Single-component Molecular Conductor Research Articles

Impact of Temperature on Seebeck Coefficient of Nodal Line Semimetal in Molecular Conductor

We examine the impact of temperature (T) on the Seebeck coefficient S, i.e., the T dependence of S for a single-component molecular conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) with a half-filled band, where the coefficient is obtained from a ratio of the thermal conductivity to the electrical conductivity. The present paper demonstrates theoretically the novel result of large anisotropy in the Seebeck coefficient components of three-dimensional Dirac electrons in a molecular conductor. The conductor exhibits a nodal line with the energy variation around the chemical potential and provides the density of states (DOS) with a minimum. Using a threedimensional tight-binding (TB) model in the presence of both impurity and electron–phonon (e–p) scatterings, we study the Seebeck coefficient Sy for the molecular stacking and the most conducting direction. The impact of T on Sy exhibits a sign change, where Sy > 0 with a maximum at high temperatures and Sy < 0 with a minimum at low temperatures. The T dependence of Sy suggests that the contribution from the conduction (valence) band is dominant at low (high) temperatures. Further, it is shown that the the Seebeck coefficient components for perpendicular directions Sx and Sz are much smaller than Sy and present no sign change, in contrast to Sy. These results are analyzed in terms of the spectral conductivity as a function of the energy ϵ close to the chemical potential μ.

A simple pure organic single-component molecular conductor, [HEDT-TTF-dc], based on protonic-defected dicarboxylic acid

Based on protonic-defected dicarboxylic acid, a simple pure organic single-component molecular conductor, [HEDT-TTF-dc] has been successfully synthesized. The neutral HEDT-TTF-dc molecules form two-dimensional conducting layers, which are connected by hydrogen bond interaction. The electrical resistivity measurement exhibits a semiconducting behavior with a low activation energy of 0.1 eV. The magnetic susceptibility can be fit by the singlet-triplet model, which provides with the small energy gap corresponding to the activation energy.

Fragment-orbital-dependent spin fluctuations in the single-component molecular conductor [Ni(dmdt)2]

Motivated by recent nuclear magnetic resonance experiments, we calculated the spin susceptibility, Knight shift, and spin-lattice relaxation rate ($1/T_{1}T$) of the single-component molecular conductor [Ni(dmdt)$_2$] using the random phase approximation in a multi-orbital Hubbard model describing the Dirac nodal line electronic system in this compound. This Hubbard model is composed of three fragment orbitals and on-site repulsive interactions obtained using ab initio many-body perturbation theory calculations. We found fragment-orbital-dependent spin fluctuations with the momentum $\textbf{q}$=$\textbf{0}$ and an incommensurate value of the wavenumber $\textbf{q}$=$\textbf{Q}$ at which a diagonal element of the spin susceptibility is maximum. The $\textbf{q}$=$\textbf{0}$ and $\textbf{Q}$ responses become dominant at low and high temperatures, respectively, with the Fermi-pocket energy scale as the boundary. We show that $1/T_{1}T$ decreases with decreasing temperature but starts to increase at low temperature owing to the $\textbf{q}$=$\textbf{0}$ spin fluctuations, while the Knight shift keeps monotonically decreasing. These properties are due to the intra-molecular antiferromagnetic fluctuations caused by the characteristic wave functions of this Dirac nodal line system, which is described by an $n$-band ($n\geq 3$) model. We show that the fragment orbitals play important roles in the magnetic properties of [Ni(dmdt)$_2$].

Introducing Selenium in Single-Component Molecular Conductors Based on Nickel Bis(dithiolene) Complexes.

Two selenated analogues of the all-sulfur single-component molecular conductor [Ni(Et-thiazdt)2] (Et-thiazdt = N-ethylthiazoline-2-thione-4,5-dithiolate) have been prepared from their precursor radical-anion complexes. Replacement of the thione by a selenone moiety gives the neutral [Ni(Et-thiazSedt)2] complex. It adopts an unprecedented solid-state organization (for neutral nickel complexes), with the formation of perfectly eclipsed dimers and very short intermolecular Se···Se contacts (81% of the van der Waals contact distance). Limited interactions between dimers leads to a large semiconducting gap and low conductivity (σRT = 1.7 × 10-5 S cm-1). On the other hand, going from the neutral [Ni(Et-thiazdt)2] dithiolene complex to the corresponding [Ni(Et-thiazds)2] diselenolene complex gives rise to a more conventional layered structure built out of uniform stacks of the diselenolene complexes, different, however, from the all-sulfur analogue [Ni(Et-thiazdt)2]. Band structure calculations show an essentially 1D electronic structure with large band dispersion and a small HOMO-LUMO gap. Under high pressures (up to 19 GPa), the conductivity increases by 4 orders of magnitude and the activation energy is decreased from 120 meV to only 13 meV, with an abrupt change observed around 10 GPa, suggesting a structural phase transition under pressure.

