Single Fermion Research Articles

Characteristics of chiral anomaly in view of various applications

In view of the recent applications of chiral anomaly to various fields beyond particle physics, we discuss some basic aspects of chiral anomaly which may help deepen our understanding of chiral anomaly in particle physics also. It is first shown that Berry's phase (and its generalization) for the Weyl model $H =v_{F} \vec{\sigma}\cdot \vec{p}(t)$ assumes a monopole form at the exact adiabatic limit but deviates from it off the adiabatic limit and vanishes in the high frequency limit of the Fourier transform of $\vec{p}(t)$ for bounded $|\vec{p}(t)|$. An effective action, which is consistent with the non-adiabatic limit of Berry's phase, combined with the Bjorken-Johnson-Low prescription gives normal equal-time space-time commutators and no chiral anomaly. In contrast, an effective action with a monopole at the origin of the momentum space, which describes Berry's phase in the precise adiabatic limit but fails off the adiabatic limit, gives anomalous space-time commutators and a covariant anomaly to the gauge current. We regard this anomaly as an artifact of the postulated monopole and not a consequence of Berry's phase. As for the recent application of the chiral anomaly to the description of effective Weyl fermions in condensed matter and nuclear physics, which is closely related to the formulation of lattice chiral fermions, we point out that the chiral anomaly for each species doubler separately vanishes for a finite lattice spacing, contrary to the common assumption. Instead a general form of pair creation associated with the spectral flow for the Dirac sea with finite depth takes place. This view is supported by the Ginsparg-Wilson fermion, which defines a single Weyl fermion without doublers on the lattice and gives a well-defined index (anomaly) even for a finite lattice spacing.

Trial wave functions for a composite Fermi liquid on a torus

We study the two-dimensional electron gas in a magnetic field at filling fraction $\nu=\frac{1}{2}$. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

Description of the 190–199Hg Nuclei Under the Frameworks of IBM-1 and IBFM-1

The energy levels and the electric quadrupole transition probabilities B(E2; Ji → Jf) for even–odd 191–199Hg have been investigated. The negative spin states of the even–odd 191–199Hg isotopes are studied within the framework of the interacting boson–fermion model (IBFM–1). The single fermion is assumed to be in one of the 2f5/2, 3p3/2, and 3p1/2 single-particle orbits. It is found that the calculated negative spin state energy spectra of the even–odd 191–199Hg isotopes agree quite well with the experimental data. The B(E2) values are also calculated and compared with the experimental data. In general, the results are in reasonably good agreement with the previous experimental values. Furthermore, the energy levels, electric quadrupole transition probabilities, and the wave function for even–even 1901–198Hg isotopes (as core for even–odd nuclei) have been calculated within the framework of the interacting boson model (IBM-1). The predicted energy levels and B(E2) transition probability results are reasonably consistent with the experimental data. These calculations have been compared with previous it and almost better than it. The study of the wave function’s structure shows that all interesting nuclei are deformed and have dynamical symmetry O(6) characters.

Mediation of entanglement and nonlocality of a single fermion

Entanglement is one of the most distinctive features of quantum mechanics and is now considered a fundamental resource in quantum information processing, such as in the protocols of quantum teleportation and quantum key distribution. In general, to extract its power in a useful form, it is necessary to generate entanglement between two or more quantum systems separated by long distances, which is not an easy task due to its fragility under environmental disturbance. Here, we propose a method to create entanglement between two distant fermionic particles, which never interact directly by using a third fermion to mediate the correlation. The protocol initiates with three indistinguishable fermions in a separable state, which are allowed to interact in pairs according to the Hong–Ou–Mandel effect. As a result, it is demonstrated that bipartite maximally entangled states can be generated with an efficiency of about 56%, which makes the method a potential candidate for practical quantum information applications. Furthermore, we use the same protocol to show how the mediator fermion exhibits nonlocal properties, giving a new insight on the long-standing discussion about nonlocality of a single particle.

Topological superconductivity in metal/quantum-spin-ice heterostructures

We propose a strategy to achieve an unconventional superconductor in a heterostructure: use a quantum paramagnet (QPM) as a substrate for heterostructure growth of metallic films to design exotic superconductors. The proposed setup allows us to “customize” electron–electron interaction imprinted on the metallic layer. The QPM material of our choice is quantum spin ice. Assuming the metallic layer forms a single isotropic Fermi pocket, we predict its coupling to spin fluctuations in quantum spin ice will drive topological odd-parity pairing. We further present guiding principles for materializing the suitable heterostructure using ab initio calculations and describe the band structure we predict for the case of Y2Sn2−xSbxO7 grown on the (111) surface of Pr2Zr2O7. Using this microscopic information, we predict topological odd-parity superconductivity at a few Kelvin in this heterostructure, which is comparable to the Tc of the only other confirmed odd-parity superconductor Sr2RuO4.

