Sequence E variables are close binary red giants that show ellipsoidal light variations. They are likely the immediate precursors of planetary nebulae (PNe) with close binary central stars as well as other binary post‐asymptotic giant branch (post‐AGB) and binary post‐red giant branch (post‐RGB) stars. We have made a Monte Carlo simulation to determine the fraction of red giant binaries that go through a common envelope event leading to the production of a close binary system or a merged star. The novel aspect of this simulation is that we use the observed frequency of sequence E binaries in the Large Magellanic Cloud (LMC) to normalize our calculations. This normalization allows us to produce predictions that are relatively independent of model assumptions. In our standard model, and assuming that the relative numbers of PNe of various types are proportional to their birth rates, we find that in the LMC today the fraction of PNe with close binary central stars is 7–9 per cent, the fraction of PNe with intermediate period binary central stars having separations capable of influencing the nebula shape (orbital periods less than 500 yr) is 23–27 per cent, the fraction of PNe containing wide binaries that are unable to influence the nebula shape (orbital period greater than 500 yr) is 46–55 per cent, the fraction of PNe derived from single stars is 3–19 per cent, and 5–6 per cent of PNe are produced by previously merged stars. We also predict that the birth rate of post‐RGB stars is ∼4 per cent of the total PN birth rate, equivalent to ∼50 per cent of the production rate of PNe with close binary central stars. These post‐RGB stars most likely appear initially as luminous low‐mass helium white dwarf binaries. The average lifetime of sequence E ellipsoidal variability with amplitude more than 0.02 mag is predicted to be ∼0.95 Myr. We use our model and the observed number of red giant stars in the top one magnitude of the RGB in the LMC to predict the number of PNe in the LMC. We predict 548 PNe in good agreement with the 541 ± 89 PNe observed by Reid & Parker. Since most of these PNe come from single or non‐interacting binary stars in our model, this means that most such stars produce PNe contrary to the ‘binary hypothesis’ which suggests that binary interaction is required to produce a PN.

Context. We present a newly discovered class of low-luminosity, dusty, evolved objects in the Magellanic Clouds. These objects have dust excesses, stellar parameters, and spectral energy distributions similar to those of dusty post-asymptotic giant branch (post-AGB) stars. However, they have lower luminosities and hence lower masses. We suggest that they have evolved off the red giant branch (RGB) instead of the AGB as a result of binary interaction. Aims. In this study we aim to place these objects in an evolutionary context and establish an evolutionary connection between RGB binaries (such as the sequence E variables) and our new sample of objects. Methods. We compared the theoretically predicted birthrates of the progeny of RGB binaries to the observational birthrates of the new sample of objects. Results. We find that there is order-of-magnitude agreement between the observed and predicted birthrates of post-RGB stars. The sources of uncertainty in the birthrates are discussed; the most important sources are probably the observational incompleteness factor and the post-RGB evolution rates. We also note that mergers are relatively common low on the RGB and that stars low on the RGB with mid-IR excesses may recently have undergone a merger. Conclusions. Our sample of dusty post-RGB stars most likely provides the first observational evidence for a newly discovered phase in binary evolution: post-RGB binaries with circumstellar dust.

Recent studies show that the electronic structures of graphene can be modified by strain and it was predicted that strain in graphene can induce peaks in the local density of states (LDOS) mimicking Landau levels (LLs) generated in the presence of a large magnetic field. Here we report scanning tunnelling spectroscopy (STS) observation of nine strain-induced peaks in LDOS at 77 K along a graphene ridge created when the graphene layer was cleaved from a sample of highly oriented pyrolytic graphite (HOPG). The energies of these peaks follow the progression of LLs of massless 'Dirac fermions' (DFs) in a magnetic field of 230 T. The results presented here suggest a possible route to realize zerofield quantum Hall-like effects at 77 K.The physics of 'Dirac fermions' (DFs) in condensedmatter has received a great deal of attention, in part because it has opened up a new area of fundamental science and also for its long-term potential applications [1][2][3][4][5][6][7]. In monolayer graphene, the DFs move as if they were massless at the Fermi velocity v F ~ 10 6 m/s. The quantumrelativistic nature of the massless DFs was obtained through the appearance of the unusual Landau levels (LLs) energy spectrum, which consists of a sequence of levels with square-root dependence on both magnetic field and level index n and a unique level n = 0 at an energy that is pinned to the Dirac point E D [5]. Upon cleaving a highly oriented pyrolytic graphite (HOPG) sample, strains can be induced in the resultant graphene layer forming foldedover structure, wrinkles, and ridges [8,9]. These surface structures provide model systems for the study of the coupling between the graphene and the underlayers [10][11][12][13][14]. Recently, it was shown that strain induced gauge field can be used to alter and tailor the electronic structure of graphene. This opens a possible avenue towards allgraphene electronics [15][16][17][18]. Defects in the form of nanobubbles are also found on chemical vapor deposited graphene layer [17]. Levy and co-authors observed three peaks in scanning tunnelling spectroscopy (STS) spectra at positive voltage bias measured at 7.5 K under zero magnetic field and show evidence that these peaks mimic LLs of massless DFs generated in the presence of large magnetic field [17]. Here, we present STS results at 77 K showing 9 distinct peaks in the tunnelling spectra along a graphene ridge on HOPG produced during the cleaving process. The energy values of these 9 peaks follows the sequence of LLs of massless DFs in a magnetic field. The deviations from the expected values of energies of the peaks are also observed. Such deviations are reasonable since these peaks are not results of Landau level quantizations in a real magentic field but the consequence of the distortion of the local density of states (LDOS) induced by strain.The scanning probe microscope (STM) system used in the experiments is an ultrahigh vacuum four-probe STM from UNISOKU. All the STM and STS measurements were carried out at liquid-nitrogen temperature in a cons...