Johan Carlstrom

Type-1.5 superconductivity in multiband systems: the eects of interband couplings

The topic of this thesis is vortex-physics in multi component Ginzburg- Landau models. These models describe a newly discovered class of super- conductors with multiple superconducting gaps, and possess many properties that set them apart from single component models. The work presented here relies on large scale computer simulations using various numerical techniques, but also on some analytical methods.In Paper I, Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors, we show that in multiband supercon- ductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vor- tices, by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields, leading to phase separation into domains of two-component Meissner states and vortex droplets.In paper II, Type-1.5 superconductivity in two-band systems, we discuss the influence of Josephson coupling and show that non-monotonic intervortex interaction can also arise in two-band superconductors where one of the bands is proximity induced by Josephson interband coupling.In paper III, Type-1.5 superconductivity in multiband systems: Effects of interband couplings, we investigate the appearance of Type-1.5 superconduc- tivity in the case with two active bands and substantial inter-band couplings such as intrinsic Josephson coupling, mixed gradient coupling, and density- density interactions. We show that in the presence of these interactions, the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by linear combinations of the density fields.In paper IV, Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors, we demonstrate the existence of nonpairwise in- tervortex forces in multicomponent and layered superconducting systems. We also consider the properties of vortex clusters in a semi-Meissner state of type- 1.5 two-component superconductors. We show that under certain conditions nonpairwise forces can contribute to the formation of complex vortex states in type-1.5 regimes.In paper V, Length scales, collective modes, and type-1.5 regimes in three- band superconductors, we consider systems where frustration in phase dif- ferences occur due to competing Josephson inter-band coupling terms. We show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. 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 domainswithbrokenU(1)andU(1)⇥Z2 symmetries.In paper VI, Topological Solitons in Three-Band Superconductors with Broken Time Reversal Symmetry, we show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topo- logical solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.In paper VII, Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory – A brief overview, we give an overview of vortex physics and magnetic response in multi component Ginzburg-Landau theory. We also examine Type-1.5 superconductivity in the context of microscopic theory.In paper VIII, Chiral CP2 skyrmions in three-band superconductors, we show that under certain conditions, three-component superconductors (and, in particular, three-band systems) allow stable topological defects different from vortices. We demonstrate the existence of these excitations, charac- terised by a CP2 topological invariant, in models for three-component super- conductors with broken time-reversal symmetry. We term these topological defects “chiral GL(3) skyrmions,” where “chiral” refers to the fact that due to broken time-reversal symmetry, these defects come in inequivalent left- and right-handed versions. In certain cases, these objects are energetically cheaper than vortices and should be induced by an applied magnetic field. In other situations, these skyrmions are metastable states, which can be produced by a quench. Observation of these defects can signal broken time-reversal sym- metry in three-band superconductors or in Josephson-coupled bilayers of s± and s-wave superconductors.In paper IX, Phase transition in multi-component superconductors, we ex- amine the thermodynamics of frustrated multi-components superconductors and show that their highly complex energy landscape can give rise new types of phase transitions not present in single component superconductors.

Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors

We show that in multiband superconductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields leading to phase separation into domains of two-component Meissner states and vortex droplets.

Topological solitons in three-band superconductors with broken time reversal symmetry

We show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topological solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.

Length Scales, Collective Modes, and Type-1.5 Regimes in Three-Band Superconductors