Instantons and entanglement entropy

We would like to put the area law — believed to be obeyed by entanglement entropies in the ground state of a local field theory — to scrutiny in the presence of nonperturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton contributions are well understood, including U(1) gauge theory in 2+1 dimensions and false vacuum decay in ϕ4 theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.

Defects in the tri-critical Ising model

We consider two different conformal field theories with central charge c = 7/10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have half-integer spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c = 7/5, using the folding trick as first proposed by Gang and Yamaguchi [1]. We then act on these with interface defects to find the new conformal defects. As part of the construction, we find the topological defects in the fermionic theory and the interfaces between the fermionic theory and the minimal model. We also consider the simpler case of defects in the theory of a single free fermion and interface defects between the Ising model and a single fermion as a prelude to calculations in the tri-critical Ising model.

Topological degeneracy and pairing in a one-dimensional gas of spinless fermions

We revisit the low energy physics of one dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground state and low energy phonon spectrum. Using a concrete microscopic model, with both single particle and pair hopping, we show that the strong pairing state is established through emergence of a new low energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from $c=1$ in the two Luttinger liquid phases to $c=3/2$ at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low energy phonon spectrum, associated with spatial interfaces between the two phases.

Descriptive study of the 120–127Xe isotopes using the IBM-1 and IBFM-1

In this work, positive parity low-spin states in 120–127Xe have been investigated using the Interacting Boson Model and the Interacting Boson–Fermion Model. The energy levels, electromagnetic transition B(E2) and B(M1), mixing ratios, relative B(E2) values and the potential energy surface for the even–even 120–126Xe isotopes have been calculated. The theoretical results are compared with the experimental data and it is seen that the obtained theoretical results are in good agreement with the experimental data. The single fermion is assumed to be in one of the 2d5/2, 2d3/2 and 3s1/2 single-particle orbits. Furthermore, the energy levels, electromagnetic transition B(E2) and B(M1) and mixing ratios have been calculated and compared with the experimental data and previous study for even–odd 121–127Xe isotope.

Anomaly-free dark matter models are not so simple

We explore the anomaly-cancellation constraints on simplified dark matter (DM) models with an extra U(1)′ gauge boson Z′. We show that, if the Standard Model (SM) fermions are supplemented by a single DM fermion χ that is a singlet of the SM gauge group, and the SM quarks have non-zero U(1)′ charges, the SM leptons must also have non-zero U(1)′ charges, in which case LHC searches impose strong constraints on the Z′ mass. Moreover, the DM fermion χ must have a vector-like U(1)′ coupling. If one requires the DM particle to have a purely axial U(1)′ coupling, which would be the case if χ were a Majorana fermion and would reduce the impact of direct DM searches, the simplest possibility is that it is accompanied by one other new singlet fermion, but in this case the U(1)′ charges of the SM leptons still do not vanish. This is also true in a range of models with multiple new singlet fermions with identical charges. Searching for a leptophobic model, we then introduce extra fermions that transform non-trivially under the SM gauge group. We find several such models if the DM fermion is accompanied by two or more other new fermions with non-identical charges, which may have interesting experimental signatures. We present benchmark representatives of the various model classes we discuss.

Generic Theory for Majorana Zero Modes in 2D Superconductors.

It is well known that non-Abelian Majorana zero modes (MZM) are located at vortex cores in a p_{x}+𝒾p_{y} topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an s-wave superconductor. Here we show that the existence of non-Abelian MZMs is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can result in a much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces that is gapped out by superconducting pairings, we show that at least a single MZM survives if there are only an odd number of Fermi surfaces of which the corresponding superconducting orders have vortices; such a MZM is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result enriches new experimental schemes for realizing non-Abelian MZMs. In particular, we propose a minimal scheme to realize the MZMs in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on recent cold-atom experiments.

