Effect of spin-orbit coupling (SOC) on Dirac electrons in the organic conductor $alpha$-(BETS)$_2$I$_3$ [BETS = bis(ethylenedithio)tetraselenafulvalene] has been examined by calculating electric conductivity and spin magnetic susceptibility. A tight-
binding (TB) model with transfer energies consisting of real and imaginary parts is evaluated using first-principles density-functional theory calculation. The conductivity without SOC depends on both anisotropies of the velocity of the Dirac cone and the tiling of the cone. Such conductivity is suppressed by the SOC, which gives rise to the imaginary part of the transfer energy. It is shown at low temperatures that the conductivity decreases due to the SOC and the Dirac cone with linear dispersion. A nearly constant conductivity at high temperatures is obtained by an electron-phonon (e--p) scattering. Further, the property of the Dirac cone is examined for spin susceptibility, which is mainly determined by the density of states (DOS). The result is compared with the case of the organic conductor $alpha$-(BEDT-TTF)$_2$I$_3$ [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene], which provides the Dirac cone without SOC. The relevance to experiments is discussed.
We examine an effect of acoustic phonon scattering on an electric conductivity of 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 tw
o-dimensional model with Dirac cone [Phys. Rev. B {bf 98},161205 (2018)], where the electric transport by the impurity scattering exhibits the noticeable interplay of the Dirac cone and the phonon scattering,resulting in a 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 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 almost 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 experiments.
We employed first-principles density-functional theory (DFT) calculations to characterize Dirac electrons in quasi-two-dimensional molecular conductor $alpha$-(BETS)$_2$I$_3$ [= $alpha$-(BEDT-TSeF)$_2$I$_3$] at a low temperature of 30K. We provide a
tight-binding model with intermolecular transfer energies evaluated from maximally localized Wannier functions, where the number of relevant transfer integrals is relatively large due to the delocalized character of Se $p$ orbitals. The spin-orbit coupling gives rise to an exotic insulating state with an indirect band gap of about 2 meV. We analyzed the energy spectrum with a Dirac cone close to the Fermi level to develop an effective Hamiltonian with site-potentials, which reproduces the spectrum obtained by the DFT band structure.
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).
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 re
spective 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.
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.
Superconductivity of quasi-one-dimensional organic conductors with a quarter-filled band is investigated using the two-loop renormalization group approach to the extended Hubbard model for which both the single electron hopping t_{perp} and the repul
sive interaction V_{perp} perpendicular to the chains are included. For a four-patches Fermi surface with deviations to perfect nesting, we calculate the response functions for the dominant fluctuations and possible superconducting states. By increasing V_{perp}, it is shown that a d-wave (singlet) to f-wave (triplet) superconducting state crossover occurs, and is followed by a vanishing spin gap. Furthermore, we study the influence of a magnetic field through the Zeeman coupling, from which a triplet superconducting state is found to emerge.
The role of interchain hopping in quasi-one-dimensional (Q-1D) electron systems is investigated by extending the Kadanoff-Wilson renormalization group of one-dimensional (1D) systems to Q-1D systems. This scheme is applied to the extended Hubbard mod
el to calculate the temperature ($T$) dependence of the magnetic susceptibility, $chi (T)$. The calculation is performed by taking into account not only the logarithmic Cooper and Peierls channels, but also the non-logarithmic Landau and finite momentum Cooper channels, which give relevant contributions to the uniform response at finite temperatures. It is shown that the interchain hopping, $t_perp$, reduces $chi (T)$ at low temperatures, while it enhances $chi(T)$ at high temperatures. This notable $t_perp$ dependence is ascribed to the fact that $t_perp$ enhances the antiferromagnetic spin fluctuation at low temperatures, while it suppresses the 1D fluctuation at high temperatures. The result is at variance with the random-phase-approximation approach, which predicts an enhancement of $chi (T)$ by $t_perp$ over the whole temperature range. The influence of both the long-range repulsion and the nesting deviations on $chi (T)$ is further investigated. We discuss the present results in connection with the data of $chi (T)$ in the (TMTTF)$_2X$ and (TMTSF)$_2X$ series of Q-1D organic conductors, and propose a theoretical prediction for the effect of pressure on magnetic susceptibility.
The temperature dependence of the magnetic susceptibility, chi (T), is investigated for one-dimensional interacting electron systems at quarter-filling within the Kadanoff-Wilson renormalization-group method. The forward scattering on the same bran
ch (the g_4-process) is examined together with the backward (g_1) and forward (g_2) scattering amplitudes on opposite branches. In connection with lattice models, we show that chi (T) is strongly enhanced by the nearest-neighbor interaction, an enhancement that surpasses one of the next-nearest-neighbor interaction. A connection between our predictions for chi (T) and experimental results for chi (T) in quasi-one-dimensional organic conductors is presented.
