Normal Fermions Research Articles

Power-law liquid in cuprate superconductors from fermionic unparticles

Recent photoemission spectroscopy measurements [arXiv:1509.01611] on cuprate superconductors have inferred that over a wide range of doping, the imaginary part of the electron self-energy scales as $\Sigma^{\prime\prime}\sim(\omega^2+\pi^2T^2)^a$ with $a=1$ in the overdoped Fermi-liquid state and $a<0.5$ in the optimal to underdoped regime. We show that this non-Fermi-liquid scaling behavior can naturally be explained by the presence of a scale-invariant state of matter known as unparticles. We evaluate analytically the electron self-energy due to interactions with fermionic unparticles. We find that, in agreement with experiments, the imaginary part of the self-energy scales with respect to temperature and energy as $\Sigma^{\prime\prime}\sim T^{2+2\alpha}$ and $\omega^{2+2\alpha}$, where $\alpha$ is the anomalous dimension of the unparticle propagator. In addition, the calculated occupancy and susceptibility of fermionic unparticles, unlike those of normal fermions, have significant spectral weights even at high energies. This unconventional behavior is attributed to the branch cut in the unparticle propagator which broadens the unparticle spectral function over a wide energy range and non-trivially alters the scattering phase space by enhancing (suppressing) the intrinsic susceptibility at low energies for negative (positive) $\alpha$. Our work presents new evidence suggesting that unparticles might be important low-energy degrees of freedom in strongly coupled systems such as the cuprate superconductors.

Probing neutrino and Higgs sectors in text{ SU(2) }_1 times text{ SU(2) }_2 times text{ U(1) }_Y model with lepton-flavor non-universality

The neutrino and Higgs sectors in the text{ SU(2) }_1 times text{ SU(2) }_2 times text{ U(1) }_Y model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. The mechanism for the generation of neutrino masses is the same as in the Zee models. This also gives a hint to solving the dark matter problem based on similar ways discussed recently in many radiative neutrino mass models with dark matter. Except the active neutrinos, the appearance of singly charged Higgs bosons and dark matter does not affect significantly the physical spectrum of all particles in the original model. We indicate this point by investigating the Higgs sector in both cases before and after singly charged scalars are added into it. Many interesting properties of physical Higgs bosons, which were not shown previously, are explored. In particular, the mass matrices of charged and CP-odd Higgs fields are proportional to the coefficient of triple Higgs coupling mu . The mass eigenstates and eigenvalues in the CP-even Higgs sector are also presented. All couplings of the SM-like Higgs boson to normal fermions and gauge bosons are different from the SM predictions by a factor c_h, which must satisfy the recent global fit of experimental data, namely 0.995<|c_h|<1. We have analyzed a more general diagonalization of gauge boson mass matrices, then we show that the ratio of the tangents of the W–W' and Z–Z' mixing angles is exactly the cosine of the Weinberg angle, implying that number of parameters is reduced by 1. Signals of new physics from decays of new heavy fermions and Higgs bosons at LHC and constraints of their masses are also discussed.

Fermion fractionalization to Majorana fermions in a dimerized Kitaev superconductor

We study theoretically a one-dimensional dimerized Kitaev superconductor model which belongs to BDI class with time-reversal, particle-hole, and chiral symmetries. There are two sources of the particle-hole symmetry, i.e., the sublattice symmetry and superconductivity. Accordingly, we define two types of topological numbers with respect to the chiral indices of normal and Majorana fermions, which offers an ideal laboratory to examine the interference between the two different physics within the same symmetry class. Phase diagram, zero-energy bound states, and conductance at normal metal/superconductor junction of this model are unveiled from this viewpoint. Especially, the electron fractionalization to the Majorana fermions showing the splitting of the local density of states is realized at the soliton of the dimerization in this model.

