Ordinary Fermions Research Articles

The parastatistics of braided Majorana fermions

This paper presents the parastatistics of braided Majorana fermions obtained in the framework of a graded Hopf algebra endowed with a braided tensor product. The braiding property is encoded in a t-dependent 4×4 braiding matrix B_tBt related to the Alexander-Conway polynomial. The nonvanishing complex parameter t defines the braided parastatistics. At t=1 ordinary fermions are recovered. The values of t at roots of unity are organized into levels which specify the maximal number of braided Majorana fermions in a multiparticle sector. Generic values of t and the t=-1 root of unity mimick the behaviour of ordinary bosons.

Thermal transport in multiple Majorana edge states of hybrid topological superconductor junctions

The hybrid topological superconductor (TSC) with multiple Majorana edge states can be formed in a system where a magnetic topological insulator (MTI) thin film is coupled with two s-wave superconductors in proximity. The band structure and thermal transport properties of the hybrid TSC hosting chiral and helical Majorana edge states are investigated. By using the nonequilibrium Green’s function method combined with the Landauer–Büttiker formula, the scattering coefficients (i.e., the normal tunneling T, the local Andreev reflection TLAR, the crossed Andreev reflection TCAR) and two-terminal electric thermal conductance κe are calculated. With the change of the exchange field Mz, the system goes through a series of topological phase transitions. The chiral Majorana edge states, the helical Majorana edge states and the multiple Majorana edge states possessing both chiral and helical edge modes are induced at the boundary of TSC. At the boundary of the central TSC, a single Majorana fermion edge state is equivalent to half an ordinary fermion to carry heat, leading to the generation of a half-integer quantized thermal conductance plateau. Thus, half-integer (i.e., 1/2, 3/2) and integer (i.e., 1, 2) quantized thermal conductance plateaus appear in different topological phases. These quantized plateaus that survive well over a certain range of temperatures can be used experimentally to detect chiral and helical Majorana fermions.

Majorana nanowires for topological quantum computation

Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle–hole symmetric, and spatially-separated end modes which are topologically protected by the particle–hole symmetry of the superconducting state. Due to their topological nature, they are robust against local perturbations and, in an ideal environment, free from decoherence. Furthermore, unlike ordinary fermions and bosons, the adiabatic exchange of Majorana modes is noncommutative, i.e., the outcome of exchanging two or more Majorana modes depends on the order in which exchanges are performed. These properties make them ideal candidates for the realization of topological quantum computers. In this tutorial, I will present a pedagogical review of 1D topological superconductors and Majorana modes in quantum nanowires. I will give an overview of the Kitaev model and the more realistic Oreg–Lutchyn model, discuss the experimental signatures of Majorana modes, and highlight their relevance in the field of topological quantum computation. This tutorial may serve as a pedagogical and relatively self-contained introduction for graduate students and researchers new to the field, as well as an overview of the current state-of-the-art of the field and a reference guide to specialists.

Half-integer quantized thermal conductance plateau in chiral topological superconductor systems

We investigate the thermal transport properties of a quantum anomalous Hall insulator nanoribbon covered by superconductors. Due to the peculiar properties of chiral Majorana fermion (CMF) edge states, we found a half-integer quantized thermal conductance plateau. Different from the ordinary superconductor which conducts electricity but does not conduct heat, in the quantum anomalous Hall insulator--topological superconductor junction, the CMF occurs at the boundary of the topological superconductor which carries heat from left to right. A chiral topological superconductor with Chern number $\mathcal{N}=\ifmmode\pm\else\textpm\fi{}1$ has a single CMF, which is equivalent to half an ordinary fermion propagating along the edge, leading to a half-integer quantized thermal conductance plateau. When the topological superconducting edge has two CMFs, it is equivalent to ejecting an ordinary fermion, resulting in an integer quantized thermal conductance plateau. Moreover, the half-integer quantized thermal conductance can also be used to study the properties of Majorana Kramer pairs in a helical topological superconductor. Finally, we also find that the half-integer quantized plateau appears against moderate disorder and with the metal leads besides the quantum anomalous Hall insulator, which is promising to be realized in experiments.

