Anyon Superconductivity Research Articles

Adiabatic heuristic principle on a torus and generalized Streda formula

Although the adiabatic heuristic argument of the fractional quantum Hall states has been successful, continuous modification of the flux/statistics of anyons is strictly prohibited due to algebraic constrains of the braid group on a torus. We have numerically shown that the adiabatic heuristic principle for anyons is still valid even though the Hamiltonians cannot be modified continuously. The Chern number of the ground state multiplet is the adiabatic invariant, while the number of the topological degeneracy behaves wildly. A generalized Streda formula is proposed that explains the degeneracy pattern. Nambu-Goldston modes associated with the anyon superconductivity are also suggested numerically.

Periodic Maxwell–Chern–Simons vortices with concentrating property

In order to study electrically and magnetically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell-Chern-Simons (MCS) model was introduced by [Lee, Lee, Min (1990)] as a unified system of the classical Abelian-Higgs model (AH) and the Chern-Simons (CS) model. In this article, the first goal is to obtain the uniform (CS) limit result of (MCS) model with respect to the Chern-Simons parameter without any restriction on either a particular class of solutions or the number of vortex points. The most important step for this purpose is to derive the relation between the Higgs field and the neutral scalar field. Our (CS) limit result also provides the critical clue to answer the open problems raised by [Ricciardi,Tarantello (2000)] and [Tarantello (2004)], and we succeed to establish the existence of periodic Maxwell-Chern-Simons vortices satisfying the concentrating property of the density of superconductive electron pairs. Furthermore, we expect that the (CS) limit analysis in this paper would help to study the stability, multiplicity, and bubbling phenomena for solutions of the (MCS) model.

Emergent Higgsless Superconductivity

We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalizable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D-1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realized as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.

Higgsless superconductivity from topological defects in compact BF terms

We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalisable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D−1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D−2)-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realised as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.

Low-energy vortex dynamics in the self-dual Chern–Simons–Higgs model

The relativistic Chern–Simons–Higgs theory finds application in anyonic superconductivity and contains topological vortices whose dynamics are poorly understood. The gauge fields are defined by a set of nonlinear constraint equations that can be accurately solved with effective Green’s functions, spectral methods, and a discretization scheme using lattice gauge techniques. Simulations show that low-energy two-vortex interactions are elastic with final scattering angles sensitive to vortex velocity; furthermore, vortex pairs form rotating breather states for certain impact parameters. In this study, a function that reproduces scattering angles in the adiabatic limit for nontangential collisions is presented. Simulation results are discussed in the context of analytical methods that extract vortex dynamics from low-energy effective Lagrangians, and a numerical method to calculate the effective Lagrangian is suggested. The numerical techniques used can be applied to the study of other Chern–Simon theories.

Non-Abelian Anyon Superconductivity

Non-Abelian anyons exist in certain spin models and may exist in quantum Hall systems at certain filling fractions. In this work, we studied the ground state of dynamical SU(2) level-kappa Chern-Simons non-Abelian anyons at finite density and no external magnetic field. We find that, in the large-kappa limit, the topological interaction induces a pairing instability and the ground state is a superconductor with d+id gap symmetry. We also develop a picture of pairing for the special value kappa=2 and argue that the ground state is a superfluid of pairs for all values of kappa.

Cooper pairs and exclusion statistics from coupled free-fermion chains

We show how to couple two free-fermion chains so that the excitations consist of Cooperpairs with zero energy, and free particles obeying (mutual) exclusion statistics. Thisbehaviour is reminiscent of anyonic superconductivity, and of a ferromagnetic version of theHaldane–Shastry spin chain, although here the interactions are local. We solve this modelusing the nested Bethe ansatz, and find all the eigenstates; the Cooper pairscorrespond to exact-string or ‘0/0’ solutions of the Bethe equations. We showhow the model possesses an infinite-dimensional symmetry algebra, which is asupersymmetric version of the Yangian symmetry algebra for the Haldane–Shastry model.

