Quasi-two dimensional organic conductors and superconductors

Organic metals are unique materials: the crystals are built by organic molecules and conduct electricity at room temperature as good as common metals; on cooling down some of these crystals become even superconducting below 13 K, some stay metallic and some undergo a metal-insulator transition.

Why does this happen?

Our research within various projects is devoted to answer this question.

TwoDimOrgCondSupra01

Fig 1: A schematic crystal structure of a BEDT-TTF based organic conductor. A single BEDT-TTF molecule is shown in red.

In a similar way to quasi-1D electron systems, the quasi-2D organic conductors are interest to various ordering phenomena. The crystals are built by layers of BEDT-TTF (bis(ethylenedithio)-tetrathiafulvalene) molecules sandwiched between the sheets of counter anions. The π-electron orbitals of the BEDT-TTF aromatic rings overlap and form a conductance band. The anion layer donates electrons to the BEDT-TTF molecules, charging them up to approximately +0.5e per molecule. This makes the conductance band partly filled and the material is metallic. The metallic properties are observed only within the layers; in the perpendicular direction the insulating anion layer blocks charge transfer. For that reason these materials are called two-dimensional conductors. The reduced dimensionality makes them attractive objects for theoretical studies and for experimental test of the predictions by theory.

The history of this field is an exciting example how a physical theory can trigger a whole new field of solid state physics and lead to the creation of new materials. In 1964 a paper was published by J. Little [1], predicting a room-temperature superconductivity in structures that can be synthesized using organic molecules (polymers at that time) rich with p-electrons. On the one hand, the paper was basically wrong as it was dealing with one-dimensional structures, which can be metallic at high temperatures, but will always have an insulating ground state, as shown by Peierls [2]. On the other hand, it was correct in predicting something possible as even today the mechanism is considered feasible for room-temperature superconductivity. Nevertheless, material scientists started to work, and in 1979 superconductivity under pressure was observed in quasi one-dimensional crystals now called Berchgaard salt, and in 1984 a first normal-pressure organic conductor β-(BEDT- TTF)2I3 appeared. By changing chemical composition and thus physical parameters of the crystals the temperature of superconducting transition was increased up to 12 K for κ-(BEDT- TTF)2Cu[N(CN)2]Br.

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Literature:

  1. W. A.
    Little Possibility of synthesizing an organic superconductor
    Phys.Rev. 134, A1416-A1424 (1964).
  2. R. Peierls
    Quantum Theory of Solid State (1956).
  3. M. Dressel und N. Drichko
    Optical Properties of Two-Dimensional Organic Conductors: Signatures of Charge Ordering and Correlation Effects
    Chemical Review 104, 5689 (2004).
  4. M. Dressel
    Quantum criticality in organic conductors? Fermi-liquid versus non-Fermi-liquid behavior
    J. Phys.: Condens. Matter 23, 293201 (2011).
Half-filled systems close to Mott insulator

BrCl_phasediagram

Fig 2: Schematic phase diagram of κ-(BEDT-TTF)2X. The on-site Coulomb repulsion with respect to the bandwidth U/W can be tuned either by external pressure or modifying the anions X. The bandwidth-controlled phase transition between the insulator and the Fermi liquid superconductor can be explored by gradually replacing Cl by Br in κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1x.The first-order insulating-to-metallic transition line is sketched based on alloy studies and the generic diagram for κ-(BEDT-TTF)2X.The data points are obtained from our transport and ESR measurements. For the insulating samples, the Mott-insulator points TM were determined from the upturn change in the dc resistivity and microwave conductivity. The antiferromagnetic ground state was declared from the vanishing of the ESR spectra. In the metallic side, the Fermi liquid and superconducting states were identified from the T0 and Tc-points, respectively.


When going across the Mott transition from κ-(BEDT-TTF)2Cu[N(CN)2]Cl to κ-(BEDT-TTF)2Cu[N(CN)2]Br by physical or chemical pressure, the optical properties change dramatically. The Mott insulator gradually opens a gap (vanishing of low-frequency conductivity) upon cooling, while the metallic κ-(BEDT-TTF)2Cu[N(CN)2]Br develops a Drude-like contribution (characteristic increased conductivity at low frequencies) linked to the coherent transport. The mid-infrared band, a wide feature centered around 2000 -- 3000 cm-1, decreases accordingly. It consists of two contributions: excitations across the BEDT-TTF dimer and excitations from the lower to the upper Hubbard band. LDA + DMFT calculations [8] confirm this assignment and the anisotropy observed.

Fig 3: Optical conductivity spectra of κ-(BEDT-TTF)2Cu[N(CN)2]BrxCl1−x for the two polarizations E||a and E||c within the highly conducting plane measured at different temperatures for crystals of different Br concentrations x.