Semiclassical Limit for Almost Fermionic Anyons

In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with magnetic interactions. We study a limit situation where the statistics/magnetic interaction is seen as a "perturbation from the fermionic end". We vindicate a mean-field approximation, proving that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional. The ground state of the latter displays anyonic behavior in its momentum distribution. Our proof is based on coherent states, Husimi functions, the Diaconis-Freedman theorem and a quantitative version of a semi-classical Pauli pinciple.

3D fermions and affine Yangian

2D (dimensional) Boson-Fermion correspondence is a well-known object. In this paper, we define 3D Fermions Γm→ and Γm→⁎ for any vertex m→ and the representation space F, we find that F is isomorphic to the vector space of 3D Young diagrams. Operators Γm→ and Γm→⁎ are defined with amplitudes, which are described by complex numbers e1,e2,e3 satisfying e1+e2+e3=0, then we find that Γm→ and Γm→⁎ have relations with the generators in affine Yangian, and states in F are corresponding to 3-Schur functions. We also discuss the slice of state in F, which corresponds to the slice of 3D Young diagram. Finally, we show that in special case, 3D Fermions and the representation space become ordinary 2D Fermions and charged zero Fermionic Fock space respectively.

Polarization effects in the search for a dark vector boson at e+e− colliders

We argue that the search for dark vector boson through $e^+e^-\to Z_d\gamma$ can determine the Lorentz structure of $Z_dl^+l^-$ couplings with the detection of leptonic decays $Z_d\to l^+l^-$. We assume a general framework that the dark vector boson interacts with ordinary fermions through vector and axial-vector couplings. As a consequence of Ward-Takahashi identity, $Z_d$ is transversely polarized in the limit $m_{Z_d}\ll \sqrt{s}$. On the other hand, the fraction of longitudinal $Z_d$ is non-negligible for $m_{Z_d}$ comparable to $\sqrt{s}$. Such polarization effects can be analyzed through angular distributions of final-state particles in $Z_d$ decays. Taking $l^{\pm}\equiv \mu^{\pm}$, we study the correlation between $Z_d$ angle relative to $e^-$ beam direction in $e^+e^-$ CM frame and $\mu^-$ angle relative to the boost direction of $Z_d$ in $Z_d$ rest frame. This correlation is shown to be useful for probing the Lorentz structure of $Z_dl^+l^-$ couplings. We discuss the measurement of such correlation in Belle II detector, taking into account the detector acceptance and energy resolution.

Mass splitting in an 331-TC coupled scenario

The root of most of the technicolor (TC) problems lies in the way the ordinary fermions acquire their masses, where an ordinary fermion [Formula: see text] couples to a technifermion [Formula: see text] mediated by an extended technicolor (ETC) boson leading to fermion masses that vary with the ETC mass scale [Formula: see text] as [Formula: see text]. Recently, we discussed a new approach consisting of models where TC and QCD are coupled through a larger theory, in this case the solutions of these equations are modified compared to those of the isolated equations, and TC and QCD self-energies are of the irregular form, which allows us to build models where ETC boson masses can be pushed to very high energies. In this work we extend these results for 331-TC models, in particular considering a coupled system of Schwinger–Dyson equations, we show that all technifermions of the model exhibit the same asymptotic behavior for TC self-energies. As an application we discuss how the mass splitting of the order [Formula: see text](100) GeV could be generated between the second and third generation of fermions.

Thermodynamic geometry of Kaniadakis statistics

We consider the thermodynamic geometry of an ideal gas with particles obeying Kaniadakis statistics. We work out the thermodynamic curvature of κ-Maxwell–Boltzmann, κ-Bose and κ-Fermi gases. Curvature of thermodynamic parameters space of an ideal ordinary classical gas is zero while it is negative for κ-classical gas. Also, the thermodynamic curvature of an ideal κ-Fermi gas is negative such as ordinary fermion gas. For an ideal κ-Bose gas, two different regimes is found. In fact, we introduce a specified value of temperature; T*, where for T > T* (T < T*) the thermodynamic curvature is negative (positive) and intrinsic statistical interaction is repulsive (attractive) while for an ordinary ideal boson gas, the thermodynamic curvature is positive and the statistical interaction is attractive in full physical range. Therefore, we argue that the κ induces repulsive interaction to particles. Finally, we consider the singular points of thermodynamic curvature of κ-Bose gas and work out the condensation temperature.

