Competing ground states of a Peierls-Hubbard nanotube

Motivated by iodo platinum complexes assembled within a quadratic-prism lattice, [Pt(C2H8N2)(C10H8N2)I]4(NO3)8, we investigate the ground-state properties of a Peierls-Hubbard four-legged tube. Making a group-theoretical analysis, we systematically reveal a variety of valence arrangements, including half-metallic charge-density-wave states. Quantum and thermal phase competition is numerically demonstrated with particular emphasis on doping-induced successive insulator-to-metal transitions with conductivity increasing stepwise. Quasi-one-dimensional halogen (X)-bridged transitionmetal (M) complexes [1–4] are unique optoelectronic materials. A platinum-chloride chain compound, [Pt(ea)4Cl]Cl2·2H2O (ea= ethylamine=C2H7N), well-known as Wolffram’s red salt, exhibits a Peierlsdistorted mixed-valent ground state [5], whereas its nickel analog has a Mott-insulating monovalent regular-chain structure [6, 7]. Microscopic electronic-structure calculations demonstrated the robustness [8] and tunability [9] of the Peierls instability. Metal binucleation leads to a wider variety of electronic states [10–12]. Diplatinumhalide chain compounds, R4[Pt2(pop)4X ]·nH2O [X =Br, I; pop=diphosphonate=P2O5H2; R =K, (C2H5)2NH2] [13,14], have a ground state with halogen-sublattice dimerization, which is reminiscent of the MX conventional, while their analog without any counter ion, Pt2(dta)4I (dta=dithioacetate=CH3CS2) [15, 16], possesses a novel ground state with metal-sublattice dimerization, where twisting of the dta ligand possibly plays an essential role [17]. The former exhibits photoand/or pressure-induced phase transitions [18–21], whereas the latter undergoes successive phase transitions with increasing temperature [22, 23]. There are further attempts [24, 25] at bridging polynuclear and/or heterometallic units by halogens. Hundreds of MX compounds have thus been synthesized and studied, but they all have single-chain-assembled structures. In such circumstances, several chemists designed MX ladders [26, 27]. Platinum-halide doublechain compounds, (μ-bpym)[Pt(en)X]2X(ClO4)3·H2O (X =Cl, Br; en= ethylendiamine=C2H8N2; μ-bpym= UM UX tMM tMX α un:l 1 M un:l 1 X ( )