Quantum oscillations and Berry's phase in topological insulator surface states with broken particle-hole symmetry

Quantum oscillations can be used to determine properties of the Fermi surface of metals by varying the magnitude and orientation of an external magnetic field. Topological insulator surface states are an unusual mix of normal and Dirac fermions. Unlike in graphene and simple metals, Berry's geometric phase in topological insulator surface states is not necessarily quantised. We show that reliably extracting this geometric phase from the phase offset associated with the quantum oscillations is subtle. This is especially so in the presence of a Dirac gap such as that associated with the Zeeman splitting or interlayer tunneling. We develop a semi-classical theory for general mixed normal-Dirac systems in the presence of a gap, and in doing so clarify the role of topology and broken particle-hole symmetry. We propose a systematic procedure of fitting Landau level index plots at large filling factors to reliably extract the phase offset associated with Berry's phase.

Millikelvin de Haas–van Alphen and magnetotransport studies of graphite

Recent studies of the electronic properties of graphite have produced conflicting results regarding the positions of the different carrier types within the Brillouin zone, and the possible presence of Dirac fermions. In this paper we report a comprehensive study of the de Haas--van Alphen, Shubnikov--de Haas, and Hall effects in a sample of highly orientated pyrolytic graphite, at temperatures in the range 30$ $mK to 4$ $K and magnetic fields up to 12$ $T. The transport measurements confirm the Brillouin-zone locations of the different carrier types assigned by Schroeder, Dresselhaus, and Javan, Phys. Rev. Lett. 20, 1292 (1968): electrons are at the $K$ point, and holes are near the $H$ points. We extract the cyclotron masses and scattering times for both carrier types from the temperature- and magnetic-field-dependences of the magneto-oscillations. Our results indicate that the holes experience stronger scattering and hence have lower mobility than the electrons. We utilize phase-frequency analysis and intercept analysis of the $1/B$ positions of magneto-oscillation extrema to identify the nature of the carriers in graphite, whether they are Dirac or normal (Schr\"odinger) fermions. These analyses indicate normal holes and electrons of indeterminate nature.

Phase separation between different pairing symmetries in trapped fermionic superfluids

We explore in this paper a harmonically trapped asymmetric fermionic superfluid in a two-dimensional optical lattice with pairing interactions between the neighboring sites, by self-consistently solving Bogliubov--de Gennes equations. We find the superfluid generally phase separates into a $d$-wave pairing component and an extended $s$-wave pairing one, mixed with the unpaired normal fermions. For sufficient large number asymmetries, the ground state is found to be a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state without fourfold rotational symmetry. Both the $d$-wave and $s$-wave order parameters show spatially varying novel patterns with nodal points or nodal lines. These features are expected to be checked by the experiments on the repulsive ultracold fermionic atoms.

Asymmetric Fermi superfluid with different atomic species in a harmonic trap

We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.

Normal and Dirac fermions in graphene multilayers: Tight-binding description of the electronic structure

Within a tight-binding approach we show that around the $K$ point of the energy spectrum Dirac fermions are present in $AB$ stacked graphene multilayers if they have mirror plane symmetry. In other words, Dirac fermions are present in graphene stacks with an odd number of layers. For an even number of stacked graphene layers, only normal fermions with a parabolic energy dispersion are found near the $K$ point.

Dirac and Normal Fermions in Graphite and Graphene: Implications of the Quantum Hall Effect

Spectral analysis of the Shubnikov-de Haas magnetoresistance oscillations and the quantum Hall effect (QHE) measured in quasi-2D highly oriented pyrolytic graphite (HOPG) [Phys. Rev. Lett. 90, 156402 (2003)] reveals two types of carriers: normal (massive) electrons with Berry phase 0 and Dirac-like (massless) holes with Berry phase pi. We demonstrate that recently reported integer- and semi-integer QHEs for bilayer and single-layer graphenes take place simultaneously in HOPG samples.

Pairing and Phase Separation in a Polarized Fermi Gas

We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter beta = -0.54 +/- 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.

