The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram

One central challenge in high-$T_c$ superconductivity (SC) is to derive a detailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and $O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-$T_c$ cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences - and thus, the material dependence to show up in the "non-universal" finite-T phase diagram ($T_c$-values).Comment: 17 pages, 9 figure

Size Doesn't Matter: Towards a More Inclusive Philosophy of Biology

notes: As the primary author, O’Malley drafted the paper, and gathered and analysed data (scientific papers and talks). Conceptual analysis was conducted by both authors.publication-status: Publishedtypes: ArticlePhilosophers of biology, along with everyone else, generally perceive life to fall into two broad categories, the microbes and macrobes, and then pay most of their attention to the latter. ‘Macrobe’ is the word we propose for larger life forms, and we use it as part of an argument for microbial equality. We suggest that taking more notice of microbes – the dominant life form on the planet, both now and throughout evolutionary history – will transform some of the philosophy of biology’s standard ideas on ontology, evolution, taxonomy and biodiversity. We set out a number of recent developments in microbiology – including biofilm formation, chemotaxis, quorum sensing and gene transfer – that highlight microbial capacities for cooperation and communication and break down conventional thinking that microbes are solely or primarily single-celled organisms. These insights also bring new perspectives to the levels of selection debate, as well as to discussions of the evolution and nature of multicellularity, and to neo-Darwinian understandings of evolutionary mechanisms. We show how these revisions lead to further complications for microbial classification and the philosophies of systematics and biodiversity. Incorporating microbial insights into the philosophy of biology will challenge many of its assumptions, but also give greater scope and depth to its investigations

Conserving indigenous relatives of crop species

Peer Revie