majorana fermions in polarized fermion-antifermion annihilation are analytically studied. We derive general symmetry relations for the production spin density matrix and for the three-particle decay matrices and obtain constraints for the polarization and the spin-spin correlations of Dirac and Majorana fermions. We prove that only for Majorana fermions the energy and opening angle distribution factorizes exactly into contributions from production and decay if CP is conserved. Received: 6 November 2001 / Revised version: 23 April 2002 / Published online: 12 July 2002     

Chain of Majorana states from superconducting Dirac fermions at a magnetic domain wall

We study theoretically a strongly type-II s-wave superconducting state of two-dimensional Dirac fermions in proximity to a ferromagnet having in-plane magnetization. It is shown that a magnetic domain wall can host a chain of equally spaced vortices in the superconducting order parameter, each of which binds a Majorana-fermion state. The overlap integral of neighboring Majorana states is sensitive to the position of the chemical potential of the Dirac fermions. Thermal transport and scanning tunneling microscopy experiments to probe the Majorana fermions are discussed.     

双量子点结构中Majorana费米子的噪声特性

Majorana费米子是其自身的反粒子, 在拓扑量子计算中有着重要的应用. 利用粒子数表象下的量子主方程方法, 研究双量子点与Majorana费米子混合结构的电子输运特性, 特别是散粒噪声. 有无Majorana费米子耦合的电流与散粒噪声存在明显差别: 有Majorana费米子耦合时稳态电流差呈反对称, 噪声谱呈现相干振荡并且低频噪声显著增强. 量子点与Majorana费米子对称弱耦合时, 零频噪声由"峰"变为"谷", 并且"边谷"展宽逐渐减小; 当对称强耦合时, 零频噪声的谷深增加, "边谷"向高频端移动. 改变系统与电极的耦合强度时, 零频噪声由谷变成峰. 因此, 稳态电流结合散粒噪声可以探测双量子点结构中Majorana费米子是否存在.     

Majorana fermion modulated nonequilibrium transport through double quantum dots

Nonequilibrium electronic transports through a double-QD-Majorana coupling system are studied with a purpose to extract the information to identify Majorana bound states (MBSs). It is found that MBSs can help form various transport processes, including the nonlocal crossed Andreev reflection, local resonant Andreev reflection, and cotunneling, depending on the relative position of two dot levels. These processes enrich the signature of average currents and noise correlations to probe the nature of MBSs. We further demonstrate the switching between the current peaks of crossed Andreev reflection and cotunneling, which is closely related to the nonlocal nature of Majorana fermions. We also propose effective physical pictures to understand these Majorana-assisted transports.     

Leptogenesis with linear,inverse or double seesaw

The left-right symmetric model with doublet and bi-doublet Higgs scalars can accommodate linear, inverse or double seesaw for generating small neutrino masses in the presence of three singlet fermions. If the singlet fermions have small Majorana masses, they can form three pairs of quasi-degenerate Majorana fermions with three right-handed neutrinos. The decays of the quasi-degenerate Majorana fermions can realize the resonant leptogenesis. Alternatively, the right-handed neutrinos can obtain seesaw suppressed Majorana masses if the singlet fermions are very heavy. In this case leptogenesis, with or without resonant effect, is allowed in the decays of the right-handed neutrinos.     

Avoidance of Majorana resonances in periodic topological superconductor-nanowire structures

Semiconducting nanowires in proximity to superconductors are promising experimental systems for Majorana fermions which may ultimately be used as building blocks for topological quantum computers. A serious challenge in the experimental realization of the Majorana fermion in these semiconductor-superconductor-nanowire structures is tuning the semiconductor chemical potential in close proximity to the metallic superconductor. We show that presently realizable structures in experiments with tunable chemical potential lead to Majorana resonances, which are interesting in their own right, but do not manifest non-Abelian statistics. To resolve this crucial barrier to the solid state realization of Majorana fermions, we propose a new topological superconducting array structure where introducing the superconducting proximity effect from adjacent nanowires generates Majorana fermions with non-Abelian statistics.     

Hole-doped semiconductor nanowire on top of an s-wave superconductor: a new and experimentally accessible system for Majorana fermions

Majorana fermions were envisioned by Majorana in 1935 to describe neutrinos. Recently, it has been shown that they can be realized even in a class of electron-doped semiconductors, on which ordinary s-wave superconductivity is proximity induced, provided the time reversal symmetry is broken by an external Zeeman field above a threshold. Here we show that in a hole-doped semiconductor nanowire the threshold Zeeman field for Majorana fermions can be very small for some magic values of the hole density. In contrast to the electron-doped systems, smaller Zeeman fields and much stronger spin-orbit coupling and effective mass of holes allow the hole-doped systems to support Majorana fermions in a parameter regime which is routinely realized in current experiments.     

