Effective Model and Magnetic Properties of the Resistive Electron Quadrupling State.

Recent experiments [Grinenko et al. Nat. Phys. 17, 1254 (2021)NPAHAX1745-247310.1038/s41567-021-01350-9] reported the observation of a condensate of four-fermion composites. This is a resistive state that spontaneously breaks the time-reversal symmetry, leading to unconventional magnetic properties, detected in muon spin rotation experiments and by the appearance of a spontaneous Nernst effect. In this Letter, we derive an effective model for the four-fermion order parameter that describes the observed spontaneous magnetic fields in this state. We show that this model, which is alike to the Faddeev-Skyrme model can host skyrmions: magnetic-flux-carrying topological excitations.

Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires.

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15-0.35 eV Å. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.

Nematic Skyrmions in Odd-Parity Superconductors.

We study topological excitations in two-component nematic superconductors, with a particular focus on Cu_{x}Bi_{2}Se_{3} as a candidate material. We find that the lowest-energy topological excitations are coreless vortices: a bound state of two spatially separated half-quantum vortices. These objects are nematic Skyrmions, since they are characterized by an additional topological charge. The inter-Skyrmion forces are dipolar in this model, i.e., attractive for certain relative orientations of the Skyrmions, hence forming multi-Skyrmion bound states.

Thermoelectric Signatures of Time-Reversal Symmetry Breaking States in Multiband Superconductors.

We show that superconductors with broken time-reversal symmetry have very specific magnetic and electric responses to inhomogeneous heating. A local heating of such superconductors induces a magnetic field with a profile that is sensitive to the presence of domain walls and crystalline anisotropy of superconducting states. A nonstationary heating process produces an electric field and a charge imbalance in different bands. These effects can be measured and used to distinguish s+is and s+id superconducting states in the candidate materials such as Ba_{1-x}K_{x}Fe_{2}As_{2}.

Properties of skyrmions and multi-quanta vortices in chiral p-wave superconductors.

Chiral p-wave superconducting state supports a rich spectrum of topological excitations different from those in conventional superconducting states. Besides domain walls separating different chiral states, chiral p-wave state supports both singular and coreless vortices also interpreted as skyrmions. Here, we present a numerical study of the energetic properties of isolated singular and coreless vortex states as functions of anisotropy and magnetic field penetration length. In a given chiral state, single quantum vortices with opposite winding have different energies and thus only one kind is energetically favoured. We find that with the appropriate sign of the phase winding, two-quanta (coreless) vortices are always energetically preferred over two isolated single quanta (singular) vortices. We also report solutions carrying more flux quanta. However those are typically more energetically expensive/metastable as compared to those carrying two flux quanta.

Domain walls and their experimental signatures in s+is superconductors.

Arguments were recently advanced that hole-doped Ba(1-x)K(x)Fe2As2 exhibits the s+is state at certain doping. Spontaneous breaking of time-reversal symmetry in the s+is state dictates that it possess domain wall excitations. Here, we discuss what are the experimentally detectable signatures of domain walls in the s+is state. We find that in this state the domain walls can have a dipolelike magnetic signature (in contrast to the uniform magnetic signature of domain walls p+ip superconductors). We propose experiments where quench-induced domain walls can be stabilized by geometric barriers and observed via their magnetic signature or their influence on the magnetization process, thereby providing an experimental tool to confirm the s+is state.

Stable cosmic vortons.

We present solutions in the gauged U(1)×U(1) model of Witten describing vortons-spinning flux loops stabilized against contraction by the centrifugal force. Vortons were heuristically described many years ago; however, the corresponding field theory solutions were not obtained and so the stability issue remained open. We construct explicitly a family of stationary vortons characterized by their charge and angular momentum. Most of them are unstable and break in pieces when perturbed. However, thick vortons with a small radius preserve their form in the 3+1 nonlinear dynamical evolution. This gives the first ever evidence of stable vortons and impacts several branches of physics where they could potentially exist. These range from cosmology, since vortons could perhaps contribute to dark matter, to QCD and condensed matter physics.

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.