Dynamical and quenched random matrices and homolumo gap

We consider a rather general type of matrix model, where the matrix M represents a Hamiltonian of the interaction of a bosonic system with a single fermion. The fluctuations of the matrix are partly given by some fundamental randomness and partly dynamically, even quantum mechanically. We then study the homolumo-gap effect, which means that we study how the level density for the single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In the case of the quenched randomness (the fundamental one) dominating the quantum mechanical one we show that in the first approximation the homolumo gap is characterized by the absence of single-fermion levels between two steep gap boundaries. The filled and empty level densities are in this first approximation just pushed, each to its side. In the next approximation these steep drops in the spectral density are smeared out to have an error-function shape. The studied model could be considered as a first step toward the more general case of considering a whole field of matrices — defined say on some phase space — rather than a single matrix.

Distinct Evolutions of Weyl Fermion Quasiparticles and Fermi Arcs with Bulk Band Topology in Weyl Semimetals.

The Weyl semimetal phase is a recently discovered topological quantum state of matter characterized by the presence of topologically protected degeneracies near the Fermi level. These degeneracies are the source of exotic phenomena, including the realization of chiral Weyl fermions as quasiparticles in the bulk and the formation of Fermi arc states on the surfaces. Here, we demonstrate that these two key signatures show distinct evolutions with the bulk band topology by performing angle-resolved photoemission spectroscopy, supported by first-principles calculations, on transition-metal monophosphides. While Weyl fermion quasiparticles exist only when the chemical potential is located between two saddle points of the Weyl cone features, the Fermi arc states extend in a larger energy scale and are robust across the bulk Lifshitz transitions associated with the recombination of two nontrivial Fermi surfaces enclosing one Weyl point into a single trivial Fermi surface enclosing two Weyl points of opposite chirality. Therefore, in some systems (e.g., NbP), topological Fermi arc states are preserved even if Weyl fermion quasiparticles are absent in the bulk. Our findings not only provide insight into the relationship between the exotic physical phenomena and the intrinsic bulk band topology in Weyl semimetals, but also resolve the apparent puzzle of the different magnetotransport properties observed in TaAs, TaP, and NbP, where the Fermi arc states are similar.

Chiral anomaly in Dirac semimetals due to dislocations

The dislocation in Dirac semimetal carries an emergent magnetic flux parallel to the dislocation axis. We show that due to the emergent magnetic field the dislocation accommodates a single fermion massless mode of the corresponding low-energy one-particle Hamiltonian. The mode is propagating along the dislocation with its spin directed parallel to the dislocation axis. In agreement with the chiral anomaly observed in Dirac semimetals, an external electric field results in the spectral flow of the one-particle Hamiltonian, in pumping of the fermionic quasiparticles out from the vacuum, and in creating a nonzero axial (chiral) charge in the vicinity of the dislocation.

Metal-insulator (fermion-boson)-crossover origin of pseudogap phase of cuprates I: anomalous heat conductivity, insulator resistivity boundary, nonlinear entropy

Among all experimental observations of cuprate physics, the metal-insulator-crossover (MIC), seen in the pseudogap (PG) region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field, when the superconductivity is suppressed, is most likely the most intriguing one. Since it was expected that the PG-normal state for these materials, as for conventional superconductors, is conducting. This MIC, revealed in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy, resistivity temperature upturn, insulating ground state, nematicity- and stripe-phases and Fermi pockets, unambiguously indicates on the insulating normal state, from which the high-temperature superconductivity (HTS) appears. In the present work (article I), we discuss the MIC phenomena mentioned in the title of article. The second work (article II) will be devoted to discussion of other listed above MIC phenomena and also to interpretation of the recent observations in the hidden magnetic order and scanning tunneling microscopy (STM) experiments spin and charge fluctuations as the intra PG and HTS pair ones. We find that all these MIC (called in the literature as non-Fermi liquid) phenomena can be obtained within the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of single fermions into those of single bosons. We show that this MIC originates from bosons of Coulomb two liquid model and fermions, whose origin is these bosons. At an increase of doping up to critical value or temperature up to PG boundary temperature, the boson system undegoes bosonic insulator - bosonic metal - fermionic metal transitions.