Theory of strongly correlated electron systems. I. Intersite Coulomb interaction and the approximation of renormalized fermions in total energy calculations

AbstractThe diagrammatic strong‐coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many‐electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one‐to‐one correspondence is found between the subset of such graphs for the many‐electron GFs and the complete set of Feynman graphs of weak‐coupling perturbation theory (WCPT) for single‐electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many‐electron quasi‐particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self‐energy and the exchange–correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LDA (RF LDA), is obtained by introducing the spectral weights of the many‐electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self‐interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part II of this study (this issue). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Fourth root of the Kogut-Susskind determinant via infinite component fields

An example of interpolation by means of local field theories between the case of normal Kogut-Susskind fermions and the case of keeping just the fourth root of the Kogut-Susskind determinant is given. For the fourth root trick to be a valid approximation certain limits need to be smooth. The question about the validity of the fourth root trick is not resolved, only cast into a local field theoretical framework.

Vortices in trapped superfluid fermi gases.

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.

SU(2) × U(1) breaking by vacuum misalignment

Currently two scenarios exist which explain SU(2) × U(1) breaking: the Higgs mechanism, and standard hypercolor schemes. In this paper, a third scenario called “oblique hypercolor” is proposed. A hyperquark condensate is formed which, although kinematically allowed to point in an SU(2) × U(1) preserving direction, is forced by Yukawa interactions of the hyperquarks to misalign by a small angle, breaking SU(2) × U(1). The low energy spectrum involves normal fermions with correct masses, a partially composite Higgs boson, and physical charged scalars.

The SO(10) × SO(5) model and the properties of fractionally charged particles

With SO(5) as the horizontal gauge symmetry, the SO(10) × SO(5) model incorporates five families of fermions, three of normal fermions (NF) and two of abnormal fermions (AF, i.e. fractionally charged leptons and quarks which can compose fractionally charged hadrons). A simple hierarchy of the model is discussed in detail. The opposite-charged abnormal leptons can have both the Dirac and Majorana masses. The prominent characteristic of AF is the twin degeneracy in the mass spectrum; the twin degeneracy is model-independent and testable. The existence of opposite-charged leptons explains why there are so few AF in the universe.

The possibility of new fermions with ΔI = 0 mass

In the Glashow-Weinberg-Salam model the fermions have ΔI = 1 2 masses from the breaking of the weak SU(2) gauge symmetry. In many enlarged models, such as those from grand unified and/or supersymmetric theories, there are additional fermions with undetermined ΔI = 0 (SU(2) invariant) masses. We study these new fermions. They induce flavour changing neutral currents. We show that the mixing angles of ΔI = 0 fermions of mass order M with normal ΔI = 1 2 fermions of mass order m ⪡ M are order η or η 2, where η = m/ M. If M > 150 δ, δ being a model-dependent mixing parameter of order a normal fermion mass, the amplitudes of all FCNC processes are below the experimental sizes and limits. Thus for δ⪅0.1 GeV, M can be as low as 20 GeV, close to the present experimental lower bound. δ is fixed, and less than 0.1 GeV for all relevant cases, if we assume the mass hierarchy of the known fermions is not the result of a particular choice of ΔI = 0 mass parameters. If produced ΔI = 0 mass fermions will be noticeable by the mass degeneracy within their isospin multiplets. There will be an enhanced ratio of neutral to charged decays over the normal fermions. Standard GUT predictions are changed little.

Suppression of lepton number violation mediated by ΔI = 0 mass fermions

We add a lepton doublet with ΔI = 0 mass M to the minimal Weinberg-Salam model. We then calculate the transition rate for μ → eγ for all M as a function of an arbitrary mixing parameter δ of order a normal lepton mass. For δ ⪅ 0.4 GeV, M can be as low as 20 GeV. We show that heavy gDI = 0 fermions decouple throught their highly but naturally suppressed mixing angles with normal fermions and not through diagrammatic cancellations. Models with heavy ΔI = 0 fermions evade the commonly used conditions for natural suppression of rare processes in gauge theories.