Fermion mass splitting in the technicolor coupled scenario

We discuss fermion mass generation in unified models where QCD and technicolor (or any two strongly interacting theories) have their Schwinger–Dyson equations coupled. In this case the technicolor (TC) and QCD self-energies are modified in comparison with the behavior observed in the isolated theories. In these models the pseudo-Goldstone boson masses are much higher than the ones obtained in different contexts, and phenomenological signals, except from a light scalar composite boson, will be quite difficult to be observed at present collider energies. The most noticeable fact of these models is how the mass splitting between the different ordinary fermions is generated. We discuss how a necessary horizontal (or family) symmetry can be implemented in order to generate the mass splitting between fermions of different generations; how the fermionic mass spectrum may be modified due to GUT interactions, as well as how the mass splitting within the same fermionic generation are generated due to electroweak and GUT interactions.

Composite Fermions as Deformed Oscillators: Wavefunctions and Entanglement

Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, п-mesons, excitons, Cooper pairs are not ideal bosons, and, likewise, baryons are not pure fermions. In our preceding papers, we studied bipartite composite boson (i.e. quasiboson) systems via a realization by deformed oscillators. Therein, the interconstituent entanglement characteristics such as entanglement entropy and purity were found in terms of the parameter of deformation. Herein, we perform an analogous study of composite Fermi-type particles, and explore them in two major cases: (i) “boson + fermion” composite fermions (or cofermions, or CFs); (ii) “deformed boson + fermion” CFs. As we show, cofermions in both cases admit only the realization by ordinary fermions. Case (i) is solved explicitly, and admissible wavefunctions are found along with entanglement measures. Case (ii) is treated within few modes both for CFs and constituents. The entanglement entropy and purity of CFs are obtained via the relevant parameters and illustrated graphically.

Perturbative unitarity bounds for effective composite models

In this paper we present the partial wave unitarity bound in the parameter space of dimension-5 and dimension-6 effective operators that arise in a compositeness scenario. These are routinely used in experimental searches at the LHC to constraint contact and gauge interactions between ordinary Standard Model fermions and excited (composite) states of mass M. After deducing the unitarity bound for the production process of a composite neutrino, we implement such bound and compare it with the recent experimental exclusion curves for Run 2, the High-Luminosity and High-Energy configurations of the LHC. Our results also applies to the searches where a generic single excited state is produced via contact interactions. We find that the unitarity bound, so far overlooked, is quite compelling and significant portions of the parameter space (M,Λ) become excluded in addition to the standard request M≥Λ.

Truncated q-deformed fermion algebras and phase transition

In this paper, we apply the q-deformed fermion theory to the phase transition from the ordinary fermion into the truncated q-deformed fermion at the critical temperature $$ T_\mathrm{c}$$ .

Parafermionic dark matter

To discuss the possible contribution of parafermions to the dark matter abundance, we extend the Boltzmann equation for fermionic dark matter to include parafermions. Parafermions can accommodate $r$ particles per quantum state $(2\le r<\infty)$, where the parafermion of order $r=1$ is identical to the ordinary fermion. It is found that the parafermionic dark matter can be more abundant than the fermionic dark matter in the present universe.

Imaging Anyons with Scanning Tunneling Microscopy

Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a property that would help realize fault tolerant quantum computation. Non-abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases (2DEG) in the presence of a large magnetic field, su ch as the $\nu=\tfrac{5}{2}$ FQH state. However, direct experimental evidence of anyons and tests that can distinguish between abelian and non-abelian quantum ground states with such excitations have remained elusive. Here we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH states with the scanning tunneling microscope (STM). Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures in such measurements that can distinguish different proposed ground states. The presence of locally trapped anyons should leave distinct signatures in STM spectroscopic maps, and enables a new approach to directly detect - and perhaps ultimately manipulate - these exotic quasi-particles.

