Length scales, collective modes, and type-1.5 regimes in three-band superconductors

Abstract

The recent discovery of iron pnictide superconductors has resulted in a rapidly growing interest in multiband models with more than two bands. In this work we specifically focus on the properties of three-band Ginzburg-Landau models which do not have direct counterparts in more studied two-band models. First we derive normal modes and characteristic length scales in the conventional U (1) three-band Ginzburg-Landau model as well as in its time reversal symmetry broken counterpart with U (1) × Z2 symmetry. We show that in the latter case, the normal modes are mixed phase/density collective excitations. A possibility of the appearance of a massless phase-difference mode associated with fluctuations of the phase difference is also discussed. Next we show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to very long-range attractive intervortex interactions and appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. In some cases it also results in the formation of a domain-like structures in the form of a ring of suppressed density around a vortex across which one of the phases shifts by π. We also show that field-induced vortices can lead to a change of broken symmetry from U (1) to U (1) × Z2 in the system. In the type-1.5 regime, it results in a semi-Meissner state where the system has a macroscopic phase separation in domains with broken U (1) and U (1) × Z2 symmetries.Superconductivity with two gaps associated with different bands was first theoretically predicted in 1959 1 . However it was not until 42 years later, with the discovery of M gB 2 2

Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems

“…These include (I) the appearance of a massless so-called Leggett mode at the Z 2 phase transition 9 ; (II) the existence of new mixed phase-density collective modes in the state with broken time-reversal symmetry (BTRS) 4,5,10 in contrast to the "phase-only" Leggett collective mode in two-band materials 11 ; and (III) the existence of (meta-)stable excitations characterized by CP 2 topological invariants 12,13 . So far the phase diagram of frustrated three-band superconductors has been investigated only at the meanfield level 3,5 .…”

“…The phase lockings are related by complex conjugation of the fields ψ α . Thus, by choosing one of these phase locking patterns the system breaks time reversal symmetry [2][3][4] . In this work, we address the phase transitions in a two dimensional three-band superconductor with broken time-reversal symmetry.…”

Type-1.5 superconductivity in multicomponent systems

“…The interaction energy for a pair of magnetic dipoles may be computed similarly. In the case of our two component GL model, the total long-range inter-vortex interaction energy has three terms, corresponding to the three sources in the composite point source (10), and turns out to be…”

“…72 There is a divergent coherence length at the critical point where the system undergoes the close to the groundstate, gives a mass-matrix whose eigenbasis is also an orthonormal basis of small perturbations to the ground state. 10 In systems that break only U (1) symmetry, these modes are segregated with respect to phase and amplitude so that small perturbations to the phase and amplitude sectors decay independently of each other. Small perturbations to the amplitude thus has no implications for the phase difference sector, and vice versa.…”

“…20 A. Type-1.5 superconductivity Multicomponent systems allow a type of superconductivity that is distinct from the type-1 and type-2. 1,7,10,18,[21][22][23][24][25] It emerges from the following circumstances: Multi-component GL models have several fundamental scales, namely the magnetic field penetration depth λ and multiple coherence lengths (characteristic scales of the variations of the density fields) ξ i , which renders the model impossible to parametrize in terms of a single dimensionless parameter κ, thus making the type-1/type-2 dichotomy insufficient for classifying and describing these systems. Rather, in a wide range of parameters, there is a separate superconducting regime with some coherence lengths that are larger and some that are smaller than the magnetic field penetration length ξ 1 / √ 2 < ξ 2 / √ 2 < ... < λ < ξ M / √ 2 < ... < ξ N / √ 2.…”