Kosterlitz-Thouless-type transition in a charge ordered state of the layered organic conductor α-(BEDT-TTF)2I3

Interacting chiral electrons at the 2D Dirac points: a review

The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)₂I₃, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)₂I₃. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)₂I₃, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)₂I₃. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.

Two-Dimensional Molecular Charge Density Waves in Single-Layer-Thick Islands of a Dirac Fermion System

Charge density waves have been intensely studied in inorganic materials such as transition metal dichalcogenides; however their counterpart in organic materials has yet to be explored in detail. Here we report the finding of robust two-dimensional charge density waves in molecular layers formed by α-(BEDT-TTF)₂-I₃ on a Ag(111) surface. Low-temperature scanning tunneling microscopy images of a multilayer thick α-(BEDT-TTF)₂-I₃ on a Ag(111) substrate reveal the coexistence of 5a₀ × 5a₀ and 31a0×31a0 R9° charge density wave patterns commensurate with the underlying molecular lattice at 80 K. Both charge density wave patterns remain in nanosize molecular islands with just a single constituent molecular-layer thickness at 80 and 5 K. Local tunneling spectroscopy measurements reveal the variation of the gap from 244 to 288 meV between the maximum and minimum charge density wave locations. Density functional theory calculations further confirm a vertical positioning of BEDT-TTF molecules in the molecular layer. While the observed charge density wave patterns are stable for the defect sites, they can be reversibly switched for one molecular lattice site by means of inelastic tunneling electron energy transfer with the electron energies exceeding 400 meV using a scanning tunneling microscope manipulation scheme.

Band Structure and Physical Properties of α-STF2I3: Dirac Electrons in Disordered Conduction Sheets

The compound being investigated is an organic charge-transfer complex of the unsymmetrical donor STF with I3 [STF = bis(ethylenedithio)diselenadithiafulvalene], which is isostructural with α-ET2I3 and α-BETS2I3 [ET = bis(ethylenedithio)tetrathiafulvalene, BETS = bis(ethylenedithio)tetraselenafulvalene]. According to recent studies, the calculated band structure should represent a zero-gap semiconductor at 1 bar that is similar to α-ET2I3 under high pressure (>15 kbar). Such materials have attracted extensive interest because the electrons at the Fermi level can be massless Dirac fermions (MDFs), with relativistic behaviors like those seen in graphene. In fact, α-STF2I3 exhibited nearly temperature-independent resistivity, ρ, (~100–300 K), a phenomenon that is widely observed in zero-gap semiconductors. The non-Arrhenius-type increase in ρ (<~100 K) was consistent with the characteristics of interacting MDFs. The paramagnetic susceptibility, χ, (2–300 K)—as well as the reflectivity, R and optical conductivity, σ, (25–300 K; 400–25,000 cm−1)—were also almost temperature independent. Furthermore, σ was practically independent of wavenumber at ~6000–15,000 cm−1. There was no structural transition based on X-ray studies (90–300 K). Considering all the electrical, magnetic, optical and structural properties of α-STF2I3 at 1 bar, it was concluded that the salt possesses a band structure characterized with Dirac cones, which was consistent with the calculation.

Insulating Nature of Strongly Correlated Massless Dirac Fermions in an Organic Crystal

Through resistivity measurements of an organic crystal hosting massless Dirac fermions with a charge-ordering instability, we reveal the effect of interactions among massless Dirac fermions on the charge transport. A low-temperature resistivity upturn appears robustly irrespective of the pressure and is enhanced while approaching the critical pressure of charge ordering, indicating that the insulating behavior originates from short-range Coulomb interactions. The observation of an apparently vanishing gap in the charge-ordered phase accords with the theoretical prediction of nontopological edge states.

Evidence of a field-induced Berezinskii-Kosterlitz-Thouless scenario in a two-dimensional spin-dimer system

Two-dimensional (2D) systems with continuous symmetry lack conventional long-range order because of thermal fluctuations. Instead, as pointed out by Berezinskii, Kosterlitz and Thouless (BKT), 2D systems may exhibit so-called topological order driven by the binding of vortex-antivortex pairs. Signatures of the BKT mechanism have been observed in thin films, specially designed heterostructures, layered magnets and trapped atomic gases. Here we report on an alternative approach for studying BKT physics by using a chemically constructed multilayer magnet. The novelty of this approach is to use molecular-based pairs of spin S=½ ions, which, by the application of a magnetic field, provide a gas of magnetic excitations. On the basis of measurements of the magnetic susceptibility and specific heat on a so-designed material, combined with density functional theory and quantum Monte Carlo calculations, we conclude that these excitations have a distinct 2D character, consistent with a BKT scenario, implying the emergence of vortices and antivortices.