Majorana fermions in equilibrium and in driven cold-atom quantum wires

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.     

Dirac returns: Non-Abelian statistics of vortices with Dirac fermions

Topological superconductors classified as type D admit zero-energy Majorana fermions inside vortex cores, and consequently the exchange statistics of vortices becomes non-Abelian, giving a promising example of non-Abelian anyons. On the other hand, types C and DIII admit zero-energy Dirac fermions inside vortex cores. It has been long believed that an essential condition for the realization of non-Abelian statistics is non-locality of Dirac fermions made of two Majorana fermions trapped inside two well-separated vortices as in the case of type D. Contrary to this conventional wisdom, however, we show that vortices with local Dirac fermions also obey non-Abelian statistics.     

Unconventional Josephson signatures of Majorana bound states

A junction between two topological superconductors containing a pair of Majorana fermions exhibits a "fractional" Josephson effect, 4π periodic in the superconductors' phase difference. An additional fractional Josephson effect, however, arises when the Majorana fermions are spatially separated by a superconducting barrier. This new term gives rise to a set of Shapiro steps which are essentially absent without Majorana modes and therefore provides a unique signature for these exotic states.     

Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions

Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform any unitary transformation with arbitrary accuracy.Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions.Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures,which enable the braiding operation and the partial exchange operation.After defining a qubit by four chiral Majorana fermions,the singlequbit T and H quantum gates are realized via one partial exchange operation and three braiding operations,respectively.The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions.Besides,we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device.Thus,our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.     

Robustness of coherence between two quantum dots mediated by Majorana fermions

We study three important measurements used to identify the quantum correlations between two quantum dots(QDs)mediated by a pair of Majorana fermions(MFs) in a superconducting quantum wire. We find that, in addition to the quantum discord, the robustness of coherence(ROC) can also be considered as a quantity to measure the quantum correlation for the special case where the quantum entanglement is vanishing. For comparison, we study the quantum correlation between two QDs mediated by other fermions, i.e., regular fermions and superconducting fermions. We find that, when the quantum entanglement is not vanishing, i.e., the concurrence is finite, the detailed difference between the concurrence and ROC can be considered as an important implication for the existence of MFs.     

Majoranized Feynman rules

We point out that the compact Feynman rules for Majorana fermions proposed by Denner et al. are in fact a convention for the complex phases of (anti)spinors, valid for both Majorana and Dirac fermions. We establish the relation of this phase convention with that common in the use of spinor techniques.     

Majorana准粒子与超导体-半导体异质纳米线

Majorana准粒子是凝聚态物理版本的Majorana费米子.由于Majorana准粒子间的交换操作服从非阿贝尔统计,并基于此可构建更稳定的量子计算机,近年来在凝聚态物理界引起广泛关注.为帮助初学者快速理解Majorana准粒子的形成机理,本文回顾了在一维超导体-半导体异质纳米线系统中Majorana准粒子模型的提出和理论演化过程,介绍Kitaev链模型并分析了模型中各要素所起的作用.还介绍了典型Majorana器件的构成和测量方法,并结合最新的实验进展对探测到的零能电导峰进行了分析和述评.最后对超越一维系统的超导体-半导体异质系统的实验前景进行了展望.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

Introduction to Majorana masses

We present a pedogogical review of Majorana masses and Majorana's theory of two-component massive fermions. We discuss the difference between Majorana and Dirac masses and show that Majorana masses are formion-number violating. We discuss the connection between Majorana and, Weyl spinors and show that the massive Majorana and Weyl field theories are equivalent. We study the second quantization of the massive Weyl theory in detail.     

Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks

A scheme in semiconducting quantum nanowire structure has been proposed to demonstrate the non-Abelian statistics for Majorana fermions in terms of braid group. The Majorana fermions are localized at the endpoints of semiconducting wires, which are deposited on an s-wave superconductor. The non-Abelian nature of Majorana fermion is manifested by the fact that the output of the different applied orders of two operations, constructed by the braid group elements, are different. In particular, the difference can be unambiguously imprinted on the quantum states of a superconducting flux qubit.     

Floquet Majorana fermions in superconducting quantum dots

We consider different configurations of ac driven quantum dots coupled to superconductor leads where Majorana fermions can exist as collective quasiparticles. The main goal is to tune the existence, localization and properties of these zero energy quasiparticles by means of periodically driven external gates. In particular, we analyze the relevance of the system and driving symmetry. We predict the existence of different sweet spots with Floquet Majorana fermions in configurations where they are not present in the undriven system.