Reply to 'Comment on "Dynamic correlations of the spinless Coulomb Luttinger liquid [Phys. Rev. B 65, 125109 (2002)]"'

We show that the criticism of our paper [Phys. Rev. B 65, 125109 (2002)] by Wang, Millis, and Das Sarma [cond-mat/0206203] is based on a trivial mathematical mistake they have committed.Comment: 2 pages, no figure

Pair spin-orbit interaction in low-dimensional electron systems

The pair spin-orbit interaction (PSOI) is the spin-orbit component of the electron-electron interaction that originates from the Coulomb fields of the electrons. This relativistic component, which has been commonly assumed small in the low-energy approximation, appears large and very significant in materials with the strong SOI. The PSOI, being determined by the spins and momenta of electrons, has highly unusual properties among which of most interest is the mutual attraction of the electrons in certain spin configurations. We review the nature of the PSOI in solids and its manifestations in low-dimensional systems that have been studied to date. The specific results depend on the configuration of the Coulomb fields in a particular structure. The main actual structures are considered: one-dimensional quantum wires and two-dimensional layers, both suspended and placed in various dielectric media, as well as in the presence of a metallic gate. We discuss the possible types of the two-electron bound states, the conditions of their formation, their spectra together with the spin and orbital structure. In a many-particle system, the PSOI breaks the spin-charge separation as a result of which spin and charge degrees of freedom are mixed in the collective excitations. At sufficiently strong PSOI, one of the collective modes softens. This signals of the instability, which eventually leads to the reconstruction of the homogeneous state of the system.Comment: Invited review article for the volume on "New Directions in the Physics of One-dimensional Electron Systems". 20 pages, 11 figure

Electron Interactions in Rashba Materials

We show that Rashba spin-orbit interaction (RSOI) modifies electron-electron interaction vertex giving rise to a spectrum of novel phenomena. First, the spin-orbit-modified Coulomb interactions induce $p$-wave superconducting order, without any need for other mediators of attraction. Remarkably, two distinct superconducting phases arise in 3D systems, mirroring the $\mathrm{A}$ or $\mathrm{B}$ phases of $^3\mathrm{He}$, depending on the sign of the SOI constant. In contrast, 2D systems exhibit $p^x\pm i p^y$ order parameter, leading to time-reversal-invariant topological superconductivity. Second, a sufficiently strong RSOI induces ferromagnetic ordering. It is associated with a deformation of the Fermi surface, which may lead to a Lifshitz transition from a spherical to a toroidal Fermi surface, with a number of experimentally observable signatures. Finally, in sufficiently clean Rashba materials, ferromagnetism and $p$-wave superconductivity may coexist. This state resembles the $\mathrm{A}_1$ phase of $^3\mathrm{He}$, yet it may avoid nodal points due to the toroidal shape of the Fermi surface.Comment: 17 pages, 10 figures; significant changes in the superconducting part in v.