Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-Tc superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of Z2 lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions, and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the Z2 slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors; Luttinger liquids; and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem. arXiv:1708.08507v2 [cond-mat.str-el]

Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting "fractional Josephson currents." Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity-even when noise spoils parity conservation. In light of these developments, the following question becomes paramount: How can one compellingly reveal topological superconductivity in these QSH setups? Most detection protocols to date focus on tunneling [23][24][25] and Josephson [7,[26][27][28][29][30][31][32][33][34][35][36] anomalies. The latter originate from the fractional Josephson effect [1] wherein a phase twist δϕ across a topological superconductor yields a supercurrent with 4π periodicity in δϕ-twice that of conventional junctions. One can view the doubled periodicity as arising from a pair of hybridized Majorana modes at the junction, which form an unusual Andreev bound state that mediates supercurrent via single electron (rather than Cooper pair) tunneling. In the simplest case this anomalous current takes the form I 4π ∝ ð−1Þ p sinðδϕ=2Þ, where the parity p ¼ 0; 1 denotes the Andreev bound state's occupation number. Directly observing this spectacular effect is, however, nontrivial. Parity switching processes-which send p → 1 − p and can arise, e.g., from quasiparticle poisoningrestore 2π periodicity to the current unless measurements occur on a time scale short compared to the typical parityflip time. (Long-time-scale measurements may still reveal subtler signatures of topological superconductivity [27,31,32,36], for instance through noise.) Inspired by recent experiments by Hart et al.[18], we study transport in an extended Josephson junction bridged

Odd-frequency superconductivity, originally proposed by Berezinskii in 1974, is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. The pair potential is an odd function of frequency, leading to a vanishing static superconducting order parameter and exotic types of pairing seemingly inconsistent with Fermi statistics. Motivated by recent experimental progress in the realization of Majorana zero modes in semiconducting nanowires, we show that odd-frequency superconductivity generically appears in a spin-polarized nanowire coupled to Majorana zero modes. We explicitly calculate the superfluid response and show that it is characterized by a paramagnetic Meissner effect.

The present study aimed to examine the effects of tocotrienol-rich fraction (TRF) on exercise endurance and oxidative stress in forced swimming rats. Rats fed on isocaloric diet were orally given 25 (TRF-25) and 50 (TRF-50) mg/kg of TRF, or 25 mg/kg D-alpha-tocopherol (T-25) whilst the control group received only the vehicle for 28 days, followed by being forced to undergo swimming endurance tests, with measurements taken of various biochemical parameters, including blood glucose, lactate and urea nitrogen, glycogen, total antioxidant capacity, antioxidant enzymes, thiobarbituric acid-reactive substances (TBARS), and protein carbonyl. Results showed that the TRF-treated animals (268.0 +/- 24.1 min for TRF-25 and 332.5 +/- 24.3 min for TRF-50) swam significantly longer than the control (135.5 +/- 32.9 min) and T-25-treated (154.1 +/- 36.4 min) animals, whereas there was no difference in the performance between the T-25 and control groups. The TRF-treated rats also showed significantly higher concentrations of liver glycogen, superoxide dismutase (SOD), catalase (CAT), and glutathione peroxidase (GPx), as well as of muscle glycogen and SOD than the control and the T-25-treated animals, but lower levels in blood lactate, plasma and liver TBARS, and liver and muscle protein carbonyl. Taken together, these results suggest that TRF is able to improve the physiological condition and reduce the exercise-induced oxidative stress in forced swimming rats.