Transport in helical Luttinger liquids in the fractional quantum Hall regime.

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations1-3. Here we investigate transport properties of hDWs in the ν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

Multivariate analysis of functional metagenomes.

Metagenomics is a primary tool for the description of microbial and viral communities. The sheer magnitude of the data generated in each metagenome makes identifying key differences in the function and taxonomy between communities difficult to elucidate. Here we discuss the application of seven different data mining and statistical analyses by comparing and contrasting the metabolic functions of 212 microbial metagenomes within and between 10 environments. Not all approaches are appropriate for all questions, and researchers should decide which approach addresses their questions. This work demonstrated the use of each approach: for example, random forests provided a robust and enlightening description of both the clustering of metagenomes and the metabolic processes that were important in separating microbial communities from different environments. All analyses identified that the presence of phage genes within the microbial community was a predictor of whether the microbial community was host-associated or free-living. Several analyses identified the subtle differences that occur with environments, such as those seen in different regions of the marine environment.

Mach-Zehnder interferometer in the fractional quantum Hall regime.

We consider tunneling between two edges of quantum Hall liquids of filling factors nu(0,1)=1/(2m(0,1)+1), with m(0)>or=m(1)>or=0, through two-point contacts forming a Mach-Zehnder interferometer. A quasiparticle description of the interferometer is derived explicitly through the instanton duality transformation. For m(0)+m(1)+1 identical withm>1, tunneling of quasiparticles of charge e/m leads to nontrivial m-state dynamics of effective flux through the interferometer, which restores the regular "electron" periodicity of the current in flux. The exact solution available for equal propagation times between the contacts shows that the interference pattern depends on voltage and temperature only through a common amplitude.