A class of P, T-invariant topological phases of interacting electrons

We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding statistics. P and T invariance are maintained by a ‘doubling’ of the low-energy degrees of freedom which occurs naturally without doubling the underlying microscopic degrees of freedom. The simplest examples have been the subject of considerable interest as proposed mechanisms for high- T c superconductivity. One is the ‘doubled’ version of the chiral spin liquid. The chiral spin liquid gives rise to anyon superconductivity at finite doping and the corresponding field theory is U(1) Chern–Simons theory at coupling constant m=2. The ‘doubled’ theory is two copies of this theory, one with m=2 the other with m=−2. The second example corresponds to Z 2 gauge theory, which describes a scenario for spin-charge separation. Our main concern, with an eye towards applications to quantum computation, are richer models which support non-Abelian statistics. All of these models, richer or poorer, lie in a tightly organized discrete family indexed by the Baraha numbers, 2cos(π/( k+2)), for positive integer k. The physical inference is that a material manifesting the Z 2 gauge theory or a doubled chiral spin liquid might be easily altered to one capable of universal quantum computation. These phases of matter have a field-theoretic description in terms of gauge theories which, in their infrared limits, are topological field theories. We motivate these gauge theories using a parton model or slave-fermion construction and show how they can be solved exactly. The structure of the resulting Hilbert spaces can be understood in purely combinatorial terms. The highly constrained nature of this combinatorial construction, phrased in the language of the topology of curves on surfaces, lays the groundwork for a strategy for constructing microscopic lattice models which give rise to these phases.

ON THE OCCURRENCE OF A POSITIVE VACUUM ENERGY IN A QUANTUM MODEL FOR SPACE–TIME

It is shown that a previously proposed quantum model for four-dimensional space–time based on an SU (∞) generalization of anyonic superconductivity can be regarded as a discrete form of Polyakov's string theory. This suggests that in a Robertson–Walker universe there is a positive vacuum energy that is on the order of the string tension divided by square of the distance scale factor. This leads to a new type of cosmological model that, even though it resembles more an open universe than an accelerating universe, is apparently consistent with current observational constraints on cosmological models.

Erratum: Thermal properties of gauge fields common to anyon superconductors and spin liquids [Phys. Rev. B51, 9348 (1995)

In this erratum to my article published in Physical Review B, vol. 51, pg. 9348 (1995), I produce the correct formula for the deconfinement temperature of compact QED in two space dimensions at weak-coupling. The context is anyon superconductivity and chiral spin-liquid physics. (Any claims of priority are welcome.)

Phase transition in anyon superconductivity at finite temperature

The magnetic response of the charged anyon fluid at temperatures higher than the fermion energy gap ( T ⪢ ω c ) is investigated in the self-consistent field approximation. In this temperature region a new phase, characterized by an inhomogeneous magnetic penetration, is found. The inhomogeneity is linked to the existence of an imaginary magnetic mass which increases with the temperature. It is explicitly proved that the electromagnetic field magnetic masses and rest-energies are different in the ( T ⪢ ω c )-phase.

Application of the magnetic-electric two-dimensional Euclidean group to the case of anyons

The magnetic-electric two-dimensional Euclidean symmetry MEE(2) is applied to the case of anyons. It is shown that in this formalism both Bloch's theorem and acceleration theorem for charged anyons in periodic fields are straightforward. The relation between these two theorems and the anyonic superconductivity is discussed and certain suggestions are put forward.

Penetration Depth in Anyon Superconductivity on Torus

We present a model for studying the Meissner effect in anyon superconductivity on torus. By obtaining the explicit forms of screening currents for different geometries of external magnetic fields, we calculate the penetration depth and its dependence on relevant parameters. We find a difference between our model and London theory of bulk superconductors. This can be traced back to the two-dimensional character of electric charge carriers that obey anyonic statistics. Our calculations show that for ground state configuration the fractional statistical nature of carriers is washed out of the final results, whereas for excited states the screening currents — and hence the penetration depth — explicitly depend on the fractional phase of the model.

Critical statistical charge for anyonic superconductivity

We examine a criterion for the anyonic superconductivity at zero temperature in Abelian matter-coupled Chern-Simons gauge field theories in three dimensions. By solving the Dyson-Schwinger equations, we obtain a critical value of the statistical charge for the superconducting phase in a massless fermion-Chern-Simons model.

