Massless Fermions Research Articles

Negative magnetoresistance in Dirac semimetal Cd3As2 with in-plane magnetic field perpendicular to current

Topological insulators and semimetals have exotic surface and bulk states with massless Dirac or Weyl fermions, demonstrating microscopic transport phenomenon based on relativistic theory. Chiral anomaly induced negative magnetoresistance (negative MR) under parallel magnetic field and current has been used as a probable evidence of Weyl fermions in recent years. Here we report a novel negative MR result with mutually perpendicular in-plane magnetic field and current in Cd3As2 nanowires. The negative MR has a considerable value of −16% around 1.5 K and could persist to room temperature of 300 K with value of −1%. The gate tuning and angle dependence of the negative MR demonstrate the mechanism of the observed negative MR is different from the chiral anomaly. Percolating current paths induced by charge puddles and disorder might be involved to produce such considerable negative MR. Our results indicate the negative MR effect in topological semimetals involves synergistic effects of many mechanisms besides chiral anomaly.

Quantum backflow for a massless Dirac fermion on a ring

We study the quantum backflow problem for a massless charged Dirac fermion constrained to move on a ring of radius R. Using the relativistic current operator for states of definite magnetic quantum number it is shown that quantum backflow takes place on the ring. We also study the backflow problem on the line and it is shown that unlike massive fermions, massless fermions do not exhibit quantum backflow.

Bound states in nonuniform superconductors

This paper shows that the WKB quantization rule is suitable for the Andreev bound states in nonuniform superconductors. We consider nonhomogeneous superconductivity gap functions $\mathrm{\ensuremath{\Delta}}(x)$ in superconductors with the Bogoliubov quasiparticle energy $E$, the Fermi level ${E}_{F}$, and the total momentum $\mathbf{p}$ at ${E}_{F}+E$. The Andreev bound states in the well of slowly varying $|\mathrm{\ensuremath{\Delta}}(x)|$ are studied, and the well may also be induced by the phase variation of $\mathrm{\ensuremath{\Delta}}(x)$ for massless Dirac fermions. By applying the WKB method to the Bogoliubov--de Gennes equation, we obtain two main results: (i) For ${E}_{F}\ensuremath{\sim}0$, the bound states are determined by ${\ensuremath{\int}}_{{L}_{E}}^{{R}_{E}}|\mathbf{p}\phantom{\rule{0.16em}{0ex}}d\mathbf{x}|=(\frac{1}{2}+n)\ensuremath{\pi}\ensuremath{\hbar}$, where $n\ensuremath{\in}{\mathbb{N}}_{0}$ and ${L}_{E}$ and ${R}_{E}$ are the boundary points between the classically allowed region and forbidden regions, and (ii) for ${E}_{F}\ensuremath{\gg}E$ and $|\mathrm{\ensuremath{\Delta}}(x)|$, the bound states are given by ${\ensuremath{\int}}_{{L}_{E}}^{{R}_{E}}|\mathbf{p}\ifmmode\pm\else\textpm\fi{}{\mathbf{p}}_{F}|dx=(\frac{1}{2}+n)\ensuremath{\pi}\ensuremath{\hbar}$ with small ${p}_{y(z)}$. Empirical quantization conditions are provided for broader parameter regions. In addition to applying the traditional WKB method, we also develop a generalized WKB method to tackle semimetals with parabolic dispersion relationships. The applications of our results are discussed, for example, Dirac $\ensuremath{\pi}$ junctions or nonchiral Majorana wires, SNS junctions, the excitation threshold, and the tunneling rate in NSN junctions. In the $\ensuremath{\pi}$ junction, the Majorana zero modes correspond to the zero-point energy in the WKB formalism. This observation may provide insights into the Majorana bound state in a vortex and the Majorana fermions in high-energy physics.

Dihedral twist liquid models from emergent Majorana fermions

We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute theSO(N)Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedralDksymmetry ofSO(2n)1, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates theC/Gtwist liquids, whereG=Z2forC=U(1)l,SU(n)1, andG=Z2,Zk,DkforC=SO(2n)1. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern inSO(2n)1/Gby identifying the non-chiral components of the twist liquids with discrete gauge theories.

Clifford Odd and Even Objects in Even and Odd Dimensional Spaces Describing Internal Spaces of Fermion and Boson Fields

In a long series of works, it has been demonstrated that the spin-charge-family theory, assuming a simple starting action in even dimensional spaces with d≥(13+1), with massless fermions interacting with gravity only, offers the explanation for all assumed properties of the second quantized fermion and boson fields in the standard model, as well as offering predictions and explanations for several of the observed phenomena. The description of the internal spaces of the fermion and boson fields by the Clifford odd and even objects, respectively, justifies the choice of the simple starting action of the spin-charge-family theory. The main topic of the present article is the analysis of the properties of the internal spaces of the fermion and boson fields in odd dimensional spaces, d=(2n+1), which can again be described by the Clifford odd and even objects, respectively. It turns out that the properties of fermion and boson fields differ essentially from their properties in even dimensional spaces, resembling the ghosts needed when looking for final solutions with Feynman diagrams.