Electronic Structure of a Single-Component Molecular Conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) under High Pressure

We examined high-pressure electronic structure of a single-component molecular conductor [Pd(dddt)$_2$] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) at room temperature, based on the crystal structure determined by single crystal synchrotron X-ray diffraction measurements at 5.9 GPa. The monoclinic unit cell contains four molecules that form two crystallographically independent molecular layers. A tight-binding model of 8 $\times$ 8 matrix Hamiltonian gives an electronic structure as a Dirac electron system. The Dirac point describes a loop within the first Brillouin zone, and a nodal line semimetal is obtained. The noticeable property of the Dirac cone with a linear dispersion is shown by calculating density of states (DOS). The Dirac cone in this system is associated with the crossing of HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) bands, which originates from the direct interaction between different molecular layers. This is a newly found mechanism in addition to the indirect one [J. Phys. Soc. Jpn., {\bf 86}, 064705 (2017)]. The Dirac points emerge as a line, when the HOMO and LUMO bands meet on the surface and the HOMO-LUMO couplings are absent. Such a mechanism is verified using a reduced model of 4 $\times$ 4 matrix Hamiltonian. The deviation of the band energy ($\delta E$) at the Dirac point from the Fermi level is very small ($\delta E < $ 0.4meV). The nodal line is examined by calculating the parity of the occupied band eigen states at TRIM (Time Reversal Invariant Momentum) showing that the topological number is 1.

Electric Transport of Nodal Line Semimetals in Single-Component Molecular Conductors

We examine an effect of acoustic phonon scattering on the electric conductivity of a single-component molecular conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) with a half-filled band by applying the previous calculation in a two-dimensional model with Dirac cone [Phys. Rev. B. 98, 161205 (2018)], wherethe electric transport by the impurity scattering exhibits a noticeable interplay of the Dirac cone and the phonon scattering, resulting in maximum of the conductivity with increasing temperature. The conductor shows a nodal line semimetal, where the band crossing of HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) provides a loop of Dirac points located close to the Fermi energy followed by the density of states (DOS) similar to that of a two-dimensional Dirac cone. Using a tight-binding (TB) model [arXiv:2008.09277], which was obtained using the crystal structure observed from a recent X ray diffraction experiment under pressure, it is shown that the obtained conductivity explains reasonably the anomalous behavior in [Pd(dddt)2] exhibiting temperature-independent resistivity at finite temperatures. This paper demonstrates a crucial role of the acoustic phonon scattering at finite temperatures in the electric conductivity of Dirac electrons. The present theoretical results of conductivity are compared with those of the experiments.

Tight-Binding Model and Electronic Property of Dirac Nodal Line in Single-Component Molecular Conductor [Pt(dmdt)2

Motivated by the recent discovery of Dirac nodal line in the single-component molecular conductor [Pt(dmdt)$_{2}$], we propose a three-orbital tight-binding model based on the Wannier fitting of the first-principles calculation, and address the problems of edge states, topological properties and magnetic susceptibility. We find that logarithmic peaks of the local density of states emerge near the Fermi energy, owing to pseudo-one-dimensional edge states that appear between the Dirac nodal lines. Magnetic susceptibility calculated in our model can explain the experimental result at a high temperature. In the presence of a realistic spin-orbit coupling, we show that [Pt(dmdt)$_{2}$] is a topological nodal line semimetal with isolated electron and hole pockets.

A Tight-binding Model of an Ambient-pressure Molecular Dirac Electron System with Open Nodal Lines

By deriving a tight-binding model, we demonstrate a mechanism of forming a nodal line of Dirac points in a single-component molecular conductor [Pt(dmtd)$_2$] [Zhou {\it et al.}, Chem. Commun. {\bfseries 55}, 3327 (2019)], consisting of HOMO and LUMO. The nodal line is obtained as the intersection of two surfaces, where one corresponds to the HOMO-LUMO band crossing and another is vanishing of the HOMO-LUMO couplings due to their different symmetries. The latter property is essential for the Dirac electron in molecular conductors. The nature of the open nodal line is discussed in terms of the parity of the wavefunctions at eight TRIMs (time reversal invariant momenta).

Role of Velocity Field and Principal Axis of Tilted Dirac Cones in Effective Hamiltonian of Non-Coplanar Nodal Loop

Nodal line in single-component molecular conductor [Pd(dddt)_2] has been examined to understand the tilted Dirac cone on the non-coplanar loop. In the previous work [J. Phys. Soc. Jpn. 87, 113701 (2018)], the velocity of the cone was calculated at respective Dirac points on the nodal loop based on our first-principles band structure calculations, which was a new method to derive an effective Hamiltonian with a 2 x 2 matrix. However, the Dirac cones on the nodal line are fully reproduced only at symmetric points. In the present paper, we show that our improved method well reproduces reasonable behaviors of all the Dirac cones and a very small energy dispersion of 6~meV among the Dirac points. The variation of velocities along the nodal line are shown by using principal axes of the gap function between the conduction and valence bands. Further, the density of states close to the chemical potential and orbital magnetic susceptibility are calculated using such an effective Hamiltonian.

