Universality of low-energy Rashba scattering

We investigate the scattering of a quantum particle with a two-dimensional (2D) Rashba spin-orbit coupled dispersion off of circularly symmetric potentials. As the energy of the particle approaches the bottom of the lowest spin-split band, i.e., the van Hove singularity, earlier work has shown that scattering off of an infinite circular barrier exhibits a number of features unusual from the point of view of conventional 2D scattering theory: the low-energy S-matrix is independent of the range of the potential, all partial waves contribute equally, the differential cross section becomes increasingly anisotropic and 1D-like, and the total cross section exhibits quantized plateaus. Via a nonperturbative determination of the T-matrix and an optical theorem which we prove here, we show that this behavior is universal for Rashba scattering off of any circularly symmetric, spin independent, finite-range potential. This is relevant both for impurity scattering in the noninteracting limit as well as for short-range two-particle scattering in the interacting problem.Comment: Editors' Suggestion. 13 pages, 6 figure

Weyl semimetals with short-range interactions

We construct a low-energy effective field theory of electrons interacting via short-range interactions in a Weyl semimetal and investigate possible broken-symmetry ground states through an unbiased one-loop renormalization group (RG) analysis. Using the symmetries of the noninteracting Weyl semimetal to constrain the form of the interaction term leads to four independent coupling constants. We investigate the stability of RG flows towards strong coupling and find a single stable trajectory. In order to determine the most likely broken-symmetry ground state, we calculate susceptibilities in the particle-hole and particle-particle channels along this trajectory and find that the leading instability is towards a fully gapped spin-density wave (SDW) ground state. The sliding mode of this SDW couples to the external electromagnetic fields like the Peccei-Quinn axion field of particle physics. We also study a maximally symmetric toy model of an interacting Weyl semimetal with a single independent coupling constant. The most likely ground states in this case are either gapless ferromagnetic states where the spin waves couple to the Weyl fermions like the spatial components of a (possibly chiral) gauge field, or a fully gapped spin-singlet Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state.Comment: 22 pages, 2 figures. Version published in Phys. Rev.

Exactly solvable Majorana-Anderson impurity models

Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the $\mathbb{Z}_2$ slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. For a spin-polarized Kitaev chain coupled to a quantum dot, we obtain exact expressions for the dot spectral functions at both zero and finite temperature. We study how the interaction strength and localization length of the end Majorana zero mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations, as well as the local electronic density of states in the superconducting chain.Comment: 4.5 pages main text and 3 pages supplemental materia

Landau theory of helical Fermi liquids

Landau's phenomenological theory of Fermi liquids is a fundamental paradigm in many-body physics that has been remarkably successful in explaining the properties of a wide range of interacting fermion systems, such as liquid helium-3, nuclear matter, and electrons in metals. The d-dimensional boundaries of (d+1)-dimensional topological phases of matter such as quantum Hall systems and topological insulators provide new types of many-fermion systems that are topologically distinct from conventional d-dimensional many-fermion systems. We construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator. In the presence of rotation symmetry, interactions between quasiparticles are described by ten independent Landau parameters per angular momentum channel, by contrast with the two (symmetric and antisymmetric) Landau parameters for a conventional spin-degenerate Fermi liquid. We then project quasiparticle states onto the Fermi surface and obtain an effectively spinless, projected Landau theory with a single projected Landau parameter per angular momentum channel that captures the spin-momentum locking or nontrivial Berry phase of the Fermi surface. As a result of this nontrivial Berry phase, projection to the Fermi surface can increase or lower the angular momentum of the quasiparticle interactions. We derive equilibrium properties, criteria for Fermi surface instabilities, and collective mode dispersions in terms of the projected Landau parameters. We briefly discuss experimental means of measuring projected Landau parameters.Comment: 6 pages + 20 pages of supplementary informatio

Rashba scattering in the low-energy limit

We study potential scattering in a two-dimensional electron gas with Rashba spin-orbit coupling in the limit that the energy of the scattering electron approaches the bottom of the lower spin-split band. Focusing on two spin-independent circularly symmetric potentials, an infinite barrier and a delta-function shell, we show that scattering in this limit is qualitatively different from both scattering in the higher spin-split band and scattering of electrons without spin-orbit coupling. The scattering matrix is purely off-diagonal with both off-diagonal elements equal to one, and all angular momentum channels contribute equally; the differential cross section becomes increasingly peaked in the forward and backward scattering directions; the total cross section exhibits quantized plateaus. These features are independent of the details of the scattering potentials, and we conjecture them to be universal. Our results suggest that Rashba scattering in the low-energy limit becomes effectively one-dimensional.Comment: corrected typo in Eq. (27). 10 pages, 6 figure