BrCl_conductivity_theory

Fig 4: Calculated LDA+DMFT optical conductivity for U = 0:6 eV together with the LDA result and the experimental curve at T = 300 K. Experiments by Faltermeier et al., [2] calculations by Ferber et al [8].

The system turns out to be the model compound for a bandwidth-tuned Mott transition. Looking at the correlated charge carriers, κ-(BEDT-TTF)2Cu[N(CN)2]Br is a perfect Fermi liquid compound with a nice ρ ∞ T2 and σ ∞ w2 behavior over an appreciable energy range: Γ(w,T) = A(kBT)2+ B(ħw)2. When going closer to the Mott transition, correlations increase, the effective mass increases (Brinckman-Rice relation) and accordingly the slope in the frequency and temperature-dependent scattering rate rises (Kadowaki-Woods relation). The prefactor of the frequency-dependent scattering rate and its change with temperature yields A/B=56, close to the factor (2p)2 predicted by Landau.

 

Fig 5: Temperature and frequency dependence of the scattering rate for k-(BEDT-TTF)2Cu[N(CN)2]BrxCl1−x with different x. (a) - (c). The frequency-dependent part of the scattering rate at low temperaures of k-(BEDT-TTF)2Cu[N(CN)2]BrxCl1−x as function of the squared frequency. We determined for the frequency-independent dc limit of the scattering rate Γ1(0) the following values: 315 cm-1 (x=0.73), 48 cm-1 (x=0.85), and 280 cm-1 (x=0.9). Note the different vertical scales for the frames. (d) - (f) The temperature dependent scattering rate 1/ζ(T) is obtained from the in-plane dc resistivity (ρ(T)-ρ0 ∞ 1/ζ(T)). The plots as a function of T2 in the low-temperature region yield a quadratic behavior up to T0. Below Tc = 12 K the systems become superconducting.

Fig 6: (a) Low-temperature optical conductivity of k-(BEDT-TTF)2Cu[N(CN)2]BrxC1-x for different Br content x, which serves as chemical pressure and decreases the effective Coulomb interaction U/W. The contributions from intradimer transitions and vibrational modes are subtracted; the σ1(w) spectra plotted here represent the correlated charge carriers. Panels (b) and (c) show the frequency dependence of the scattering rate and effective mass extracted from an extended Drude model analysis of the conductivity (a). In (d) and (e) the corresponding results of DMFT calculations are plotted for different U/W and T=50 K. Clearly as the Mott insulating phase is approached, the effective mass and the scattering rate increase significantly.


Literature:

  1. M. Dressel und N. Drichko
    Optical Properties of Two-Dimensional Organic Conductors: Signatures of Charge Ordering and Correlation Effects
    Chemical Review 104, 5689 (2004).
  2. D. Faltermeier, J. Barz, M. Dumm, M. Dressel, N. Drichko, B. Petrov, V. Semkin, R. Vlasova, C. Meziere und P. Batail
    Bandwidth-controlled Mott transition in κ-(BEDT-TTF)2-Cu[N(CN)2]-BrxCl1-x I: Optical studies of localized charge excitations
    Phys. Rev. B 76, 165113 (2007).
  3. J. Merino, M. Dumm, N. Drichko, M. Dressel und R. H. McKenzie
    Quasiparticles at the verge of localization near the Mott metal-insulator transition in a two-dimensional material
    Phys. Rev. Lett. 100, 086404 (2008).
  4. M. Dumm, D. Faltermeier, N. Drichko und M. Dressel
    Bandwidth-controlled Mott transition in κ-(BEDT-TTF)2-Cu[N(CN)2]-BrxCl1-x II: Optical studies of correlated carriers
    Phys. Rev. B 79, 195106 (2009).
  5. M. Dressel, D. Faltermeier, M. Dumm, N. Drichko, B. Petrov, V. Semkin, R. Vlasova, C. Meziere und P. Batail
    Disentangling the conductivity spectra of two-dimensional organic conductors
    Physica B 404, 541 (2009).
  6. S. Yasin, M. Dumm, B. Salameh, P. Batail, C. Mézière und M. Dressel
    Transport studies at the Mott transition of the two-dimensional organic metal k-(BEDT-TTF)2Cu[N(CN)2]BrxCl1-x
    Eur. Phys. J. B 79, 383 - 390 (2011).
  7. M. Dressel
    Quantum criticality in organic conductors? Fermi-liquid versus non-Fermi-liquid behavior
    J. Phys.: Condens. Matter 23, 293201 (2011).
  8. Johannes Ferber, Kateryna Foyevtsova, Harald O. Jeschke, Roser Valenti
    <em > LDA+DMFT for organic molecular crystals: spectral and optical properties of kappa-(BEDT-TTF)2Cu[N(CN)2]Cl arXiv:1209.4466.
Quarter-filled systems close to charge order

Fig 7: Phase diagram proposed [2] for 1/4-filled organic conductors. Arrows show positions we suggest for the recently studied in our projects compounds: α-(BEDT-TTF)2MHg(SCN)4 (M=Tl, K, NH4) and α-(BEDT-TTF)2I3.

