Magnetic fluctuations near to quantum criticality can have profound effects. They lead to characteristic scaling at high temperature which may ultimately give way to a reconstruction of the phase diagram and the formation of new phases at low temperatures. The ferromagnet UGe 2 is unstable to p-wave superconducting order-an effect presaged by the superfluidity in 3 He-whereas in CeFePO fluctuations drive the formation of spiral magnetic order. Here we develop a general quantum order-by-disorder description of these systems that encompasses both of these instabilities within a unified framework. This allows us to demonstrate that in fact these instabilities intertwine to form a pair density wave.

A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.

Two-particle backscattering in time-reversal invariant interacting helical electron systems can lead to the formation of quasiparticles with charge e/2. We propose a way to detect such states by means of the Josephson effect in the presence of proximity-induced superconductivity. In this case, the existence of e/2 charges leads to an 8π-periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit time-reversal symmetry breaking, which causes the two-particle backscattering to be a sub-leading effect at low energies, its presence can still be detected in driven, current-biased Shapiro step measurements. The disappearance of some of these steps as a function of the drive frequency is directly related to the existence of non-Abelian zero-energy states. We suggest that this effect can be measured in current state-of-the-art Rashba wires.

Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting one-dimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron density differs significantly from the weakly interacting case. In particular, we find that the critical magnetic field for opening the gap becomes an oscillatory function of electron density. This changes strongly the expected signature of the helical gap in conductance measurements.Comment: 4 pages main text, 6 pages appendix, 6 figure

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk instability towards d-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spinrotation and spatial rotation symmetries. This order is characterized by spin antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first-order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is pre-empted by the formation of a helical spin-triplet d-density wave. Such a state is closely related to d-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, p-wave superconducting state.