The topic of this thesis is vortex-physics in multi component Ginzburg- Landau models. These models describe a newly discovered class of super- conductors with multiple superconducting gaps, and possess many properties that set them apart from single component models. The work presented here relies on large scale computer simulations using various numerical techniques, but also on some analytical methods.In Paper I, Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors, we show that in multiband supercon- ductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vor- tices, by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields, leading to phase separation into domains of two-component Meissner states and vortex droplets.In paper II, Type-1.5 superconductivity in two-band systems, we discuss the influence of Josephson coupling and show that non-monotonic intervortex interaction can also arise in two-band superconductors where one of the bands is proximity induced by Josephson interband coupling.In paper III, Type-1.5 superconductivity in multiband systems: Effects of interband couplings, we investigate the appearance of Type-1.5 superconduc- tivity in the case with two active bands and substantial inter-band couplings such as intrinsic Josephson coupling, mixed gradient coupling, and density- density interactions. We show that in the presence of these interactions, the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by linear combinations of the density fields.In paper IV, Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors, we demonstrate the existence of nonpairwise in- tervortex forces in multicomponent and layered superconducting systems. We also consider the properties of vortex clusters in a semi-Meissner state of type- 1.5 two-component superconductors. We show that under certain conditions nonpairwise forces can contribute to the formation of complex vortex states in type-1.5 regimes.In paper V, Length scales, collective modes, and type-1.5 regimes in three- band superconductors, we consider systems where frustration in phase dif- ferences occur due to competing Josephson inter-band coupling terms. We show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. 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 domainswithbrokenU(1)andU(1)⇥Z2 symmetries.In paper VI, Topological Solitons in Three-Band Superconductors with Broken Time Reversal Symmetry, we show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topo- logical solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.In paper VII, Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory – A brief overview, we give an overview of vortex physics and magnetic response in multi component Ginzburg-Landau theory. We also examine Type-1.5 superconductivity in the context of microscopic theory.In paper VIII, Chiral CP2 skyrmions in three-band superconductors, we show that under certain conditions, three-component superconductors (and, in particular, three-band systems) allow stable topological defects different from vortices. We demonstrate the existence of these excitations, charac- terised by a CP2 topological invariant, in models for three-component super- conductors with broken time-reversal symmetry. We term these topological defects “chiral GL(3) skyrmions,” where “chiral” refers to the fact that due to broken time-reversal symmetry, these defects come in inequivalent left- and right-handed versions. In certain cases, these objects are energetically cheaper than vortices and should be induced by an applied magnetic field. In other situations, these skyrmions are metastable states, which can be produced by a quench. Observation of these defects can signal broken time-reversal sym- metry in three-band superconductors or in Josephson-coupled bilayers of s± and s-wave superconductors.In paper IX, Phase transition in multi-component superconductors, we ex- amine the thermodynamics of frustrated multi-components superconductors and show that their highly complex energy landscape can give rise new types of phase transitions not present in single component superconductors.

Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors

The topic of this thesis is vortex-physics in multi component Ginzburg- Landau models. These models describe a newly discovered class of super- conductors with multiple superconducting gaps, and possess many properties that set them apart from single component models. The work presented here relies on large scale computer simulations using various numerical techniques, but also on some analytical methods.In Paper I, Type-1.5 Superconducting State from an Intrinsic Proximity Effect in Two-Band Superconductors, we show that in multiband supercon- ductors, even an extremely small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vor- tices, by producing long-range intervortex attraction. This type of vortex interaction results in an unusual response to low magnetic fields, leading to phase separation into domains of two-component Meissner states and vortex droplets.In paper II, Type-1.5 superconductivity in two-band systems, we discuss the influence of Josephson coupling and show that non-monotonic intervortex interaction can also arise in two-band superconductors where one of the bands is proximity induced by Josephson interband coupling.In paper III, Type-1.5 superconductivity in multiband systems: Effects of interband couplings, we investigate the appearance of Type-1.5 superconduc- tivity in the case with two active bands and substantial inter-band couplings such as intrinsic Josephson coupling, mixed gradient coupling, and density- density interactions. We show that in the presence of these interactions, the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by linear combinations of the density fields.In paper IV, Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors, we demonstrate the existence of nonpairwise in- tervortex forces in multicomponent and layered superconducting systems. We also consider the properties of vortex clusters in a semi-Meissner state of type- 1.5 two-component superconductors. We show that under certain conditions nonpairwise forces can contribute to the formation of complex vortex states in type-1.5 regimes.In paper V, Length scales, collective modes, and type-1.5 regimes in three- band superconductors, we consider systems where frustration in phase dif- ferences occur due to competing Josephson inter-band coupling terms. We show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. 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 domainswithbrokenU(1)andU(1)⇥Z2 symmetries.In paper VI, Topological Solitons in Three-Band Superconductors with Broken Time Reversal Symmetry, we show that three-band superconductors with broken time reversal symmetry allow magnetic flux-carrying stable topo- logical solitons. They can be induced by fluctuations or quenching the system through a phase transition. It can provide an experimental signature of the time reversal symmetry breakdown.In paper VII, Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory – A brief overview, we give an overview of vortex physics and magnetic response in multi component Ginzburg-Landau theory. We also examine Type-1.5 superconductivity in the context of microscopic theory.In paper VIII, Chiral CP2 skyrmions in three-band superconductors, we show that under certain conditions, three-component superconductors (and, in particular, three-band systems) allow stable topological defects different from vortices. We demonstrate the existence of these excitations, charac- terised by a CP2 topological invariant, in models for three-component super- conductors with broken time-reversal symmetry. We term these topological defects “chiral GL(3) skyrmions,” where “chiral” refers to the fact that due to broken time-reversal symmetry, these defects come in inequivalent left- and right-handed versions. In certain cases, these objects are energetically cheaper than vortices and should be induced by an applied magnetic field. In other situations, these skyrmions are metastable states, which can be produced by a quench. Observation of these defects can signal broken time-reversal sym- metry in three-band superconductors or in Josephson-coupled bilayers of s± and s-wave superconductors.In paper IX, Phase transition in multi-component superconductors, we ex- amine the thermodynamics of frustrated multi-components superconductors and show that their highly complex energy landscape can give rise new types of phase transitions not present in single component superconductors.

