Higgsless superconductivity from topological defects in compact BF terms (original) (raw)
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Physical Review B, 2015
We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axion-like magnetoelectric term with the phase difference of the superconducting order parameters playing the role of the axion field. Due to this additional term, quantum electromagnetic and phase fluctuations lead to a robust topologically non-trivial state that holds also in the presence of interactions. In this sense, we show that the renormalization flow of the topologically nontrivial phase cannot be continuously deformed into a topologically non-trivial one. One consequence of our analysis of quantum critical fluctuations, is the possibility of having a first-order phase transition in the bulk and a second-order phase transition on the surface. We also explore another consequence of the axionic Higgs electrodynamics, namely, the anomalous Hall effect. In the low frequency London regime an anomalous Hall effect is induced in the presence of an applied electric field parallel to the surface. This anomalous Hall current is induced by a Lorentz-like force arising from the axion term, and it involves the relative superfluid velocity of the superconducting components. The anomalous Hall current has a negative sign, a situation reminiscent of, but quite distinct in physical origin from the anomalous Hall effect observed in high-T c superconductors. In contrast to the latter, the anomalous Hall effect in topological superconductors is non-dissipative and occurs in the absence of vortices.
Higgs Mechanism and Anomalous Hall Effect in Three-Dimensional Topological Superconductors
2015
We demonstrate that the Higgs mechanism in three-dimensional topological superconductors exhibits unique features with experimentally observable consequences. The Higgs model we discuss has two superconducting components and an axion-like magnetoelectric term with the phase difference of the superconducting order parameters playing the role of the axion field. Due to this additional term, quantum electromagnetic and phase fluctuations lead to a robust topologically non-trivial state that holds also in the presence of interactions. In this sense, we show that the renormalization flow of the topologically nontrivial phase cannot be continuously deformed into a topologically non-trivial one. One consequence of our analysis of quantum critical fluctuations, is the possibility of having a first-order phase transition in the bulk and a second-order phase transition on the surface. We also explore another consequence of the axionic Higgs electrodynamics, namely, the anomalous Hall effect. In the low frequency London regime an anomalous Hall effect is induced in the presence of an applied electric field parallel to the surface. This anomalous Hall current is induced by a Lorentz-like force arising from the axion term, and it involves the relative superfluid velocity of the superconducting components. The anomalous Hall current has a negative sign, a situation reminiscent of, but quite distinct in physical origin from the anomalous Hall effect observed in high-T c superconductors. In contrast to the latter, the anomalous Hall effect in topological superconductors is non-dissipative and occurs in the absence of vortices.
From topological insulators to superconductors and confinement
New Journal of Physics, 2012
Topological matter in 3D is characterized by the presence of a topological BF term in its longdistance effective action. We show that, in 3D, there is another marginal term that must be added to the action in order to fully determine the physical content of the model. The quantum phase structure is governed by three parameters that drive the condensation of topological defects: the BF coupling, the electric permittivity and the magnetic permeability of the material. For intermediate levels of electric permittivity and magnetic permeability the material is a topological insulator. We predict, however, new states of matter when these parameters cross critical values: a topological superconductor when electric permittivity is increased and magnetic permeability is lowered and a charge confinement phase in the opposite case of low electric permittivity and high magnetic permeability. Synthetic topological matter may be fabricated as 3D arrays of Josephson junctions.
Gapless topological superconductors: Model Hamiltonian and realization
Physical Review B, 2015
The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two dimensional Hamiltonians that yield an unusual class D topological superconductor with a gapless bulk spectrum but welllocalized Majorana edge states. We perform a numerical analysis for a representative model of this phase and suggest a concrete physical realization by analyzing the effect of magnetic impurities on the surface of strong topological insulators.
