Types Of Quasiparticles Research Articles

ChemInform Abstract: Topological Effects in Nanomagnetism: From Superparamagnetism to Chiral Quantum Solitons

AbstractReview: 367 refs.

Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons

Micromagnetics has been the method of choice to interpret experimental data in the area of microscopic magnetism for several decades. In this article, we show how progress has been made to extend this formalism to include thermal and quantum fluctuations in order to describe recent experimental developments in nanoscale magnetism. For experimental systems with constrained dimensions such as nanodots, atomic chains, nanowires, and thin films, topological defects such as solitons, vortices, skyrmions, and monopoles start to play an increasingly important role, all forming novel types of quasiparticles in patterned low-dimensional magnetic systems. We discuss in detail how soliton–antisoliton pairs of opposite chirality form non-uniform energy barriers against thermal fluctuations in nanowires or pillars. As a consequence of their low barrier energy compared to uniform reversal, they limit the thermal stability of perpendicular recording media. For sufficiently short samples, the non-uniform energy barrier continuously merges into the conventional uniform Néel–Brown barrier. Partial formation of chiral domain walls also determines the magnetic properties of granular nanostructured magnets and exchange spring systems. For a long time, the reconciliation between micromagnetics and quantum mechanics has remained an unresolved challenge. Here it is demonstrated how inclusion of Berry's phase in a micromagnetic action allows for a semiclassical quantization of spin systems, a method that is demonstrated by the simple example of an easy-plane spin. This powerful method allows for a description of quantum dynamics of solitons and breathers which in the latter case agrees with the anisotropic spin-½ XYZ-model. The domain wall or soliton chirality plays an important role as it is coupled to the wavevector of the quasiparticle dispersion. We show how this quantum soliton chirality is detected by polarized neutron scattering in one-dimensional quantum antiferromagnets.

Coexistence of superfluid and metallic-like state in two-component fermionic systems

We study the possibility of coexistence in a two component fermionic system of a superfluid state with a metallic-like state with gapless excitations at a Fermi surface. We consider a two-component system with mixing (hybridization) between them and attractive interactions between only one type of quasi-particles. Besides a conventional BCS regime, we find for sufficiently strong interactions a superfluid state of Bose condensed pairs at zero temperature. We investigate whether these pairs can coexist with a metallic-like state characterized by gapless electronic excitations. The zero temperature phase diagram as a function of the strength of the attractive interaction and the mixing is obtained. For simplicity and to clarify the nature of the quantum phase diagram we consider the case of s-wave pairing.

Quantum criticality in inter-band superconductors

In fermionic systems with different types of quasi-particles, attractive interactionscan give rise to exotic superconducting states, such as pair density wave (PDW)superconductivity and breached pairing. In recent years the search for these newtypes of ground states in cold atoms and in metallic systems has been intense. Inthe case of metals the different quasi-particles may be the up and down spinbands in an external magnetic field or bands arising from distinct atomic orbitalsthat coexist at a common Fermi surface. These systems present a complex phasediagram as a function of the difference between the Fermi wavevectors of thedifferent bands. This can be controlled by external means, varying the density in thetwo-component cold atom system or, in a metal, by applying an external magnetic field orpressure. Here we study the zero temperature instability of the normal system as theFermi wavevector mismatch of the quasi-particles (bands) is reduced and find asecond order quantum phase transition to a PDW superconducting state. From thenature of the quantum critical fluctuations close to the superconducting quantumcritical point (SQCP), we obtain its dynamic critical exponent. It turns out to bez = 2 and this allows us to fully characterize the SQCP for dimensionsd ≥ 2.

Quasiparticle Nernst effect in the cuprate superconductors from thed-density-wave theory of the pseudogap phase

We consider the Nernst effect in the underdoped regime of the cuprate high temperature superconductors within the d-density wave (DDW) model of the pseudogap phase. By a combination of analytical and numerical arguments, we show that there is a robust low-temperature positive peak (i.e., maximum) in the temperature dependence of the Nernst coefficient when the DDW state is ambipolar, i.e., when the broken symmetry supports the coexistence of both electron- and hole-like quasiparticles in the excitation spectrum, and the electron pocket dominates at the low temperatures. In contrast, the Nernst coefficient is negative and there is no such positive peak if the underlying state is non-ambipolar, i.e., when it supports only one type of quasiparticles. More generally, in the ambipolar state, the sign of the Nernst coefficient can be positive or negative depending on the dominance of the electron or hole pockets, respectively, in the low temperature thermoelectric transport. By modeling the pseudogap phase by a doping-dependent DDW order parameter with a Fermi surface topology that supports both hole and electron pockets, and assuming energy-independent transport scattering times, we analyze the evolution of the Nernst effect with doping concentration at low temperatures in the cuprate phase diagram.

