Narrow Results

The emergence of Majorana fermion bound states has been studied in several environments. In this paper, we discuss the current-voltage characteristics of a Majorana fermion state as a function of the voltage, temperature, and magnetic field and compare the results to experiment. Based on the agreement and identified parameters, we calculate the noise as possible proof of the emergence of Majorana fermions.

Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain “doubling” of the Hilbert space. In this work, we show that this redundancy in the Hilbert space can be completely lifted if the relevant orthogonal structure is taken into account. Such an approach allows for a treatment of Majorana fermions which is both physically and mathematically transparent. Furthermore, an explicit connection between orthogonal complex structures and the topological ${\mathbb{Z}}_2$-invariant is given.

Generation of the neutrino masses and leptogenesis (LG) in the standard model extended by the heavy Majorana fermions is considered. Classification of LG scenarios according to the new fermion mass spectra is given, where singlet–triplet LG is considered for the first time. The upper bound on the CP asymmetry relevant for LG with hierarchical heavy neutrinos (Davidson–Ibarra bound) is revised, and shown that in the case of one massless neutrino it essentially depends on the type of the light neutrino mass hierarchy. The resonant scenarios, which help to avoid the problem of extremely high reheating temperature in the early universe, are discussed. In particular, we present new simplified, generalized and detailed formulation of freed LG, which violates Davidson–Ibarra bound in a special class of models.

Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k_⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.

It is an honor and a pleasure to have been invited to give a talk in this conference celebrating the memory of the late Professor Abdus Salam. To my regret, I did not know Professor Salam personally, but I am very aware of his work and of his impact on my area of specialization, condensed matter physics, both intellectually through his ideas on spontaneously broken symmetry and more practically through his foundation of the ICTP. Since I assume that most of this audience are not specialized in condensed-matter physics, I thought I would talk about one topic which to some extent bridges this field and the particle-physics interests of Salam, namely Majorana fermions (M.F.s). However, as we shall see, the parallels which are often drawn in the current literature may be a bit too simplistic. I will devote most of this talk to a stripped-down exposition of the current orthodoxy concerning M.F.s. in condensed-matter physics and their possible applications to topological quantum computing (TQC), and then at the end briefly indicate why I believe this orthodoxy may be seriously misleading.

Recently, Majorana fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation. They are proposed to exist in various two-dimensional (2D) topological systems, such as $p_x+i{p}_y$ topological superconductor (SC) and nanowire–superconducting hybridization system. In this paper, we point out that Majorana fermions in different topological systems obey different types of polygon sign rules. A numerical approach is described to identify the type of polygon sign rule of the Majorana fermions. Applying the approach to study two 2D topological systems, we find that vortex-induced Majorana fermions obey topological polygon sign rule and line-defect-induced Majorana fermions obey normal polygon sign rule.

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation.

The Andreev conductance in $\mathrm{\Delta }$-shaped quantum dots (QDs) system coupled with Majorana bound states (MBSs) is studied and resulting conductance spectrum displays resonant and non-resonant processes. These fluctuated resonances render features like insulating band, bonding (antibonding) in the low-bias region due to non-trivial role of interdot coupling $t_c$ and dots-MBSs coupling $\lambda$. On comparing QD levels $({𝜀}_1,{𝜀}_2,{𝜀}_3)$, and the coupling between the MBSs, coherent oscillating dynamics of an electron between the nanowire and the QDs can be portrayed. The insulating band is robust against $\lambda$, but highly sensitive to $t_c$, which causes to increase (decrease) the conductance. We can claim that under finite bias voltage, transport can facilitate the researchers to expose the essential features of the Majorana fermion in such closed systems composed of MBSs.

It is an honor and a pleasure to have been invited to give a talk in this conference celebrating the memory of the late Professor Abdus Salam. To my regret, I did not know Professor Salam personally, but I am very aware of his work and of his impact on my area of specialization, condensed matter physics, both intellectually through his ideas on spontaneously broken symmetry and more practically through his foundation of the ICTP. Since I assume that most of this audience are not specialized in condensed-matter physics, I thought I would talk about one topic which to some extent bridges this field and the particle-physics interests of Salam, namely Majorana fermions (M.F.s). However, as we shall see, the parallels which are often drawn in the current literature may be a bit too simplistic. I will devote most of this talk to a stripped-down exposition of the current orthodoxy concerning M.F.s. in condensed-matter physics and their possible applications to topological quantum computing (TQC), and then at the end briefly indicate why I believe this orthodoxy may be seriously misleading…

What is a topological superfluid in a particle-number conserving system? Motivated by this question we report on a novel pathway to topological superfluidity with fermionic atoms in an optical lattice. We consider a situation where atoms in two internal states experience different lattice potentials: one species is localized and the other itinerant, and show how quantum fluctuations of the localized fermions give rise to an attraction and strong effective spin-orbit coupling in the itinerant band. At low temperature, these effects stabilize a topological superfluid of mobile atoms even if their bare interactions are repulsive. This emergent state can be engineered with ⁸⁷Sr atoms in a dimerized superlattice. To probe its unique properties we describe protocols that use high spectral resolution and controllability of the Sr clock transition, such as momentum-resolved spectroscopy and supercurrent response to a synthetic (laser-induced) magnetic field.

This article provides an overview, primarily from an experimental perspective, of recent progress and future prospects in using helium to realize a range of quantum materials of generic interest, by “top-down” and “bottom-up” nanotechnology. We can grow model systems to realise new quantum states of matter, and explore key issues in condensed matter physics. In the language of cold atomic gases, two dimensional and confined ³He and ⁴He provide “quantum simulators”, with the potential to uncover new emergent quantum states. These include: strictly 2D Fermi system with Mott-Hubbard transition; interacting coupled 2D fermion-boson system; heavy fermion quantum criticality; ideal 2D frustrated ferromagnetism; 2D quantum spin liquid; intertwined superfluid and density wave order with emergent large symmetry; topological mesoscopic superfluidity (new materials and emergent excitations).

The present paper is a discussion of how the idea of a distinction gives rise to fundamental physics. We discuss everything and nothing, and in the end we see that they are not distinct.