Vortices and magnetic bags in Abelian models with extended scalar sectors and some of their applications

Abstract

A detailed study of vortices is presented in Ginzburg-Landau (or Abelian Higgs) models with two complex scalars (order parameters) assuming a general U(1)×U(1) symmetric potential. Particular emphasis is given to the case, when only one of the scalars obtains a vacuum expectation value (VEV). It is found that for a significantly large domain in parameter space vortices with a scalar field condensate in their core (condensate core, CC) coexist with Abrikosov-Nielsen-Olesen (ANO) vortices. Importantly CC vortices are stable and have lower energy than the ANO ones. Magnetic bags or giant vortices of the order of 1000 flux quanta are favoured to form for the range of parameters ("strong couplings") appearing for the superconducting state of liquid metallic hydrogen (LMH). Furthermore, it is argued that finite energy/unit length 1VEV vortices are smoothly connected to fractional flux 2VEV ones. Stable, finite energy CC-type vortices are also exhibited in the case when one of the scalar fields is neutral.In a considerable number of physical theories describing rather different situations, vortices play often an essential rôle to understand key phenomena. In gauge field theories spontaneously broken by scalar fields, the vortex of reference is undoubtedly the celebrated Abrikosov-NielsenOlesen (ANO) one [1] associated to the breaking of a U(1) gauge symmetry by a complex scalar doublet. ANO vortices correspond to the planar cross-sections of static, straight, magnetic flux-tubes, with an SO(2) cylindrical symmetry. Their magnetic flux is quantized as Φ = nΦ 0 , where Φ 0 is an elementary flux unit and n is an integer. The integer n can be identified with a topological invariant, the winding number of the complex scalar, which is also responsible for their remarkable stability. Rotationally symmetric ANO vortex solutions form families labelled by n and by the mass ratio β = m s /m v , where m s , resp. m v denote the mass of the scalar resp. of the vector field.The ubiquity of vortices in different branches of physics, ranging from condensed matter systems, such as superfluids, superconductors [2,3,4] to cosmic strings in high energy physics [5,6] greatly contributes to their importance. By now models of superconductors with several order parameters (scalar doublets) have become the subject of intense theoretical and experimental studies [7,8]. Under extremely high pressure liquid metallic hydrogen (LMH) is expected to undergo a phase transition to a superconducting state, where two types of Cooper pairs are formed, one from electrons and another one from protons [9,10,11,12,13,14]. For experimental data on the existence of liquid metallic hydrogen see Refs. [15,16], for numerical simulations, 1

Excited cosmic strings with superconducting currents

“…The numerical values ofŨ /n as well asT /n are given in Table II. This relates to the observations made in [44,45]. Finally, let us mention that we also find that the value of the current C decreases with increasing n. A more detailed analysis of this fact is out of the scope of this paper and is left as future work.…”

“…We have also constructed superconducting string solutions with n > 1, motivated by a recent study done in a very similar model [44,45]. As our stability analysis below shows, the qualitative behaviour of our results is independent of n. To demonstrate this, we have constructed numerically solutions with n = 2 and n = 3 and compared these to the n = 1 case.…”

New color-magnetic defects in dense quark matter

“…One may ask, however, whether the other two components are induced inside the flux tube, similarly to the flux tubes discussed in Refs. [43,44]. We shall investigate this possibility by considering 2SC flux tubes within the full three-component calculation.…”

First Order Framework for Gauge k-Vortices

“…Again, to find the functions K(|ϕ|), Q(|ϕ|), P (|ϕ|) and V (|ϕ|) we must suggest two of them and use Eqs. (21). We take the potential in the form…”

“…Vortices have also been investigated in generalized models with distinct motivations in several works; see, e.g., Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In particular, k-vortices, which are vortices in models with generalized kinematics, similar to the models studied before in Refs.…”