3He Experiments: Insights into Cosmology and Atomic Physics

Superfluid 3He, since its discovery by Osheroff, Richardson and Lee in 1972, has become one of the main systems for experimental studies of quantum field theories. This is due to the very rich order parameter of the quantum state for the triplet Cooper pairing of superfluid 3He, which exhibits, in addition to superfluid properties, properties of a magnetically-ordered quantum liquid crystal! The superfluid state, particularly at very low temperatures, is a quantum vacuum with a complicated order parameter, which carries various types of quasiparticles and topological defects. It can be considered a test system for the experimental investigations of many general physical problems in cosmology, atomic and nuclear physics, which are otherwise difficult or even impossible to investigate experimentally.

Structure of quasiparticles and their fusion algebra in fractional quantum Hall states

It was recently discovered that fractional quantum Hall (FQH) states can be classified by the way ground state wave functions go to zero when electrons are brought close together. Quasiparticles in the FQH states can be classified in a similar way, by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper we combine the pattern-of-zero approach and the conformal-field-theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to obtain the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach.

Josephson effects in MgB 2 /Thin Insulator/ MgB 2 tunnel junction

The Josephson currents in MgB 2/I/MgB 2 tunnel junction for both c -axis and a b -plane orientation alignments are calculated by using the B-dG equation to derive the Andreev reflection coefficients at the interface. The differences between the insulating barrier strengths due to the differences in the interactions between the π ( σ ) -bands electron (hole)-like quasi particles with the insulator are taken into account in the calculations of the Josephson currents. Also, the difference in the effective cross sectional area for the two types of quasi-particles (the π - and σ -bands) flow through the junction is taken into account. Both the current-phase relation and the temperature dependence of the maximum (or critical) Josephson current are studied. The results show that the temperature dependence of the maximum Josephson current for c -axis and a b -plane orientation junctions are quite different from those of an S/I/S Josephson tunnel junction when S is a conventional superconductor. When the insulator is absent and S is MgB 2, the calculated maximum Josephson current in a c -axis orientation junction exhibits a ( T − T C ) 2 dependence. However, the calculated current in the a b -plane orientation junction exhibits a nearly linear temperature dependence when the effective cross sectional areas and the interface interaction between the insulator and the two types of quasi particles ( π and σ ) are taken to be the same. The calculated current for c -axis orientation junction agrees very well with the experimental data. The prediction that the Josephson current will be a combination of two sinusoidal functions is observed in the current-phase relation of an a b -plane orientation junction.

Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros

It has been shown that different Abelian and non-Abelian fractional quantum Hall states can be characterized by patterns of zeros described by sequences of integers ${{S}_{a}}$. In this paper, we will show how to use the data ${{S}_{a}}$ to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as well as the actions of the quasiparticle tunneling and modular transformations on the degenerate ground states on torus.

3 He: cosmological and atomic physics experiments

Because the superfluid 3He order parameter exhibits many similarities with that of our Universe, the superfluid condensate may be considered as a quantum vacuum that carries various types of quasiparticles and topological defects. The condensate thus provides a test system for the experimental investigation of many general physics problems in cosmology, atomic or nuclear physics that are otherwise difficult or even impossible to investigate experimentally.

Interior gap superconductivity in heavy fermions

We study the possibility of interior gap superconductivity in two-band systems in the presence of hybridization. This type of superconductivity arises in a system composed of two types of quasi-particles and it develops at the Fermi surface of the quasi-particles with the smallest Fermi momentum. Possible candidates to present this phenomenon are heavy fermion materials. We find that mixing among the particles gives rise to a new superconducting state with gapless excitations.

