Interacting Dirac fermions under spatially alternating pseudo-magnetic field: Realization of spontaneous quantum Hall effect

Both topological crystalline insulators surfaces and graphene host multi-valley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal invariant gauge field, leading to the formation of pseudo-Landau levels (PLL). Here we study periodic pseudo-magnetic fields originating from strain superlattices. We study the low-energy Dirac PLL spectrum induced by the strain superlattice and analyze the effect of various polarized states. Through self-consistent Hartree-Fock calculations we establish that, due to the strain superlattice and PLL electronic structure, a valley-ordered state spontaneously breaking time-reversal and realizing a quantum Hall phase is favored, while others are suppressed.Comment: 13 pages + 2 appendices, 9 figure

Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node

Motivated by the recent experiment indicating that superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing symmetry with rotational symmetry breaking, we study the general class of odd-parity superconductors with two-component order parameters in trigonal and hexagonal crystal systems. In the presence of strong spin-orbit interaction, we find two possible superconducting phases below $T_c$, a time-reversal-breaking (i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine their relative energetics from the gap function in momentum space. The nematic superconductor generally has a full quasi-particle gap, whereas the chiral superconductor with a three-dimensional (3D) Fermi surface has point nodes with lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk and topological Majorana arcs on the surface.Comment: 4+ pages, 2 figures; 20 pages suppl mat + 4 figures; published versio

Three-Dimensional Majorana Fermions in Chiral Superconductors

Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-non-degenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum $J$ formed by Bloch electrons with angular momentum $j$ in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the non-unitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions, and find that the nuclear magnetic resonance (NMR) spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface that form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs$_4$Sb$_{12}$ and related materials as promising candidates for non-unitary chiral superconductors hosting three-dimensional Majorana fermions.Comment: 12 pages, 3 figures + appendices; published versio

Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene

Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory shades light on the recent observation of rotational symmetry breaking in the superconducting state of twisted bilayer graphene

Are Education and Entrepreneurial Income Endogenous and Do Family Background Variables Make Sense as Instruments?: A Bayesian Analysis

Education is a well-known driver of (entrepreneurial) income. The measurement of its influence, however, suffers from endogeneity suspicion. For instance, ability and occupational choice are mentioned as driving both the level of (entrepreneurial) income and of education. Using instrumental variables can provide a way out. However, three questions remain: whether endogeneity is really present, whether it matters and whether the selected instruments make sense. Using Bayesian methods, we find that the relationship between education and entrepreneurial income is indeed endogenous and that the impact of endogeneity on the estimated relationship between education and income is sizeable. We do so using family background variables and show that relaxing the strict validity assumption of these instruments does not lead to strongly different results. This is an important finding because family background variables are generally strongly correlated with education and are available in most datasets. Our approach is applicable beyond the field of returns to education for income. It applies wherever endogeneity suspicion arises and the three questions become relevant.Education, income, entrepreneurship, self-employment, endogeneity, instrumental variables, Bayesian analysis, family background variables