Topological quantum phase transitions in topological superconductors
EPL (Europhysics Letters), 2010
In this paper we show that BF topological superconductors (insulators) exibit phase transitions between different topologically ordered phases characterized by different ground state degeneracy on manifold with non-trivial topology. These phase transitions are induced by the condensation (or lack of) of topological defects. We concentrate on the (2+1)-dimensional case where the BF model reduce to a mixed Chern-Simons term and we show that the superconducting phase has a ground state degeneracy k and not k 2. When the symmetry is U (1) × U (1), namely when both gauge fields are compact, this model is not equivalent to the sum of two Chern-Simons term with opposite chirality, even if naively diagonalizable. This is due to the fact that U (1) symmetry requires an ultraviolet regularization that make the diagonalization impossible. This can be clearly seen using a lattice regularization, where the gauge fields become angular variables. Moreover we will show that the phase in which both gauge fields are compact is not allowed dynamically.
Unusual Superconducting transition in Topological Insulators
Journal of Physics: Conference Series, 2014
Superconducting transition generally belongs to the U (1) class of phase transitions. However it was pointed out long time ago that if the normal state dispersion relation is "ultrarelativistic" the transition is unusual: even the mean field critical exponents are different from the standard ones leading to a number of observable effects. Attempts to experimentally discover such a system included chiral condensate in graphene. Recently it was found that some 3D topological insulators (that possess the ultrarelativistic metal on its surface) exhibit surface superconductivity.Starting from microscopic TI Hamiltonian with local four fermions interaction, we calculated the total set of the Gor'kov equations allowing to build the Ginzburg-Landau (GL) theory including the magnetic field effects. It was shown that the GL equations reflect the novel chiral universality class, very different from original GL equations. For example the temperature dependence of the coherence length diverges at the critical temperature with critical exponent ν = −1 in rather than customary ν = −1/2, magnetization near the upper critical magnetic field is quadratic as a function of deviation from the upper critical field while the Superfluid density is ψ 2 = (Tc − T) β , β = 2, not β = 1.
Topological superconductivity, topological confinement, and the vortex quantum Hall effect
Physical Review B, 2011
Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors and topological confinement. In conventional superconductivity, due to spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stückelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
Non-Abelian bosonization of topological insulators and superconductors
Physical review, 2022
Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic free fermions, we derive the (non-Abelian) bosonized theory for free fermion topological insulators and superconductors that have, in addition to the U(1) charge, time reversal and charge conjugation symmetries and flavor symmetries. For the case we consider, the flavor symmetries render the topological classification Z. The results are nonlinear σ models with the topological θ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.
The Higgs mode in disordered superconductors close to a quantum phase transition
Nature Physics, 2015
The concept of mass-generation via the Higgs mechanism was strongly inspired by earlier works on the Meissner-Ochsenfeld effect in superconductors. In quantum field theory, the excitations of longitudinal components of the Higgs field manifest as massive Higgs bosons. The analogous Higgs mode in superconductors has not yet been observed due to its rapid decay into particle-hole pairs. Following recent theories, however, the Higgs mode should decrease below the pairing gap 2∆ and become visible in two-dimensional systems close to the superconductor-insulator transition (SIT). For experimental verification, we measured the complex terahertz transmission and tunneling density of states (DOS) of various thin films of superconducting NbN and InO close to criticality. Comparing both techniques reveals a growing discrepancy between the finite 2∆ and the threshold energy for electromagnetic absorption which vanishes critically towards the SIT. We identify the excess absorption below 2∆ as a strong evidence of the Higgs mode in two dimensional quantum critical superconductors.
An Abelian two-Higgs model and high temperature superconductivity
2005
We study a three dimensional Abelian Higgs model containing singly-and doubly-charged scalar fields coupled to a compact Abelian gauge field in the London limit. The model attracts interest because of its relevance to high-T c superconductors with charge 1 holon and charge 2 spinon-pair fields. It contains two types of vortices carrying magnetic flux and one type of instanton-like monopoles. Using thermodynamic and topological observables we present the phase diagram in the parameter space of the gauge and holon and spinon-pair couplings. The Fermi liquid, the spin gap, the superconductor and the strange metallic phases have been identified in a wide region of parameters. The model may serve as a toy system modelling non-perturbative properties of the Yang-Mills theory.