Chiral Honeycomb Lattices of Nonplanar π-Conjugated Supramolecules with Protected Dirac and Flat Bands.

The honeycomb lattice is a fundamental two-dimensional (2D) network that gives rise to surprisingly rich electronic properties. While its expansion to 2D supramolecular assembly is conceptually appealing, its realization is not straightforward because of weak intermolecular coupling and the strong influence of a supporting substrate. Here, we show that the application of a triptycene derivative with phenazine moieties, Trip-Phz, solves this problem due to its strong intermolecular π-π pancake bonding and nonplanar geometry. Our scanning tunneling microscopy (STM) measurements demonstrate that Trip-Phz molecules self-assemble on a Ag(111) surface to form chiral and commensurate honeycomb lattices. Electronically, the network can be viewed as a hybrid of honeycomb and kagome lattices. The Dirac and flat bands predicted by a simple tight-binding model are reproduced by total density functional theory (DFT) calculations, highlighting the protection of the molecular bands from the Ag(111) substrate. The present work offers a rational route for creating chiral 2D supramolecules that can simultaneously accommodate pristine Dirac and flat bands.

Diamond lattice in single-component molecular crystals comprising tetrabenzoporphyrin neutral radicals.

A single-component molecular radical crystal of CoIII(tbp˙-)(CN)2, where tbp = tetrabenzoporphyrinato ligand, exhibiting a diamond lattice was fabricated as a potential candidate for a three-dimensional Dirac electron system. Band structure calculations revealed that the Fermi energy level was located at the Dirac point. A small electrical resistivity of 160 Ω cm was observed at 2 K under the application of 2.4 GPa. Furthermore, substituting CoIII by FeIII or MnIII led to the introduction of local magnetic moments into the diamond-lattice system. MIII(tbp˙-)L2 crystals will open up uncharted fields in the study of the Dirac electron systems.

Ideal trigonal prismatic coordination geometry of Co(II) in a honeycomb MOF with a triptycene-based ligand.

A metal-organic framework (MOF) comprised of cobalt ions and triptycene-based 3-fold symmetric bridging ligands 9,10-[1,2]benzenoanthracene-2,3,6,7,14,15(9H,10H)-hexaone (o-TT) was prepared. Single-crystal structure analysis revealed a 2D honeycomb network structure and the ideal trigonal prismatic geometry of the Co(II) ion. The magnetic anisotropy of the Co(II) ion in the trigonal prism coordination geometry was analyzed via magnetic measurements and model calculations.

Quantum Spin Liquid State in a Two-Dimensional Semiconductive Metal-Organic Framework.

Two-dimensional metal-organic frameworks (2D MOFs) have attracted much attention, as they are the crystalline materials that exhibit both conductivity and microporosity. Numerous efforts have been made to advance their application as chemiresistive sensors or electrochemical capacitors. However, the intrinsic physical properties and spin states of these materials remain poorly understood. Most of these 2D MOFs possess a honeycomb lattice, with a Kagomé lattice arrangement of metal cations. These structural characteristics suggest that these MOFs would be candidates for geometrically frustrated spin systems with unprecedented magnetic phenomena. Herein, by performing magnetic susceptibility and specific heat measurements at an ultralow temperature down to 38mK on a 2D semiconductive MOF, Cu3(HHTP)2, a quantum spin liquid state that arises from the geometrical frustration was suggested. This result illustrates the potential of strongly correlated MOFs as systems with emergent phenomena induced by unusual structural topologies.

An exotic band structure of a supramolecular honeycomb lattice formed by a pancake π-π interaction between triradical trianions of triptycene tribenzoquinone.

A supramolecular honeycomb lattice was successfully formed by using triradical trianion species of triptycene tribenzoquinone (TT) which forms strong intermolecular π-π pancake bonds toward three directions. The crystal structure of Rb3TT·2H2O belongs to the hexagonal P6/m space group, the tight-binding band calculation of which reveals Dirac cones and flat bands.

3D Spin-Liquid State in an Organic Hyperkagome Lattice of Mott Dimers.