Type-1.5 superconductivity in multiband systems: Magnetic response, broken symmetries and microscopic theory – A brief overview

Abstract A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth λ and the coherence length ξ . Their ratio κ determines the response of a superconductor to an external field, sorting them into two categories as follows; type-I when κ 1 / 2 and type-II when κ > 1 / 2 . We overview here multicomponent systems which can possess three or more fundamental length scales and allow a separate “type-1.5” superconducting state when, e.g. in two-component case ξ 1 2 λ ξ 2 . In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges. As a consequence the system should form an additional Semi-Meissner state which properties we discuss below. In that state vortices form clusters in low magnetic fields. Inside the cluster one of the component is depleted and the superconductor-to-normal interface has negative energy. In contrast the current in second component is mostly concentrated on the cluster’s boundary, making the energy of this interface positive. Here we briefly overview recent developments in Ginzburg–Landau and microscopic descriptions of this state.

Chiral CP^2 Skyrmions in Three-Band Superconductors

It is shown that under certain conditions, three-component superconductors (and, in particular, three-band systems) allow stable topological defects different from vortices. We demonstrate the exis ...

Type-1.5 superconductivity in multicomponent systems

Abstract In general a superconducting state breaks multiple symmetries and, therefore, is characterized by several different coherence lengths ξi, i = 1 , … , N . Moreover in multiband material even superconducting states that break only a single symmetry are nonetheless described, under certain conditions by multi-component theories with multiple coherence lengths. As a result of that there can appear a state where some coherence lengths are smaller and some are larger than the magnetic field penetration length λ: ξ 1 ≤ ξ 2 … 2 λ ξ M ≤ … ξ N . That state was recently termed “type-1.5” superconductivity. This breakdown of type-1/type-2 dichotomy is rather generic near a phase transition between superconducting states with different symmetries. The examples include the transitions between U(1) and U(1) × U(1) states or between U(1) and U(1) × Z2 states. The later example is realized in systems that feature transition between s-wave and s + i s states. The extra fundamental length scales have many physical consequences. In particular in these regimes vortices can attract one another at long range but repel at shorter ranges. Such a system can form vortex clusters in low magnetic fields. The vortex clustering in the type-1.5 regime gives rise to many physical effects, ranging from macroscopic phase separation in domains of different broken symmetries, to unusual transport properties. Prepared for the proceedings of Vortex IX conference, Rhodes 12–17 September 2015.

Quantum Walk in Degenerate Spin Environments.

We study the propagation of a hole in degenerate (paramagnetic) spin environments. This canonical problem has important connections to a number of physical systems, and is perfectly suited for experimental realization with ultracold atoms in an optical lattice. At the short-to-intermediate time scale that we can access using a stochastic-series-type numeric scheme, the propagation turns out to be distinctly nondiffusive with the probability distribution featuring minima in both space and time due to quantum interference, yet the motion is not ballistic, except at the beginning. We discuss possible scenarios for long-term evolution that could be explored with an unprecedented degree of detail in experiments with single-atom resolved imaging.

Spontaneous Breakdown of Time-Reversal Symmetry Induced by Thermal Fluctuations

In systems with broken U(1) symmetry, such as superfluids, superconductors, or magnets, the symmetry restoration is driven by the proliferation of topological defects in the form of vortex loops (u ...