Mott transition in the asymmetric Hubbard model at half-filling within dynamical mean-field theory

We apply the approximate analytic methods to the investigation of the band structure of the asymmetric Hubbard model where the chemical potentials and electron transfer parameters depend on the electron spin (type of quasiparticles). The Hubbard-I and alloy-analogy approximations are the simplest approximations which are used. Within the alloy-analogy approximation, the energy band of particles does not depend on the transfer parameter of particles of another sort. It means that the gap in the spectrum opens at the critical value $U_{c}$ that is the same in two different limiting cases: the Falicov-Kimball model and the standard Hubbard model. The approximate analytic scheme of the dynamical mean-field theory is developed to include into the theory the scattering of particles responsible for the additional mechanism (due to the transfer of particles of another sort) of the band formation. We use the so-called GH3 approach that is a generalization of the Hubbard-III approximation. The approach describes the continuous Mott transition with the $U_{c}$ value dependent on a ratio of transfer parameters of different particles.

Realizing non-Abelian statistics in time-reversal-invariant systems

We construct a series of 2+1-dimensional models whose quasiparticles obey non-Abelian statistics. The adiabatic transport of quasiparticles is described by using a correspondence between the braid matrix of the particles and the scattering matrix of 1+1-dimensional field theories. We discuss in depth lattice and continuum models whose braiding is that of SO(3) Chern-Simons gauge theory, including the simplest type of non-Abelian statistics, involving just one type of quasiparticle. The ground-state wave function of an SO(3) model is related to a loop description of the classical two-dimensional Potts model. We discuss the transition from a topological phase to a conventionally-ordered phase, showing in some cases there is a quantum critical point.

Theory of strongly correlated electron systems: Hubbard–Anderson models from an exact Hamiltonian, and perturbation theory near the atomic limit within a nonorthogonal basis set

AbstractThe theory of correlated electron systems is formulated in a form that allows the use as a reference point a density functional theory in the local density approximation (LDA DFT) for solids or molecules. The theory is constructed in two steps. As a first step, the total Hamiltonian is transformed into a correlated form. To elucidate the microscopic origin of the parameters of the periodic Hubbard–Anderson model (PHAM) the terms of the full Hamiltonian that have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion configuration‐ and number of particles‐dependent contributions from the Coulomb interaction. In a second step the diagram technique (DT) is developed by means of generalization of the Baym–Kadanoff method for correlated systems. The advantages of the method are that: (1) A nonorthogonal basis can be used, in particular the one generated by LDA DFT; (2) the equations for Green's functions (GFs) for the Fermi and Bose types of quasiparticles can be formulated in the form of a closed system of functional equations. The latter allows us to avoid the question of the nonunique decoupling procedure existing in previous versions of the DT and perform the expansion in terms of dressed GFs. Although the expressions for all interactions depend on the overlap matrix, it is shown that the theory is formally equivalent to one with orthogonal states with redefined interactions. When the PHAM is treated from the atomic‐limit side the vertexes are generated by kinematic interactions. The latter arise due to nontrivial commutation relations between X‐operators and come from the mixing, hopping, and overlap of states. The equations for GFs are derived within the nonorthogonal basis set in Hubbard‐I, one‐loop and random‐phase approximations with respect to kinematic interactions. The self‐consistent equation for “Hubbard Us” is derived. The technique developed is general, in particular its “bosonic” part can be used for description of spin systems with arbitrary anisotropy, systems with orbital ordering, or ordering of multipoles. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 113–143, 2003

TWO-DIMENSIONAL ELECTRON SYSTEM IN ELECTROMAGNETIC RADIATION FIELD

We consider a two-dimensional electron gas in the presence of a monochromatic linear polarized electromagnetic field, within the Floquet formalism. The Floquet states have a simple relation with the energy eigenstates in the absence of the field. Therefore the single-particle and the two-particle Green functions of the many-body system with Coulomb interactions, in the radiation field, can be formally calculated by the standard diagrammatic techniques, as for the conservative system. We derive the elementary excitations of quasi-particle type, the plasma dispersion relation, and the ground state quasi-energy, and we relate them to the corresponding results for the conservative system.

Photoemission spectra of LaMnO3 controlled by orbital excitations

We investigate the spectral function of a hole moving in the orbital-ordered ferromagnetic planes of LaMnO3, and show that it depends critically on the type of orbital ordering. While the hole does not couple to the spin excitations, it interacts strongly with the excitations of e(g) orbitals (orbitons), leading to a new type of quasiparticle with a dispersion on the orbiton energy scale and with strongly enhanced mass and reduced weight. Therefore we predict a large redistribution of spectral weight with respect to the bands found in local density approximation (LDA) or in LDA+U.