Kondo screening in two-dimensional p -type transition-metal dichalcogenides

Systems with strong spin orbit coupling support a number of new phases of matter and novel phenomena. This work focuses on the interplay of spin orbit coupling and interactions in yielding correlated phenomena in two dimensional transition metal dichalcogenides. In particular we explore the physics of Kondo screening resulting from the lack of centro-symmetry, large spin splitting and spin valley locking in hole doped systems. The key ingredients are i) valley dependent spin-momentum locking perpendicular to the two dimensional crystal; ii) single nondegenerate Fermi surface per valley, and iii) nontrivial Berry curvature associated with the low energy bands. The resulting Kondo resonance has a finite triplet component and nontrivial momentum space structure which facilitates new approaches to both probe and manipulate the correlated state. Using a variational wave function and the numerical renormalization group approaches we study the nature of the Kondo resonance both in the absence and presence of circularly polarized light. The latter induces an imbalance in the population of the two valleys leading to novel magnetic phenomena in the correlated state.

Quantum oscillations in a lead chalcogenide three-dimensional Dirac system

The de Haas–van Alphen (dHvA) and the Shubnikov–de Haas (SdH) oscillations were used to probe the properties of the Fermi surface in single crystals of Pb0.83Sn0.17Se with reduced charge concentration. Pronounced low-frequency oscillations of ∼8 T in the [001] direction were observed, confirming the single Fermi surface cross section. Due to the low effective charge concentration, the ultraquantum limit is reached already at ∼10 T. We observe π-Berry phase shift in the phase of both dHvA and SdH oscillations, which confirms the 3D Dirac nature of the energy band dispersion. In the construction of the Landau level diagram we use a combined indexing method for conductivity, magnetic susceptibility, and magnetization, which is based on the indexing used in the topological insulators. Moreover, the reliability of the indexing method is increased because we use, beside minima and maxima, zeros of the oscillations as well. Different microscopic parameters were calculated from the quantum oscillations in the magnetization, conductivity, and resistivity.

The One-loop Improved Lagrangian of the Grimus--Neufeld Model

Adding a single gauge singlet fermion and a second Higgs doublet to the original Standard Model allows an explanation for the observed smallness of the neutrino masses using the seesaw mechanism. This model predicts two neutral fermions with vanishing mass. The one-loop contribution to the neutral fermion masses due to the second Higgs doublet lifts this degeneracy and allows to fit the model parameters to the observed neutrino mass differences. We determine the values of the additional Yukawa couplings by requiring the correct prediction of the mass differences and mixings in the neutrino sector. We also discuss the ambiguities of the model parameters.

Signatures of shape phase transitions in odd-mass nuclei

Quantum phase transitions between competing ground-state shapes of atomic nuclei with an odd number of protons or neutrons are investigated in a microscopic framework based on nuclear energy density functional theory and the particle-plus-boson-core coupling scheme. The boson-core Hamiltonian, as well as the single-particle energies and occupation probabilities of the unpaired nucleon, are completely determined by constrained self-consistent mean-field calculations for a specific choice of the energy density functional and paring interaction, and only the strength parameters of the particle-core coupling are adjusted to reproduce selected spectroscopic properties of the odd-mass system. We apply this method to odd-A Eu and Sm isotopes with neutron number $N \approx 90$, and explore the influence of the single unpaired fermion on the occurrence of a shape phase transition. Collective wave functions of low-energy states are used to compute quantities that can be related to quantum order parameters: deformations, excitation energies, E2 transition rates and separation energies, and their evolution with the control parameter (neutron number) is analysed.

Displacement and annihilation of Dirac gap nodes in d -wave iron-based superconductors

Several experimental and theoretical arguments have been made in favor of a $d-$wave symmetry for the superconducting state in some Fe-based materials. It is a common belief that a $d-$wave gap in the Fe-based superconductors must have nodes on the Fermi surfaces centered at the $\Gamma$ point of the Brillouin zone. Here we show that, while this is the case for a single Fermi surface made out of a single orbital, the situation is more complex if there is an even number of Fermi surfaces made out of different orbitals. In particular, we show that for the two $\Gamma$-centered hole Fermi surfaces made out of $d_{xz}$ and $d_{yz}$ orbitals, the nodal points still exist near $T_{c}$ along the symmetry-imposed directions, but are are displaced to momenta between the two Fermi surfaces. If the two hole pockets are close enough, pairs of nodal points can merge and annihilate at some $T<T_{c}$, making the $d-$wave state completely nodeless. These results imply that photoemission evidence for a nodeless gap on the $d_{xz}/d_{yz}$ Fermi surfaces of KFe$_{2}$As$_{2}$ does not rule out $d-$wave gap symmetry in this material, while a nodeless gap observed on the $d_{xy}$ pocket in K$_{x}$Fe$_{2-y}$Se$_{2}$ is truly inconsistent with the $d-$wave gap symmetry.