The semimetal-superconductor quantum phase transition on the two-dimensional (2D) surface of a 3D topological insulator is conjectured to exhibit an emergent N = 2 supersymmetry, based on a one-loop renormalization group (RG) analysis in the expansion. We provide additional support for this conjecture by performing a three-loop RG analysis and showing that the supersymmetric fixed point found at this order survives the extrapolation to 2D. We compute critical exponents to order 3 , obtaining the more accurate value ν ≈ 0.985 for the correlation length exponent and confirming that the fermion and boson anomalous dimensions remain unchanged beyond one loop, as expected from non-renormalization theorems in supersymmetric theories. We further couple the system to a dynamical U (1) gauge field, and argue that the transition becomes fluctuation-induced first order in an appropriate type-I regime. We discuss implications of this result for quantum phase transitions between certain symmetry-preserving correlated surface states of 3D topological insulators.

We classify and construct models for two-dimensional (2D) interacting fermionic symmetryprotected topological (FSPT) phases with general finite Abelian unitary symmetry G f . To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group G f and study braiding statistics in the resulting gauge theory. Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry. The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases. Interestingly, using these two kinds of models, we are able to realize almost all FSPT phases in our classification, except for one class. We argue that this exceptional class of FSPT phases can never be realized through models (i) and (ii), and therefore can be thought of as intrinsically interacting and intrinsically fermionic. The simplest example of this class is associated with Z f 4 × Z4 × Z4 symmetry. We show that all 2D FSPT phases with a finite Abelian symmetry of the form Z f 2 × G can be realized through the above models (i), or (ii), or a simple stack of them. Finally, we study the stability of BSPT phases when they are embedded into fermionic systems.

[1] Previous studies report unexpected electron density reductions, termed "plasma caves," located underneath the equatorial ionization anomaly (EIA) crests. A radio occultation (RO) observation simulation experiment has been built to evaluate possible biases introduced by the spherical symmetry assumption in the standard (Abel) RO inversion processes. The experiment simulates the electron density profiles and reconstructs the plasma structure of the EIA at low latitudes, where the horizontal gradient is most significant. The reconstruction shows that artificial plasma caves are created underneath the EIA crests along with three density enhancements in adjacent latitudes. The artifact appears mainly below 250 km altitudes and becomes pronounced when the EIAs are well developed. Above that altitude, the two EIA features in the original (truth) model, the International Reference Ionosphere (IRI-2007), and in the inversion are similar, but the inversion reconstructs less distinct EIA crests with underestimation of the electron density. A simple correction has been introduced by multiplying the ratio between the truth and inversion with actual FORMOSAT-3/COSMIC observations. This initial correction shows that the artificial plasma caves are mitigated. Results also reveal that the RO technique is not suitable to detect or rule out possible existence of the plasma caves.

We ask which topological phases can and cannot be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely those with abelian braiding statistics. Specifically, we find that an abelian topological phase can be realized by a string-net model if and only if (i) it has a vanishing thermal Hall conductance and (ii) it has at least one Lagrangian subgroup --- a subset of quasiparticles with particular topological properties. Equivalently, we find that an abelian topological phase is realizable if and only if it supports a gapped edge. We conjecture that the latter criterion generalizes to the non-abelian case. We establish these results by systematically constructing all possible abelian string-net models and analyzing the quasiparticle braiding statistics in each model. We show that the low energy effective field theories for these models are multicomponent U(1) Chern-Simons theories, and we derive the K-matrix description of each model. An additional feature of this work is that the models we construct are more general than the original string-net models, due to several new ingredients. First, we introduce two new objects $\gamma, \alpha$ into the construction which are related to $\mathbb{Z}_2$ and $\mathbb{Z}_3$ Frobenius-Schur indicators. Second, we do not assume parity invariance. As a result, we can realize topological phases that were not accessible to the original construction, including phases that break time-reversal and parity symmetry.Comment: 36 pages, 17 figure

[1] The wave 3 and wave 4 modulations of the Equatorial Ionization Anomalies are a robust feature of the low-latitude ionosphere, when viewed at constant local time. Although initially associated, respectively, with DE2 and DE3, nonmigrating diurnal tides in the mesosphere and lower thermosphere region, recent results have suggested that the wave 3 and wave 4 may also have significant contributions from other tidal and stationary planetary wave (SPW) signatures. We present observations of total electron content (TEC) variations associated with tidal and SPW signatures comprising the ionospheric wave 3 and wave 4 structures from FORMOSAT-3/COSMIC from 2007 to 2011. We find that the wave 3 (wave 4) feature is comprised predominately by DE2 (DE3) and SPW3 (SPW4) signatures in TEC throughout all 5 years, with contributions from SE1 (SE2) being less significant. The wave 3 component also has recurring contributions from DW4 during December/January. The absolute amplitudes of all the aforementioned tidal and SPW signatures are directly related to the level of solar activity and the semiannual variation in zonal mean TEC. After normalizing by the zonal mean, the relative amplitudes of the wave 4 signatures are inversely related to solar activity through 2010, which is not seen with the wave 3-related signatures. The seasonal variation and phases of the main constituents of wave 3 and wave 4 are consistent from year to year, as evidenced by the interannual recurrence in the peak and trough locations of wave 3 and wave 4.