Stripe Structure, Spectral Feature and Soliton Gap in HighTcCuprates

We show that the lightly doped La_{2-x}Sr_{x}CuO_{4} can be described in terms of a stripe magnetic structure or soliton picture. The internal relationship between the recent neutron observation of the diagonal (x=0.05) to vertical (x >= 0.06) stripe transition, which was predicted, and the concomitant metal-insulator transition is clarified by this solitonic physics. The phase diagram with the unidentified transition lines between antiferromagnetic to stripe phases, the doping dependence of the modulation period, the origin of the mid-infrared optical absorption are investigated comparatively with other single layer systems: La_{2-x}Sr_{x}NiO_{4} and (La,Nd)_{2-x}Sr_{x}CuO_{4}. The novel type of quasi-particles and holes is fully responsible for metallic conduction and ultimately superconductivity.

Stripes, non-fermi-liquid behavior, and high-T c superconductivity

The electronic structure of the high-Tc cuprates is studied in terms of "large-U" and "small-U" orbitals. A striped structure and three types of quasiparticles are obtained, polaron-like "stripons" carrying charge, "svivons" carrying spin, and "quasielectrons" carrying both. The anomalous properties are explained, and specifically the behavior of the resistivity, Hall constant, and thermoelectric power. High-temperature superconductivity results from transitions between pair states of quasielectrons and stripons.

Spinon basis for higher level SU(2) WZW models

We propose a spinon basis for the integrable highest weight modules of sl̂ 2 at levels k ≥ 1, and discuss the underlying Yangian symmetry. Evaluating the characters in this spinon basis provides new quasi-particle type expressions for the characters of these integrable modules, and explicitly exhibits the structure of an RSOS times a Yangian part, known e.g. from S-matrix results. We briefly discuss generalizations to other groups and more general conformal field theories.

Optical properties of large and small polarons and bipolarons.

In systems that are two and three dimensional electronically, a large polaron and a small polaron are distinct types of quasiparticles. The type of polaron formed depends on which electron-lattice interaction is of primary importance. A large polaron forms when the electron-lattice interaction due to the long-range Coulombic interactions between an electronic carrier and a solid's ions are of paramount importance. Competing effects then determine the radius of a large polaron. By contrast, a small polaron can form when a short-range electron-lattice interaction, such as the deformation-potential interaction, is dominant. A small polaron forms as its self-trapped carrier shrinks without limit until it is confined to a single site. Fundamental differences between large and small polarons produce optical spectra with distinguishing features. The absorption due to photoionization of a large polaron depends on products of the matrix elements for exciting a carrier from its self-trapped states to a free-carrier state and the density of these free-carrier states. These matrix elements fall sharply with increasing free-carrier wave vector k when kRg1, where R is the large polaron's radius. A large polaron's photoionization produces a temperature-independent absorption band. This band is asymmetric with the absorption intensity on the high-energy side of the peak exceeding that on the low-energy side of the peak.By contrast, the small-polaron absorption arises as the self-trapped carrier is induced to transfer from its well-localized state to a localized state at an adjacent site. Phonon broadening of these local electronic energy levels produces the widths of these absorption bands. Small-polaron absorption bands are asymmetric with the absorption intensity below the peak energy exceeding that above the peak energy. With rising temperature the phonon broadening of the local electronic energy levels progressively broadens these absorption bands. In addition, the motion of a polaron in response to an ac field can produce a (Drude-like) free-carrier absorption. A large polaron's free-carrier absorption occurs at frequencies below the characteristic phonon frequency. By contrast, if the narrow bands that characterize small polarons did not result in their localization, their coherent motion would produce a free-carrier absorption that is restricted to frequencies far below the phonon frequency. The optical spectra of large and small bipolarons are similar to those for large and small polarons, respectively. Finally, carrier-induced absorption bands observed in semiconducting and superconducting cuprates are compared with the expectations of large- and small-polaronic absorptions. The high-frequency absorption bands are consistent with the existence of large-polaronic carriers. However, taken together, the free-carrier absorptions and the dc transport in the superconductors depart from expectations of independent polaronic carriers. It is suggested that if the carriers in the cuprates are polaronic, their transport in the superconductors' normal states is collective.