Anomalous temperature dependence of resistivity in quasi-one-dimensional conductors in a strong magnetic field

We present a heuristic, semiphenomenological model of the anomalous temperature (T) dependence of resistivity ρxx recently observed experimentally in the quasi-one-dimensional (Q1D) organic conductors of the (TMTSF)2X family in moderately strong magnetic fields. We suggest that a Q1D conductor behaves like an insulator (dρxx/dT < 0), when its effective dimensionality is one, and like a metal (dρxx/dT > 0), when its effective dimensionality is greater than one. Applying a magnetic field reduces the effective dimensionality of the system and switches the temperature dependence of resistivity between the insulating and metallic laws depending on the magnitude and orientation of the magnetic field. We critically analyze whether various microscopic models suggested in literature can produce such a behavior and find that none of the models is fully satisfactory. In particular, we perform detailed analytical and numerical calculations within the scenario of magneticfield-induced spin-density-wave precursor effect suggested by Gor’kov and find that the theoretical results do not agree with the experimental observations. 72.10.-d, 72.15.Gd, 75.30.Fv, 74.70.Kn Typeset using REVTEX 1 I. EXPERIMENTAL INTRODUCTION In recent experiments [1–4], a very unusual temperature (T ) dependence of resistivity was observed in quasi-one-dimensional (Q1D) organic conductors (TMTSF)2ClO4 (at the ambient pressure) and (TMTSF)2PF6 (at a pressure about 9 kbar) [5] in moderately strong magnetic fields H of the order of 10 T at T < ∼ 50 K. Unexpectedly large magnetoresistance in these materials has already attracted attention in earlier measurements [6–8]. The (TMTSF)2X materials consist of one-dimensional (1D) conducting chains parallel to the crystal axis a (for general reviews of the (TMTSF)2X materials, see Refs. [1,9–12]). The chains are weakly coupled in the two others directions b and c, the coupling in the c direction being much weaker than in the b direction. In zero magnetic field or in the field parallel to the b axis, the resistivity of (TMTSF)2PF6 along the chains, ρaa, depends on temperature approximately quadratically: ρaa ∼ T 2 [1,4,13], which is consistent with the standard Fermi-liquid theory [14], provided resistivity is dominated by electron-electron scattering. When a magnetic field is applied along the c axis, ρaa does not change appreciably at high temperatures; however, below a certain magnetic-field-dependent temperature Tmin ∼ 20 K, resistivity starts to grow with decreasing temperature: dρaa/dT < 0 at T < Tmin [1,3,4]. In other words, the behavior of the system changes from metallic, dρaa/dT > 0, to insulating, dρaa/dT < 0, when the temperature is lowered below Tmin. The temperature Tmin increases with the increase of magnetic field. Such a behavior is very surprising in view of the fact that no thermodynamic phase transition is observed in the system at this relatively high temperature Tmin ∼ 20 K. (A phase transition into the magnetic-field-induced spindensity-wave (FISDW) state takes place at the transition temperature Tc ∼ 2 K, which is an order of magnitude lower than Tmin.) As the temperature is lowered further below Tmin, ρaa(T ) continues to grow until another temperature scale Tmax ∼ 8 K < Tmin is reached. Magnetoresistance is huge at T ∼ Tmax: ρaa at H = 7.8 T is about 10 times greater than ρaa at H = 0 [4]. At the lower temperatures T < Tmax, behavior of the system starts to depend crucially on the exact orientation of the magnetic field [4,15]. If the magnetic field