# Half-filled systems close to Mott insulator

## Half-filled systems close to Mott insulator |

*Fig 2: Schematic phase diagram of κ-(BEDT-TTF) _{2}X. 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)_{2}Cu[N(CN)_{2}]Br_{x}Cl_{1}*

_{−}*.*

_{x}*The first-order insulating-to-metallic transition line is sketched based on alloy studies and the generic diagram for κ-(BEDT-TTF)*

_{2}X.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 T_{0}and T_{c}-points, respectively.When going across the Mott transition from κ-(BEDT-TTF)

_{2}Cu[N(CN)

_{2}]Cl to κ-(BEDT-TTF)

_{2}Cu[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)

_{2}Cu[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) _{2}Cu[N(CN)_{2}]Br_{x}Cl_{1−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. *

*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)_{2}Cu[N(CN)_{2}]Br is a perfect Fermi liquid compound with a nice ρ ∞ T^{2} and σ ∞ w^{2} behavior over an appreciable energy range: Γ(w,T) = A(k_{B}T)^{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) _{2}Cu[N(CN)_{2}]Br_{x}Cl_{1−x} *

*with different x. (a) - (c). The frequency-dependent part of the scattering rate at low temperaures of k*

*-(BEDT-TTF)*

_{2}Cu[N(CN)_{2}]Br_{x}Cl_{1−x}*as function of the squared frequency. We determined for the frequency-independent dc limit of the scattering rate*

*Γ*

_{1}(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)-*ρ

_{0 }*∞ 1/*

*ζ(T)). The plots as a function of T*

^{2}in the low-temperature region yield a quadratic behavior up to T_{0}. Below T_{c =}12 K the systems become superconducting.*Fig 6:* *(a) Low-temperature optical conductivity of **k**-(BEDT-TTF) _{2}Cu[N(CN)_{2}]Br_{x}C_{1-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 *

*σ*

_{1}*(*

*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:**

- M. Dressel und N. Drichko

*Optical Properties of Two-Dimensional Organic Conductors: Signatures of Charge Ordering and Correlation Effects*

Chemical Review**104**, 5689 (2004). - 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}]-Br_{x}Cl_{1-x }I: Optical studies of localized charge excitations

Phys. Rev. B**76**, 165113 (2007). - 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). - M. Dumm, D. Faltermeier, N. Drichko und M. Dressel

*Bandwidth-controlled Mott transition in κ-(BEDT-TTF)*_{2}-Cu[N(CN)_{2}]-Br_{x}Cl_{1-x }II: Optical studies of correlated carriers

Phys. Rev. B**79**, 195106 (2009). - 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). - 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)*_{2}Cu[N(CN)_{2}]Br_{x}Cl_{1-x}

Eur. Phys. J. B**79**, 383 - 390 (2011). - M. Dressel

*Quantum criticality in organic conductors? Fermi-liquid versus non-Fermi-liquid behavior*

J. Phys.: Condens. Matter**23**, 293201 (2011). - 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.

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