These materials are of a great interest both to experimental and theoretical physicists not only for their superconducting properties, but because they are ideal models of two-dimensional conductors. It was proposed recently that the exotic ground states observed for BEDT-TTF-based conductors, superconductivity, charge ordered insulating state, and deviations from the Drude behavior in the metallic state, are all driven by the same effect - strong electron-electron interactions (see e.g. [2]). As a result, a tiny change of the ratio of electronic correlations to bandwidth leads to a change of a ground state of a system. An example is a phase diagram in Fig.7, where a dependence of a ground state on a ratio between electronic repulsion and bandwidth is displayed; by arrows we suggest positions of the materials we recently studied in our project.

The characteristic features of each ground state are nicely observed in the optical conductivity spectra (Fig. 8) received through polarized reflectance measurements . In the spectra of α-(BEDT-TTF)2I3 an insulating gap is present at temperatures below TMI =135 K. A superconducting gap of 25 cm-1 was observed below Tc=8 K for αt-(BEDT-TTF)2I3. In the spectra of this material and of a superconductor (Tc~1 K) α-(BEDT-TTF)2NH4Hg(SCN)4 a robust Drude peak is present in low-frequency spectra of the normal state. Of superior interest are the systems α-(BEDT-TTF)2MHg(SCN)4 (M=K, Tl): d.c. conductivity shows that they are metals down to 4 K, while in optical spectra a pseudogap at about 300 cm-1 appears below 100 K. We interpret it as an evidence of charge order fluctuations close to the phase transition; part of the electronic system becomes ordered, while a narrow Drude peak is responsible for metallic conductivity. Indeed, these experimental results support the calculated phase diagram (Fig. 7).

Fig 8: Optical conductivity of ½ and ¼ filled compounds. k-(BEDT-TTF)2Cu(NCS)2 is a superconductor close to a Mott insulator and magnetic order. (BEDT_TTF)4[Ni(dto)2] is also half filled but exhibits very peculiar optical properties due to correlation effects. The Superconductor α-(BEDT-TTF)2NH4Hg(SCN)4: large U and small V: metallic at any temperature; metals α-(BEDT-TTF)2MHg(SCN)4 (M=K, Tl): large U and moderate V: pseudogap below 200 K due to presence of V, charge-order fluctuations; complete charge order α-(BEDT-TTF)2I3 large U and large V: metal-to-insulator transition at 135 K due to charge ordering.


The dependence on the band filling was also probed by optical measurements. In agreement with theoretically predicted behavior, in the strongly-correlated 1/5-filled system β"-(BEDO-TTF)5[CsHg(SCN)4]2, the pseudogap also exists in the spectra, but the Drude peak has a much higher intensity, since commensurate ordering is not possible for this filling [4]. These resent results gave us an idea of a general phase diagram showing a dependence of a ground state on the size of electronic correlations and on band filling. The aim of our present project is to prove this picture.

Theoretical predictions of a charge-fluctuation driven superconductivity could be verified by experimental studies of a quarter filled compounds close to the charge-ordered insulating state of b²-(BEDT-TTF)2SF5CH2CF2SO3. Vibrational spectroscopy of molecular vibrations can locally probe the fluctuating charge order, in addition a strong fluctuation band appears in infrared reflectance spectroscopy. The decrease of the effective electronic interaction in an isostructural metal suppresses both charge-order fluctuations and superconductivity, pointing to their interplay. The results can be described by calculations on the extended Hubbard model.


Literature:

  1. M. Dressel, N. Drichko, J. Schlueter und J. Merino
    Proximity of the Layered Organic Conductors alpha-(BEDT-TTF)2MHg(SCN)4 (M = K,NH4) to a Charge-Ordering Transition
    Phys. Rev. Lett. 90, 167002 (2003).
  2. M. Dressel und N. Drichko
    Optical Properties of Two-Dimensional Organic Conductors: Signatures of Charge Ordering and Correlation Effects
    Chemical Review 104, 5689 (2004).
  3. N. Drichko, K. Petukhov, M. Dressel, O. Bogdanova, E. Zhilyaeva, R. Lyubovskaya, A. Greco und J. Merino
    Indications of electronic correlations in the 1/5-filled two-dimensional conductor &beta"-(BEDO-TTF)5[CsHg(SCN)4]2
    Phys. Rev. B 72, 024524 (2005).
  4. M. Dressel, N. Drichko und J. Merino
    Evidence of charge ordering in the electronic spectra of two-dimensional organic conductors
    Physica B 359–361, 454 - 456 (2005).
  5. N. Drichko, M. Dressel, C. A. Kuntscher, A. Pashkin, A. Greco, J. Merino und J. Schlueter
    Electronic properties of correlated metals in the vicinity of a charge-order transition: Optical spectroscopy of α-(BEDT-TTF)2MHg(SCN)4 (M=NH4, Rb, Tl)
    Phys. Rev. B 74, 235121 (2006).
  6. J. Merino, A. Greco, N. Drichko und M. Dressel
    Non-Fermi Liquid Behavior in Nearly Charge Ordered Layered Metals
    Phys. Rev. Lett. 96, 216402 (2006).
  7. N. Drichko, S. Kaiser, Y. Sun, C. Clauss, M. Dressel, H. Mori, J. Schlueter, E. Zhilyaeva, S.A. Torunova und R. Lyubovskaya
    Evidence for charge order in organic superconductors obtained by vibrational spectroscopy
    Physica B 404, 490 (2009).
  8. S. Kaiser, M. Dressel, Y. Sun, A. Greco, J. Schlueter, G.L. Gard und N. Drichko
    Bandwidth Tuning Triggers Interplay of Charge Order and Superconductivity in Two-Dimensional Organic Materials
    Phys. Rev. Lett. 105, 206402 (2010).
  9. M. Dressel
    Quantum criticality in organic conductors? Fermi-liquid versus non-Fermi-liquid behavior
    J. Phys.: Condens. Matter 23, 293201 (2011).
Frustrated lattice

The quasi-two-dimensional organic conductors of the BEDT-TTF family crystallize in different phases, labeled by Greek letters. The k-phase compounds draw particular attention since the molecules form dimers within the plane.

Due to the rather strong intradimer coupling a dimer can be considered as a single site with one charge (hole). The system can then be treated as half-filled with Mott physics being relevant. According to the crystallographic arrangement, the overlap between the dimers forms a triangular lattice with coupling t and t’. Since each dimer can also carry one spin, the system is close to frustration when t » t’. While k-(BEDT-TTF)2Cu[N(CN)2]Cl is a Mott insulator with magnetic order below 40 K, k-(BEDT-TTF)2Cu2(CN)3 does not order despite the appreciable coupling of J = 250 K among the spins. Hence it is proposed to be a spin liquid. The optical properties between both compounds are rather different. k-(BEDT-TTF)2Cu[N(CN)2]Cl shows a clear Mott-gap, while for k-(BEDT-TTF)2Cu2(CN)3 a power-law behavior is found all the way to high frequencies and temperatures.

Fig 9: The temperature dependence of the in-plane dc resistivity of κ -(BEDT-TTF)2Cu2(CN)3 (bold blue line) and κ-(BEDT-TTF)2Cu[N(CN)2]Cl (light red line) evidences an insulating behavior. (b) The low-temperature optical conductivity (κ-CN: T=13 K; κ-Cl: T=20 K) does not show a Mott gap, but also reveals important differences between both compounds.

Various methods (NMR, Raman and IR spectroscopy) clearly rule out any charge disproportionation on the dimers. The vibrational lines do not split or shift appreciably. In the case of k-(BEDT-TTF)2Hg(SCN)Cl2 a clear splitting of the vibrational features is observed at the charge order transition TCO = 30 K.

Fig 10: Temperature evolution of the out-of-plane optical conductivity of κ-(BEDT-TTF)2Cu[N(CN)2]Br, κ-(BEDT-TTF)2Cu[N(CN)2]Cl, and κ-(BEDT-TTF)2Cu2(CN)3, measured at the small side of crystals with the electric field polarized perpendicular to the BEDT-TTF planes. The dominant vibrational mode ν27(b1u)of BEDT-TTF molecules is a very sensitive local probe of charge per molecule, namely its frequency depends on the valency (charge) of the molecule. In the case of the three κ-compounds no significant shifts in its frequency are observed with cooling.


Literature:

  1. K. Sedlmeier, S. Elsässer, D. Neubauer, R. Beyer, D. Wu, T. Ivek, S. Tomić, J. A. Schlueter, M. Dressel
    Absence of charge order in the dimerized κ-phase BEDT-TTF salts
    Phys. Rev. B 86, 245103 (2012).
  2. S. Elsässer, D. Wu, M. Dressel, J.A. Schlueter
    Power-law dependence of the optical conductivity observed in the quantum spin-liquid compound κ-(BEDT-TTF)2Cu2(CN)3
    Phys. Rev. B 86, 155150 (2012).