Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F ≤ −1 in the angular momentum = 2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters F of the composite fermion Fermi liquid with a finite layer width. We consider F in different Landau levels n = 0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η c is higher for the n = 2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n = 2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.

There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodalantinodal dichotomy in the structure of the single-particle spectral functions. In this context, we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting "nodal points" and the nematic "cold-spots" on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angleresolved photoemission) and the local density of states (from scanning tunneling microscopy).

Sharp magnetization switching and large magnetoresistance (MR) were previously discovered in single crystals of 2H-FexTaS2 and attributed to the Fe superstructure and its defects. We report similar sharp switching and large MR in 1T-FexTiS2 (0.086 ≤ x ≤0.703), while providing a side by side comparison of the only two such ferromagnetic transition metal dichalcogenides. The switching field Hs and MR values are similar in both 1T-FexTiS2 and 2H-FexTaS2, with a larger than expected bowtie ρ(H) and a sharper hysteresis loop for H c in the former. The Curie and Weiss temperatures remain roughly constant below x ∼ 1/3 in the T = Ti single crystals, before monotonically increasing for higher x, while Hs and MR reach maxima where defects in the superstructure exist, or a minimum near superstructures compositions, and remain constant above x ∼ 0.4. Despite previous reports, electron diffraction shows only the √ 3× √ 3 superstructure in 1T-FexTiS2. Glassy behavior is shown to coexist within the ferromagnetic state in 1T-FexTiS2 for compositions between 0.1 and 0.703. A simple theoretical model considering first-, second-and third-neighbor interactions yields a phase diagram which accounts for both spin glass behavior and for different superstructures.

Much interest in the superconducting proximity effect in three-dimensional (3D) topological insulators (TIs) has been driven by the potential to induce Majorana bound states at the interface. Most candidate materials for 3D TI, however, are bulk metals, with bulk states at the Fermi level coexisting with well-defined surface states exhibiting spin-momentum locking. In such topological metals, the proximity effect can differ qualitatively from that in TIs. By studying a model topological metal-superconductor (TM-SC) heterostructure within the Bogoliubov-de Gennes formalism, we show that the pair amplitude reaches the naked surface, unlike in a topological insulator-superconductor (TI-SC) heterostructure where it is confined to the interface. Furthermore, we predict vortex-bound-state spectra to contain a Majorana zero-mode localized at the naked surface, separated from the bulk vortex-bound-state spectra by a finite energy gap in such a TM-SC heterostructure. These naked-surface-bound modes are amenable to experimental observation and manipulation, presenting advantages of TM-SC over TI-SC.

We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number ±1 with equal-spin-pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of three different interactions, onsite attraction U, nearest-neighbor density-density attraction V , and nearest-neighbor antiferromagnetic exchange J, within self-consistent Bogoliubov-de Gennes theory. Transition metal dichalcogenides and cold atom experiments are promising platforms to explore these phases. arXiv:1806.08795v3 [cond-mat.supr-con]