Elucidating the Electronic Structure and Magnetic and Conducting Properties of μ-Oxo Mn-phthalocyanine [MnPc(CN)]2O Complex

The μ-oxo phthalocyanine dimer complex [Mn(Pc)(CN)]2O has been characterized as the first single-component molecular conductor exhibiting magnetoresistance at room temperature. Herewith, we report a detailed study of the electronic structure and the magnetic and conducting properties of this μ-oxo MnPc dimer complex. A combined strategy of wave-function-based quantum chemistry calculations on the complex and plane-wave-based periodic calculations on the crystal has been employed together with semiclassical Boltzmann transport theory calculations. Our results provide information about the ligand field parameters of the Mn ions, clarify their spin states on the [Mn(Pc)(CN)]2O complex, and explain the temperature dependence of both the magnetic susceptibility and the effective magnetic moment, taking into account the presence of excited low-lying states with S = 2 and weak intermolecular magnetic interactions, as key ingredients of the magnetic behavior. The analysis of the density of states of the low-spin and high-spin density functional theory + U magnetic solutions and their respective temperature dependence of the electric resistivity give some clues about the conducting properties and the negative magnetoresistance reported for this system.

Single-component molecular conductor [Pt(dmdt)2]-a three-dimensional ambient-pressure molecular Dirac electron system.

The single-component molecular conductor [Pt(dmdt)2] is a sought-after ambient-pressure molecular Dirac electron system, which exhibits a high temperature-insensitive conductivity and temperature-dependent magnetic susceptibility nearly vanishing below 120 K. First-principles DFT calculations reveal that Dirac cones emerge along the a* direction, and form Dirac nodal lines.

Effective Hamiltonian of Topological Nodal Line Semimetal in Single-Component Molecular Conductor [Pd(dddt)2] from First-Principles

Using first-principles density-functional theory calculations, we obtain the non-coplanar nodal loop for a single-component molecular conductor [Pd(dddt)$_2$] consisting of HOMO and LUMO with different parity. Focusing on two typical Dirac points, we present a model of an effective 2 $\times$ 2 matrix Hamiltonian in terms of two kinds of velocities associated with the nodal line. The base of the model is taken as HOMO and LUMO on each Dirac point, where two band energies degenerate and the off diagonal matrix element vanishes. The present model, which reasonably describes the Dirac cone in accordance with the first-principles calculation, provides a new method of analyzing electronic states of a topological nodal line semimetal.

Berry Phase of Dirac Nodal Line Semimetal in Single-Component Molecular Conductor

The Berry phase and curvature are studied for the Dirac nodal line semimetal of single-component molecular conductor [Pd(dddt)$_2$]. Using two-band model on the basis of a tight-binding model, it is shown that the Berry curvature, $\bm{B}(\bm{k})$, exists along a loop of the nodal line, on which the Berry phase is obtained from surface integral of $\bm{B}(\bm{k})$. The Berry phase, which is called Zak phase, is also calculated from one-dimensional integral of the Berry connection along a line between two equivalent points of boundaries of Brillouin zone. The possible experiment is discussed in terms of the Berry phase.

Conductivity and Resistivity of Dirac Electrons in Single-Component Molecular Conductor [Pd(dddt)2

Dirac electrons, which have been found in the single-component molecular conductor [Pd(dddt)_2] under pressure, are examined by calculating the conductivity and resistivity in terms of a tight-binding model for several pressures of P GPa, which give a nodal line semimetal or insulator. The temperature (T) dependence of the conductivity shows that the conductivity increases linearly under pressure at low T due to the Dirac cone but stays almost constant at high T. Further, at lower pressures, the conductivity is suppressed due to an unconventional gap, which is examined by calculating the resistivity. The resistivity exhibits a pseudogap-like behavior even in the case described by the Dirac cone. Such behavior originates from a novel role of the nodal line semimetal followed by a pseudogap that is different from a band gap. The present result reasonably explains the resistivity observed in the experiment.

Anisotropic Conductivity of Nodal Line Semimetal in Single-Component Molecular Conductor [Pd(dddt)2

Using a tight-binding model, we theoretically examine the anisotropic conductivity of the nodal line semimetal of a three-dimensional Dirac electron in a single-component molecular conductor [Pd(dddt)$_2$], which consists of four molecules with HOMO and LUMO orbitals per unit cell. The conductivity shows an anisotropy given by $\sigma_y > \sigma_x > \sigma_z$ in accordance with that of the velocity of the Dirac cone where $z$ is the interlayer direction and $y$ is the molecular stacking direction. With increasing pressure, the nodal line semimetal emerges, followed by a loop of the Dirac point where $\sigma_x$ takes its maximum at a pressure. Such a pressure dependence is studied by calculating the density of states and chemical potential. The temperature dependence of anisotropic conductivity is examined at low temperatures to obtain a constant behavior, which is ascribed to the Dirac electron. The relevance of the present calculation to the experiment is discussed.