ON THE MEISSNER EFFECT AND THE HIGGS-LIKE MECHANISM IN ANYON SUPERCONDUCTORS

The problem of the Meissner effect in the exotic anyon superconductor is rediscussed from the point of view of the spontaneous breaking of symmetry and the Higgs mechanism idea. It is shown that the inclusion of electromagnetic interactions leads to the typical Higgs mechanism only in the case of the two-dimensional Coulomb interaction. The qualitative difference between anyon superconductivity—where the Meissner effect and the Higgs mechanism are independent—and ordinary BCS superconductivity is underlined.

Explicit quantization of anyon superconductivity Lagrangian

The explicit quantization of the Lagrangian describing anyon superconductivity is performed using the Dirac-Bergmann method. At first, it is pointed out that it is not possible to choose the gauge-fixing conditiona0 = 0 (with the Coulomb gauge). Secondly, the canonical commutation relations between operators are obtained. Thirdly, the correct effective Hamiltonian is derived. Also, the spontaneous projectivation is discussed. Finally, it is shown that by solving the constraints, the Meissner effect is obtained.

Magnetic field induced by a point charge located between two anyon planes

The circulating currents and magnetic field induced by a point charge placed between two electrostatically coupled and antiferromagnetically ordered planes of semions are calculated. Although the magnetic field at the charge vanishes when the charge is midway between the planes, this field approaches values of the same order as that induced by a single plane when the charge is moved significantly (>10%) off-center. These results could be relevant to future searches for anyon superconductivity using positive muon spin rotation measurements.

Thermal properties of gauge fields common to anyon superconductors and spin liquids.

The thermally driven confinement-deconfinement transition exhibited by lattice quantum electrodynamics in two space dimensions is re-examined in the context of the statistical gauge-fields common to anyon superconductors and to spin-liquids. Particle-hole excitations in both systems are bound by a confining string at temperatures below the transition temperature $T_c$. We argue that $T_c$ coincides with the actual critical temperature for anyon superconductivity. The corresponding specific-heat contribution, however, shows a {\it smooth} peak just below $T_c$ characteristic of certain high-temperature superconductors.

MAGNETIC AND SUPERCONDUCTING PROPERTIES OF HIGH-Tc SUPERCONDUCTORS

High-Tc superconductors, distorted-perovskite cuprates, are derived, by means of suitable doping, from a Mott-insulating and antiferromagnetic parent material. The most important ingredient of their structure is the stacks of Cu-O planes which carry superconductivity. Magnetic, transport and other properties that characterize the supercon-ducting state are very unusual and highly anisotropic. Density of states at the Fermi level in these materials is rather small but Tc is very high (highest reported Tc~125 K). In the high-Tc systems that contain magnetic moment bearing rate earth (RE)-atoms, antiferromagnetic ordering (TN<2 K) of RE-moments coexists with superconductivity. Some of them are ideal two-dimensional magnetic systems. Flux line lattices in these materials have rather unusual structural properties. There are both hole-type as well as electron-type superconductors. The available experimental evidence does not favour odd-parity pairing. It is not yet clear, however, whether even-parity pairing is d-wave or s-wave type. Antiferromagnetic fluctuations may be possible mechanism of Cooper pairing. Anyonic superconductivity is ruled out.

Energy density in the Maxwell-Chern-Simons theory.

A two-dimensional nonrelativistic fermion system coupled to both electromagnetic gauge fields and Chern-Simons gauge fields is analysed. Polarization tensors relevant in the quantum Hall effect and anyon superconductivity are obtained as simple closed integrals and are evaluated numerically for all momenta and frequencies. The correction to the energy density is evaluated in the random phase approximation (RPA), by summing an infinite series of ring diagrams. It is found that the correction has significant dependence on the particle number density. In the context of anyon superconductivity, the energy density relative to the mean field value is minimized at a hole concentration per lattice plaquette (0.05 \sim 0.06) (p_c a/\hbar)^2 where p_c and a are the momentum cutoff and lattice constant, respectively. At the minimum the correction is about -5 % \sim -25 %, depending on the ratio (2m \omega_c)/(p_c^2) where \omega_c is the frequency cutoff. In the Jain-Fradkin-Lopez picture of the fractional quantum Hall effect the RPA correction to the energy density is very large. It diverges logarithmically as the cutoff is removed, implying that corrections beyond RPA become important at large momentum and frequency.