Massive Dirac states bound to vortices by a boson-fermion interaction

Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon-Dirac equations. The introduction of a boson-fermion interaction allows a scalar vortex to act as a harmonic trap that can confine massive Dirac bound states. A parametric analysis is performed to understand the range of boson-fermion coupling strengths, Ginzburg-Landau parameters, and fermion effective masses that support the existence of bound state solutions; results are shown to be comparable to quasiparticle bound states in gapped Dirac materials. Solutions are time evolved and are observed to be stable until the fermion field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>ψ</a:mi> </a:mrow> </a:math> becomes large enough to collapse the spontaneously broken vacuum of the condensate. Head-on scattering simulations are performed, and traditional vortex right-angle scattering is shown to break down with increased fermion field strength. For sufficiently large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ψ</c:mi> </c:math> and low velocity, the collision of two <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>m</e:mi> <e:mo>=</e:mo> <e:mn>1</e:mn> </e:math> vortices results in a pseudostable <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>m</g:mi> <g:mo>=</g:mo> <g:mn>2</g:mn> </g:math> bound state that eventually becomes unstable and decays back into two <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>m</i:mi> <i:mo>=</i:mo> <i:mn>1</i:mn> </i:math> vortices. For large <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>ψ</k:mi> </k:math> and collision velocity, vortex scattering is observed to produce nontopological (zero winding number) scalar bound states that are ejected from the collision. The scalar bubbles contain coherent fermion bound states in their interiors and interpolate between the spontaneously broken vacuum of the bulk and the modified vacuum induced by the boson-fermion interaction.