Novel Dirac Electron in Single-Component Molecular Conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate)

Dirac electrons in a single-component molecular conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate) under pressure have been examined using a tight-binding model which consists of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) functions in four molecules per unit cell. The Dirac cone between the conduction and valence bands originates from the property that the HOMO has ungerade symmetry and the LUMO has gerade symmetry. The Dirac point forms a loop in the three-dimensional Brillouin zone, which is symmetric with respect to the plane of ky = 0, where ky is the intralayer momentum along the molecular stacking direction, i.e., with the largest (HOMO–HOMO, LUMO–LUMO) transfer energy. The parity at time reversal invariant momentum (TRIM) is calculated using the inversion symmetry around the lattice point of the crystal. It is shown that such an exotic Dirac electron can be understood from the parity of the wave function at the TRIM and also from an e...

Magnetic susceptibility of Dirac electrons in single-component molecular conductor [Pd(dddt)2] under pressure

Using a tight-binding model with four lattice sites per unit cell, we examine a three-dimensional Dirac electron in a single-component molecular conductor [Pd(dddt)2], which consists of HOMO and LUMO orbitals. The Dirac cone, which originates from the interplay of the intralayer and interlayer transfer energies, gives a semimetallic state owing to a slight variation in energy along the line of the Dirac point. Electronic states of the Dirac electron are examined by calculating the temperature (T) dependence of magnetic (spin) susceptibility. It is shown that magnetic susceptibility remains finite at zero temperature and the variation with increasing temperature exhibits a T-linear dependence. The role of the HOMO and LUMO orbitals is discussed in terms of local susceptibility.

Emergence of the Dirac Electron System in a Single-Component Molecular Conductor under High Pressure

Single-component molecular conductors can provide a variety of electronic states. We demonstrate here that the Dirac electron system emerges in a single-component molecular conductor under high pressure. First-principles density functional theory calculations revealed that Dirac cones are formed in the single-component molecular conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate), which shows temperature-independent resistivity (zero-gap behavior) at 12.6 GPa. The Dirac cone formation in [Pd(dddt)2] can be understood by a tight-binding model. The Dirac points originate from the HOMO and LUMO bands, each of which is associated with different molecular layers. Overlap of these two bands provides a closed intersection at the Fermi level (Fermi line) if there is no HOMO-LUMO coupling. Two-step HOMO-LUMO couplings remove the degeneracy on the Fermi line, resulting in gap formation. The Dirac cones emerge at the points where the Fermi line intersects with a line on which the HOMO-LUMO coupling is zero.

Phthalocyanine-Based Single-Component Molecular Conductor [Mn(III)(Pc)(CN)]2O.

A new manganese complex, [Mn(Pc)(CN)]2O, was prepared by an electrocrystallization method. This material is a single-component molecular conductor that displays semiconducting behavior with room temperature conductivity of 4.5 × 10(-3) S cm(-1). Furthermore, we observed negative magnetoresistance at room temperature due to interaction between conduction π electrons and localized d spins. X-ray structural analysis and IR absorption spectroscopy indicated structural disorder. The magnetic susceptibility measurements suggested the unequal spin states of two manganese atoms owing to this structural disorder.

Single-Component Conductors: A Sturdy Electronic Structure Generated by Bulky Substituents.

While the introduction of large, bulky substituents such as tert-butyl, -SiMe3, or -Si(isopropyl)3 has been used recently to control the solid state structures and charge mobility of organic semiconductors, this crystal engineering strategy is usually avoided in molecular metals where a maximized overlap is sought. In order to investigate such steric effects in single component conductors, the ethyl group of the known [Au(Et-thiazdt)2] radical complex has been replaced by an isopropyl one to give a novel single component molecular conductor denoted [Au(iPr-thiazdt)2] (iPr-thiazdt: N-isopropyl-1,3-thiazoline-2-thione-4,5-dithiolate). It exhibits a very original stacked structure of crisscross molecules interacting laterally to give a truly three-dimensional network. This system is weakly conducting at ambient pressure (5 S·cm(-1)), and both transport and optical measurements evidence a slowly decreasing energy gap under applied pressure with a regime change around 1.5 GPa. In contrast with other conducting systems amenable to a metallic state under physical or chemical pressure, the Mott insulating state is stable here up to 4 GPa, a consequence of its peculiar electronic structure.