Topological order in a correlated Chern insulator

We study the effect of electron-electron interactions in a spinful Chern insulator. For weak on-site repulsive interactions at half-filling, the system is a weakly correlated Chern insulator adiabatically connected to the noninteracting ground state, while in the limit of infinitely strong repulsion the system is described by an effective spin model recently predicted to exhibit a chiral spin liquid ground state. In the regime of large but finite repulsion, we find an exotic gapped phase with characteristics partaking of both the noninteracting Chern insulator and the chiral spin liquid. This phase has an integer quantized Hall conductivity $2e^2/h$ and quasiparticles with electric charges that are integer multiples of the electron charge $e$, but the ground state on the torus is four-fold degenerate and quasiparticles have fractional statistics. We discuss how these unusual properties affect the outcome of a charge pumping experiment and, by deriving the topological field theory, elucidate that the topological order is of the exotic $\mathbb{Z}_2$ double-semion type.Comment: Published version. Main text: 5+ pages, 2 figures; supplementary material: 5 pages, 1 figur

Revisiting the Ramond sector of the N ⁣= ⁣1\mathcal{N}\!=\!1 superconformal minimal models

Key to the exact solubility of the unitary minimal models in two-dimensional conformal field theory is the organization of their Hilbert space into Verma modules, whereby all eigenstates of the Hamiltonian are obtained by the repeated action of Virasoro lowering operators onto a finite set of highest-weight states. The usual representation-theoretic approach to removing from all modules zero-norm descendant states generated in such a way is based on the assumption that those states form a nested sequence of Verma submodules built upon singular vectors, i.e., descendant highest-weight states. We show that this fundamental assumption breaks down for the Ramond-sector Verma module with highest weight $c/24$ in the even series of $\mathcal{N}\!=\!1$ superconformal minimal models with central charge $c$. To resolve this impasse, we conjecture, and prove at low orders, the existence of a nested sequence of linear-dependence relations that enables us to compute the character of the irreducible $c/24$ module. Based on this character formula, we argue that imposing modular invariance of the torus partition function requires the introduction of a non-null odd-parity Ramond-sector ground state. This symmetrization of the ground-state manifold allows us to uncover a set of conformally invariant boundary conditions not previously discussed and absent in the odd series of superconformal minimal models, and to derive for the first time a complete set of fusion rules for the even series of those models.Comment: 6 pages main text and 13 pages supplemental materia

Unconventional transport in low-density two-dimensional Rashba systems

Rashba spin-orbit coupling appears in 2D systems lacking inversion symmetry, and causes the spin-splitting of otherwise degenerate energy bands into an upper and lower helicity band. In this paper, we explore how impurity scattering affects transport in the ultra-low-density regime where electrons are confined to the lower helicity band. A previous study has investigated the conductivity in this regime using a treatment in the first Born approximation. In this work, we use the full T-matrix to uncover new features of the conductivity. We first compute the conductivity within a semiclassical Boltzmann framework and show that it exhibits an unconventional density dependence due to the unusual features of the group velocity in the single particle dispersion, as well as quantized plateaus as a function of the logarithm of the electron density. We support this with a calculation using the Kubo formula and find that these plateaus persist in the full quantum theory. We suggest that this quantization may be seen in a pump-probe experiment.Comment: 15 pages, 13 figure

Fractionalized Topological Insulators

Topological insulators have emerged as a major topic of condensed matter physics research with several novel applications proposed. Although there are now a number of established experimental examples of materials in this class, all of them can be described by theories based on electronic band structure, which implies that they do not possess electronic correlations strong enough to fundamentally change this theoretical description. Here, we review recent theoretical progress in the description of a class of strongly correlated topological insulators - fractionalized topological insulators - where band theory fails dramatically due to the fractionalization of the electron into other degrees of freedom.Comment: 5 pages, 3 figures. Published versio

Optical conductivity of topological surface states with emergent supersymmetry

Topological states of electrons present new avenues to explore the rich phenomenology of correlated quantum matter. Topological insulators (TIs) in particular offer an experimental setting to study novel quantum critical points (QCPs) of massless Dirac fermions, which exist on the sample's surface. Here, we obtain exact results for the zero- and finite-temperature optical conductivity at the semimetal-superconductor QCP for these topological surface states. This strongly interacting QCP is described by a scale invariant theory with emergent supersymmetry, which is a unique symmetry mixing bosons and fermions. We show that supersymmetry implies exact relations between the optical conductivity and two otherwise unrelated properties: the shear viscosity and the entanglement entropy. We discuss experimental considerations for the observation of these signatures in TIs.Comment: 5 pages, 1 figure; 12 pages of supplemental material. v2: presentation substantially simplified; published version. v3: included missing supplemental materia