Effects of a Uniform Magnetic Field on Twisted Graphene Nanoribbons

AbstractIn the present work, the relativistic quantum motion of massless fermions in a helicoidal graphene nanoribbon under the influence of a uniform magnetic field is investigated. Considering a uniform magnetic field (B) aligned along the axis of helicoid, this problem is explored in the context of Dirac equation in a curved space‐time. As this system does not support exact solutions due to considered background, the bound‐state solutions and local density of states (LDOS) are obtained numerically by means of the Numerov method. The combined effects of width of the nanoribbon (D), length of ribbon (L), twist parameter (ω), and B on the equations of motion and LDOS are analyzed and discussed. It is verified that the presence of B produces a constant minimum value of local density of state on the axis of helicoid, which is possible only for values large enough of ω, in contrast to the case for already studied in the literature.

Partition functions on squashed seven-spheres and holography

Our paper presents two main results. First, we study the renormalized free energies of Euclidean Einstein gravity in asymptotically AdS8 and various field theories on a squashed seven sphere. In the gravity theory, we demonstrate the absence of the Hawking-Page transition, while in the field theory, we focus on the O(N) vector model and the massless free fermion model. The conformal symmetry governs the universal behaviors of the free energies for small and large squashings, which we confirm numerically and analytically. Second, we evaluate the second-order derivative of CFT free energy with respect to the squashing parameter, finding universal results that hold for generic conformal field theories. We examine two different squashings, one with an SU(2) bundle, which is the primary focus of our paper, and another with a U(1) bundle, where our results align with the conjectured formula from the gravity side in the literature.

Strain-induced massless Dirac fermion state of the molecular conductor α-(BEDT-TTF)2I3

Uniaxial pressure can dramatically change the properties of low-dimensional systems and induce electronic phase transitions. The first-discovered molecular massless Dirac electron system α-(BEDT-TTF)2I3 has intensively been studied because of its unique features, such as the Fermi energy being very close to the Dirac point, strong electron correlation, and the quantum phase transition from the charge-ordered insulating state. However, the Dirac state is realized only under high pressure of 15 kbar, which limits the measurement of physical properties (e.g., experimental determination of band dispersion and density of states). Here, we demonstrate that the Dirac state of α-(BEDT-TTF)2I3 can be realized by applying uniaxial bending strain without confining it in a pressure cell. Uniaxial strain below 1% completely suppresses the metal–insulator transition observed at ambient pressure. Under strain, a characteristic temperature dependence of magnetoresistance associated with the formation of the n = 0 Landau level is observed, indicating the realization of the massless Dirac state.

Entanglement resolution of free Dirac fermions on a torus

Whenever a system possesses a conserved charge, the density matrix splits into eigenspaces associated to the each symmetry sector and we can access the entanglement entropy in a given subspace, known as symmetry resolved entanglement (SRE). Here, we first evaluate the SRE for massless Dirac fermions in a system at finite temperature and size, i.e. on a torus. Then we add a massive term to the Dirac action and we treat it as a perturbation of the massless theory. The charge-dependent entropies turn out to be equally distributed among all the symmetry sectors at leading order. However, we find subleading corrections which depend both on the mass and on the boundary conditions along the torus. We also study the resolution of the fermionic negativity in terms of the charge imbalance between two subsystems. We show that also for this quantity, the presence of the mass alters the equipartition among the different imbalance sectors at subleading order.

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules.

Materials such as graphene and topological insulators host massless Dirac fermions that enable the study of relativistic quantum phenomena. Single quantum dots and coupled quantum dots formed with massless Dirac fermions can be viewed as artificial relativistic atoms and molecules, respectively. Such structures offer a unique testbed to study atomic and molecular physics in the ultrarelativistic regime (particle speed close to the speed of light). Here we use a scanning tunnelling microscope to create and probe single and coupled electrostatically defined graphene quantum dots to unravel the magnetic-field responses of artificial relativistic nanostructures. We observe a giant orbital Zeeman splitting and orbital magnetic moment up to ~70 meV T-1 and ~600μB (μB, Bohr magneton) in single graphene quantum dots. For coupled graphene quantum dots, Aharonov-Bohm oscillations and a strong Van Vleck paramagnetic shift of ~20 meV T-2 are observed. Our findings provide fundamental insights into relativistic quantum dot states, which can be potentially leveraged for use in quantum information science.