We report the first 3D spin liquid state of isotropic organic spins. Structural analysis, and magnetic and heat-capacity measurements were carried out for a chiral organic radical salt, (TBA)_{1.5}[(-)-NDI-Δ] (TBA denotes tetrabutylammonium and NDI denotes naphthalene diimide), in which (-)-NDI-Δ forms a K_{4} structure due to its triangular molecular structure and an intermolecular π-π overlap between the NDI moieties. This lattice was identical to the hyperkagome lattice of S=1/2 Mott dimers, and should exhibit 3D spin frustration. In fact, even though the high-temperature magnetic susceptibility followed the Curie-Weiss law with a negative Weiss constant of θ=-15 K, the low-temperature magnetic measurements revealed no long-range magnetic ordering down to 70 mK, and suggested the presence of a spin liquid state with a large residual paramagnetism χ_{0} of 8.5×10^{-6} emu g^{-1} at the absolute zero temperature. This was supported by the ^{14}N NMR measurements down to 0.38 K. Further, the low-temperature heat capacities c_{p} down to 68 mK clearly indicated the presence of c_{p} for the spin liquid state, which can be fitted to the power law of T^{0.62} in the wide temperature range 0.07-4.5 K.

Discovery of the K4 Structure Formed by a Triangular π Radical Anion.

The K4 structure was theoretically predicted for trivalent chemical species, such as sp(2) carbon. However, since attempts to synthesize the K4 carbon have not succeeded, this allotrope has been regarded as a crystal form that might not exist in nature. In the present work, we carried out electrochemical crystallization of the radical anion salts of a triangular molecule, naphthalene diimide (NDI)-Δ, using various electrolytes. X-ray crystal analysis of the obtained crystals revealed the K4 structure, which was formed by the unique intermolecular π overlap directed toward three directions from the triangular-shape NDI-Δ radical anions. Electron paramagnetic resonance and static magnetic measurements confirmed the radical anion state of NDI-Δ and indicated an antiferromagnetic intermolecular interaction with the Weiss constant of θ = -10 K. The band structure calculation suggested characteristic features of the present material, such as a metallic ground state, Dirac cones, and flat bands.

Orbital nematic instability in the two-orbital Hubbard model: renormalization-group + constrained RPA analysis.

Motivated by the nematic electronic fluid phase in Sr(3)Ru(2)O(7), we develop a combined scheme of the renormalization-group method and the random-phase-approximation-type method, and analyze orbital susceptibilities of the (d(xz), d(yz))-orbital Hubbard model with high accuracy. It is confirmed that the present model exhibits a ferro-orbital instability near the magnetic or superconducting quantum criticality, due to the Aslamazov-Larkin-type vertex corrections. This mechanism of orbital nematic order presents a natural explanation for the nematic order in Sr(3)Ru(2)O(7), and is expected to be realized in various multiorbital systems, such as Fe-based superconductors.

Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals.

From configuration interaction (CI) ab initio calculations, we derive an effective two-orbital extended Hubbard model based on the gerade (g) and ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular conductor (TTM-TTP)I(3) and the single-component molecular conductor [Au(tmdt)(2)]. First, by focusing on the isolated molecule, we determine the parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian matrix. Next, we extend the analysis to two neighboring molecule pairs in the crystal and we perform similar calculations to evaluate the inter-molecular interactions. From the resulting tight-binding parameters, we analyze the band structure to confirm that two bands overlap and mix in together, supporting the multi-band feature. Furthermore, using a fragment decomposition, we derive the effective model based on the fragment MOs and show that the staking TTM-TTP molecules can be described by the zig-zag two-leg ladder with the inter-molecular transfer integral being larger than the intra-fragment transfer integral within the molecule. The inter-site interactions between the fragments follow a Coulomb law, supporting the fragment decomposition strategy.

Intramolecular charge ordering in the multi molecular orbital system (TTM-TTP)I3.

Starting from the structure of the (TTM-TTP)I(3) molecular-based material, we examine the characteristics of frontier molecular orbitals using ab initio (CASSCF/CASPT2) configurations interaction calculations. It is shown that the singly occupied and second-highest-occupied molecular orbitals are close to each other, i.e., this compound should be regarded as a two-orbital system. By dividing virtually the [TTM-TTP] molecule into three fragments, an effective model is constructed to rationalize the origin of this picture. In order to investigate the low-temperature, symmetry breaking experimentally observed in the crystal, the electronic distribution in a pair of [TTM-TTP] molecules is analyzed from CASPT2 calculations. Our inspection supports and explains the speculated intramolecular charge ordering which is likely to give rise to low-energy magnetic properties.