Vortex with fractional quantum numbers in a chiral<b><i>p</i></b>-wave superconductor

Goryo, Jun

doi:10.1103/physrevb.61.4222

Cited by 27 publications

(23 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fourth and fifth terms, as we now show, carry significant information about the dynamics of vortices. Previous work on the effective low-energy theory of the p-wave superconductor, using only the U(1) part of our transformation 18,20 , yielded an action similar to that of an s-wave superconductor but with an additional partial CS term. Stone and Roy 21 attributed this partial CS term to the existence of a Hall-like response to external fields.…”

Section: Vortex Dynamics and Exchangementioning

confidence: 86%

Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

2015

View full text Add to dashboard Cite

We propose a U(1)×Z2 effective gauge theory for vortices in a px+ipy superfluid in two dimensions. The combined gauge transformation binds U(1) and Z2 defects so that the total transformation remains single-valued and manifestly preserves the the particle-hole symmetry of the action. The Z2 gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the U(1) gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. More importantly, it predicts a universal Abelian phase, exp(iπ/8), upon the exchange of two vortices. This phase is modified by non-universal corrections due to the partial Chern-Simon term, which are nevertheless screened in a charged superfluid at distances that are larger than the penetration depth.

show abstract

Section: Vortex Dynamics and Exchangementioning

confidence: 86%

Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

2015

View full text Add to dashboard Cite

show abstract

“…According to [41], the N = 1 vortex in a chiral superconductor must have a spin S = 1/4 (per layer); this implies the spin S = 1/8 per layer for N = 1/2 vortex. Similarly there can be an anomalous fractional electric charge of the N = 1/2 vortex, which is 1/2 of the fractional charge e/4 discussed for the N = 1 vortex [42]. There is still some work to be done to elucidate the problem with the fractional charge, spin and statistics, related to the topological defects in chiral superconductors.…”

Section: Discussion: Fermions In the Presence Of Topological Defectsmentioning

confidence: 99%

Monopoles and fractional vortices in chiral superconductors

Volovik

2000

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

I discuss two exotic objects that must be experimentally identified in chiral superfluids and superconductors. These are (i) the vortex with a fractional quantum number (N ‫؍‬ 1͞2 in chiral superfluids, and N ‫؍‬ 1͞2 and N ‫؍‬ 1͞4 in chiral superconductors), which plays the part of the Alice string in relativistic theories and (ii) the hedgehog in theˆl field, which is the counterpart of the Dirac magnetic monopole. These objects of different dimensions are topologically connected. They form the combined object that is called a nexus in relativistic theories. In chiral superconductors, the nexus has magnetic charge emanating radially from the hedgehog, whereas the half-quantum vortices play the part of the Dirac string. Each half-quantum vortex supplies the fractional magnetic flux to the hedgehog, representing 1͞4 of the ''conventional'' Dirac string. I discuss the topological interaction of the superconductor's nexus with the 't Hooft-Polyakov magnetic monopole, which can exist in Grand Unified Theories. The monopole and the hedgehog with the same magnetic charge are topologically confined by a piece of the Abrikosov vortex. Such confinement makes the nexus a natural trap for the magnetic monopole. Other properties of half-quantum vortices and monopoles are discussed as well, including fermion zero modes. Magnetic monopoles do not exist in classical electromagnetism. Maxwell equations show that the magnetic field is divergenceless, ٌ⅐B ϭ 0, which implies that the magnetic flux through any closed surface is zero: ͛ S dS⅐B ϭ 0. If one tries to construct the monopole solution B ϭ gr͞r 3 , the condition that magnetic field is nondivergent requires that magnetic flux ⌽ ϭ 4g from the monopole must be accompanied by an equal singular flux supplied to the monopole by an attached Dirac string. Quantum electrodynamics, however, can be successfully modified to include magnetic monopoles. In 1931, Dirac (1) showed that the string emanating from a magnetic monopole becomes invisible for electrons if the magnetic flux of the monopole is quantized in terms of the elementary magnetic fluxwhere e is the charge of the electron. In 1974, it was shown by 't Hooft (2) and Polyakov (3) that a magnetic monopole with quantization of the magnetic charge, according to Eq. 1, can really occur as a physical object if the U(1) group of electromagnetism is a part of the higher symmetry group. The magnetic flux of a monopole in terms of the elementary magnetic flux coincides with the topological charge of the monopole: this quantity remains constant under any smooth deformation of the quantum fields. Such monopoles can appear only in Grand Unified Theories, where all interactions are united by, say, the SU(5) group.In the Standard Model of electroweak interactions, such monopoles do not exist, but the combined objects monopole ϩ string can be constructed without violating of the condition ٌ⅐B ϭ 0. Further, following the terminology of ref. 4, I shall call such a combined object a nexus. In a nexus, the magnetic monopole looks like a Dirac m...

show abstract

“…It describes the magneto-electric effect, i.e., a change in the electric charge density in response to an applied magnetic field B z . As a consequence of this effect, a magnetic vortex would acquire the fractional electric charge e/4 [34]. A setup for an experimental detection of the magneto-electric effect in chiral superconductors was proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

2009

View full text Add to dashboard Cite

We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral px +ipy superconductor, such as Sr2RuO4, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across the superconducting gap, and decays as some power of the high frequency ω. The Hall conductivity increases linearly with the decrease of temperature below the superconducting transition and saturates at zero temperature. Using our results for the high-frequency Hall conductivity, we estimate the polar Kerr angle for light reflection from the material and compare it with the experimental measurements in Sr2RuO4 by Xia et al., Phys. Rev. Lett. 97, 167002 (2006).

show abstract

Vortex with fractional quantum numbers in a chiralp-wave superconductor

Cited by 27 publications

References 49 publications

Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

Monopoles and fractional vortices in chiral superconductors

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

Contact Info

Product

Resources

About