Searching for an exotic spin-dependent interaction with a single electron-spin quantum sensor

Searching for new particles beyond the standard model is crucial for understanding several fundamental conundrums in physics and astrophysics. Several hypothetical particles can mediate exotic spin-dependent interactions between ordinary fermions, which enable laboratory searches via the detection of the interactions. Most laboratory searches utilize a macroscopic source and detector, thus allowing the detection of interactions with submillimeter force range and above. It remains a challenge to detect the interactions at shorter force ranges. Here we propose and demonstrate that a near-surface nitrogen-vacancy center in diamond can be utilized as a quantum sensor to detect the monopole–dipole interaction between an electron spin and nucleons. Our result sets a constraint for the electron–nucleon coupling, g_{{mathrm{s}}}^{mathrm{N}}g_{mathrm{p}}^{mathrm{e}}, with the force range 0.1–23 μm. The obtained upper bound of the coupling at 20 μm is g_{{mathrm{s}}}^{mathrm{N}}g_{mathrm{p}}^{mathrm{e}} < 6.24 × 10−15.

Spontaneous mirror left-right symmetry breaking for leptogenesis parametrized by Majorana neutrino mass matrix

We introduce a mirror copy of the ordinary fermions and Higgs scalars for embedding the SU(2)L × U(1)Y electroweak gauge symmetry into an SU(2)L × SU(2)R × U(1)B−L left-right gauge symmetry. We then show the spontaneous left-right symmetry breaking can automatically break the parity symmetry motivated by solving the strong CP problem. Through the SU(2)R gauge interactions, a mirror Majorana neutrino can decay into a mirror charged lepton and two mirror quarks. Consequently we can obtain a lepton asymmetry stored in the mirror charged leptons. The Yukawa couplings of the mirror and ordinary charged fermions to a dark matter scalar then can transfer the mirror lepton asymmetry to an ordinary lepton asymmetry which provides a solution to the cosmic baryon asymmetry in association with the SU(2)L sphaleron processes. In this scenario, the baryon asymmetry can be well described by the neutrino mass matrix up to an overall factor.

On the [formula omitted]-deformed fermion algebra: Thermodynamics of [formula omitted]-fermion gas

In this paper we introduce the p-deformed fermion algebra as a kind of generalization of the ordinary fermion algebra. We discuss the p-fermion algebra and its representation. We also find the generalized Pauli matrices related to the p-fermion algebra. As applications we discuss the thermodynamics in the canonical ensemble of the p-fermion and the p-fermion gas model.

Realizing anomalous anyonic symmetries at the surfaces of three-dimensional gauge theories

The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to conventional Landau-Ginzburg-Wilson phases, which are classified on the basis of the spontaneous breaking of an underlying symmetry, topologically ordered phases, such as those occurring in the fractional quantum Hall effect, are absolutely stable, not requiring any such symmetry. Recently, though, it has been realized that symmetries, which may still be present in such systems, can give rise to a host of new, distinct, many-body phases, all of which share the same underlying topological order. A useful approach to classifying SETs is to determine all possible such symmetry actions on the anyons that are algebraically consistent with the anyons' statistics. Remarkably, however, there exist symmetry actions that, despite being algebraically consistent, cannot be realized in any physical system, and hence do not lead to valid 2d SETs. One class of such `anomalous' SETs, characterized by certain disallowed symmetry fractionalization patters, finds a physical interpretation as an allowed surface state of certain 3d short-range entangled phases, but another, characterized by some seemingly valid but anomalous permutation actions of the symmetry on the anyons, has so far eluded a physical interpretation. In this work, we find a physical realization for these anomalously permuting SETs as surface theories of certain 3d long-range entangled phases, completing our understanding of general anomalous SETs in 2 dimensions.

The B − L + xY Model and the Higgs-strahlung Processes at a Collider**Supported by the National Natural Science Foundation of China under Grant Nos 11275088 and 11545012, and the Natural Science Foundation of Liaoning Scientific Committee under Grant No 2014020151.

The gauge extension of the standard model with the symmetry predicts the existence of a light gauge boson with small couplings to ordinary fermions. We discuss its contributions to the muon anomalous magnetic moment . Taking account of the constraints on the relevant free parameters, we further calculate the contributions of the light gauge boson to the Higgs-strahlung processes and .