Phase structure of linear quiver gauge theories from anomaly matching

We consider the phase structure of the linear quiver gauge theory, using the 't Hooft anomaly matching condition. This theory is characterized by the length $K$ of the quiver diagram. When $K$ is even, the symmetry and its anomaly are the same as those of massless QCD. Therefore, one can expect that the spontaneous symmetry breaking similar to the chiral symmetry breaking occurs. On the other hand, when $K$ is odd, the anomaly matching condition is satisfied by the massless composite fermions. We also consider the thermal partition function under the twisted boundary conditions. When $K$ is even, from the anomaly at finite temperature, we estimate the relation between the critical temperatures associated with the confinement/deconfinement and the breaking of the global symmetry. Finally we discuss the anomaly matching at finite temperature when $K$ is odd.

Callan-Rubakov effect and higher charge monopoles

In this paper we study the interaction between magnetic monopoles and massless fermions. In the low energy limit, the monopole’s magnetic field polarizes the fermions into purely in-going and out-going modes. Consistency requires that the UV fermion-monopole interaction leads to non-trivial IR boundary conditions that relate the in-going to out-going modes. These non-trivial boundary conditions lead to what is known as the Callan-Rubakov effect. Here we derive the effective boundary condition by explicitly integrating out the UV degrees of freedom for the general class of spherically symmetric SU(N) monopoles coupled to massless fermions of arbitrary representation. We then show that the boundary conditions preserve symmetries without ABJ-type anomalies. As an application we explicitly derive the boundary conditions for the stable, spherically symmetric monopoles associated to the SU(5) Georgi-Glashow model and comment on the relation to baryon number violation.

Gauge theory geography: charting a path between semiclassical islands

We study two semiclassical limits of SU(2) Yang-Mills theory on a spatial torus with a ’t Hooft twist: the “femtouniverse,” where all \U0001d54b3 directions are small, and deformed Yang-Mills theory on \U0001d54b2 × \U0001d54a1, with small \U0001d54a1 and large or infinite \U0001d54b2. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch θ-dependent vacuum structure of these theories. We then calculate the one-loop potential for the \U0001d54a1-holonomy in the presence of twists on \U0001d54b2. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial \U0001d54b2 × \U0001d54a1, with a twist in the \U0001d54b2. The results point towards some interesting features worthy of further study.

The dark dimension and the Swampland

Motivated by principles from the Swampland program, which characterize requirements for a consistent UV completion of quantum gravity, combined with observational data, we are led to a unique corner of the quantum gravity landscape. In particular, using the Distance/Duality conjecture and the smallness of dark energy, we predict the existence of a light tower of states and a unique extra mesoscopic dimension of length lsim {Lambda}^{-frac{1}{4}}sim {10}^{-6}m , with extra massless fermions propagating on it. This automatically leads to a candidate for a tower of sterile neutrinos, and an associated active neutrino mass scale {m}_{nu}sim {leftlangle Hrightrangle}^2{Lambda}^{-frac{1}{12}}{M}_{textrm{pl}}^{-frac{2}{3}} . Moreover, assuming the mechanism for stabilization of this dark dimension leads to similar masses for active and sterile neutrinos we are led to the prediction of a Higgs vev leftlangle Hrightrangle sim {Lambda}^{frac{1}{6}}{M}_{textrm{pl}}^{frac{1}{3}} . Another prediction of the scenario is a species scale hat{M}sim {Lambda}^{frac{1}{12}}{M}_{textrm{pl}}^{frac{2}{3}}sim {10}^9hbox{--} {10}^{10} GeV, corresponding to the higher-dimensional Planck scale. This energy scale may be related to the resolution of the instability of the Higgs effective potential present at a scale of ~1011 GeV. We also speculate about the interplay between this energy scale and the GZK limit on ultra-high energy cosmic rays.

Realization of the topological Hopf term in two-dimensional lattice models

It is known that a two-dimensional spin system can acquire a topological Hopf term by coupling to massless Dirac fermions whose energy spectrum has a single cone. But it is challenging to realize the Hopf term in condensed matter physics due to the fermion-doubling in the low-energy spectrum. In this work we propose a scenario to realize the Hopf term in lattice models. The central aim is tuning the coupling between the spins and the Dirac fermions such that the topological terms contributed by the two cones do not cancel each other. To this end, we consider $p_x$ and $p_y$ orbitals for the Dirac fermions on the honeycomb lattice such that there are totally four bands. By utilizing the orbital degrees of freedom, a $\theta=2\pi$ Hopf term is successfully generated for the spin system after integrating out the Dirac fermions. If the fermions have a small gap $m_0$ or if the spin-orbit coupling is considered, then $\theta$ is no longer quantized, but it may flow to multiple of $2\pi$ under renormalization. The ground state and the physical response of a spin system having the Hopf term are discussed.

Rényi Mutual Information in Quantum Field Theory.

We study a proper definition of Rényi mutual information (RMI) in quantum field theory as defined via the Petz Rényi relative entropy. Unlike the standard definition, the RMI we compute is a genuine measure of correlations between subsystems, as evidenced by its non-negativity and monotonicity under local operations. Furthermore, the RMI is UV finite and well defined in the continuum limit. We develop a replica path integral approach for the RMI in quantum field theories and evaluate it explicitly in 1+1D conformal field theory using twist fields. We prove that it bounds connected correlation functions and check our results against exact numerics in the massless free fermion theory.

Chiral fermions on lattice axion strings

I discretize axion string configuration coupled to a Dirac fermion, which in the continuum binds a massless chiral fermion in its core when the winding is one. I show that such a configuration can host one or more chiral fermions when regulated on the lattice. To realize these chiral fermions I introduce Wilson-like terms similar to the Wilson term used in lattice domain wall fermions. The number of chiral fermions on the string jumps as the Wilson-like parameter is varied with respect to the other mass scales in the problem. A one-loop Feynman diagram is used to demonstrate how anomaly inflow works in this lattice regularized theory.

Dynamical chiral magnetic current and instability in Weyl semimetals

Weyl semimetals realize massless relativistic fermions with two Weyl nodes separated in energy and momentum space, whose low-energy physics is described by Dirac fermions with an axial gauge constant. Here, we study their electromagnetic linear responses based on the effective field theory and on the chiral kinetic theory. Although the static chiral magnetic effect is canceled by the Chern-Simons current under the Pauli-Villars regularization, a dynamical magnetic field is found capable of driving an electric current along its direction, with the total transported charge being independent of temperature and chemical potential for a uniform field. We also incorporate dissipation in the relaxation-time approximation and study collective excitations coupled with Maxwell electromagnetic fields when Weyl node populations deviate from equilibrium. Their dispersion relations at low frequency and long wavelength are determined only by electric, chiral magnetic, and anomalous Hall conductivities, which predict unstable modes leading to anisotropic generation of electromagnetic waves oriented to the direction of Weyl node separation.

Method to preserve the chiral-symmetry protection of the zeroth Landau level on a two-dimensional lattice

The spectrum of massless Dirac fermions on the surface of a topological insulator in a perpendicular magnetic field B contains a B-independent “zeroth Landau level”, protected by chiral symmetry. If the Dirac equation is discretized on a lattice by the method of “Wilson fermions”, the chiral symmetry is broken and the zeroth Landau level is broadened when B has spatial fluctuations. We show how this lattice artefact can be avoided starting from an alternative nonlocal discretization scheme introduced by Stacey. A key step is to spatially separate the states of opposite chirality in the zeroth Landau level, by adjoining +B and −B regions.

The Complex Field Theory and Mass Formation—An Alternative Model to Higgs Mechanism

The electromagnetic force, strong nuclear force, weak nuclear force, and gravitational force are the four fundamental forces of nature. The Standard Model (SM) succeeded in combining the first three forces to describe the most basic building blocks of matter and govern the universe. Despite the model’s great success in resolving many issues in particle physics but still has several setbacks and limitations. The model failed to incorporate the fourth force of gravity. It infers that all fermions and bosons are massless contrary to experimental facts. In addition, the model addresses neither the 95% of the universe’s energy of Dark Matter (DM) and Dark Energy (DE) nor the universe’s expansion. The Complex Field Theory (CFT) identifies DM and DE as complex fields of complex masses and charges that encompasses the whole universe, and pervade all matter. This presumption resolves the issue of failing to detect DM and DE for the last five decades. The theory also presents a model for the universe’s expansion and presumes that every material object carries a fraction of this complex field proportional to its mass. These premises clearly explain the physical nature of the gravitational force and its complex field and pave the way for gravity into the SM. On the other hand, to solve the issue of massless bosons and fermions in the SM, Higgs mechanism introduces a pure and abstractive theoretical model of unimaginable four potentials to generate fictitious bosons as mass donors to fermions and W± and Z bosons. The CFT in this paper introduces, for the first time, a physical explanation to the mystery of the mass formation of particles rather than Higgs’ pure mathematical derivations. The analyses lead to uncovering the mystery of electron-positron production near heavy nuclei and never in a vacuum. In addition, it puts a constraint on Einstein’s mass-energy equation that energy can never be converted to mass without the presence of dense dark matter and cannot be true in a vacuum. Furthermore, CFT provides different perspectives and resolves real-world physics concepts such as the nuclear force, Casimir force, Lamb’s shift, and the anomalous magnetic moment to be published elsewhere.