Temperature Evolution of the Quantum Hall Eeect in Quasi-one-dimensional Organic Conductors

The Hall conductivity in the magnetic-eld-induced spin-density-wave (FISDW) state of the quasi-one-dimensional organic conductors (TMTSF) 2 X at a nite temperature is calculated. The temperature dependence of the Hall conductivity is found to be the same as the temperature dependence of the Frr ohlich current of a regular charge/spin-density wave. Predicted dependence xy (T) can be veriied experimentally in the (TMTSF) 2 X compounds if all components of the resistivity tensor are measured and the conductivity tensor is reconstructed. Organic metals of the (TMTSF) 2 X family, where TMTSF is tetramethyltetraselenafulvalene and X represents an inorganic anion, are highly anisotropic, quasi-one-dimensional crystals that consist of parallel conducting chains. The overlap of the electron wave functions and the electric conductivity are the highest in the direction of the chains (the a direction) and are much smaller in the b direction perpendicular to the chains. In this paper, we neglect the coupling between the chains in the third, c direction, which is weaker than in the b direction, and study the properties of a single layer (the a-b plane), modeling (TMTSF) 2 X as a system of the uncoupled two-dimensional layers. When a strong magnetic eld is applied perpendicular to the a-b plane, the magnetic-eld-induced spin-density-wave (FISDW) appears in the system (see Ref. 1] for a review). In the FISDW phase, the Hall conductivity per one layer, xy , is quantized at zero temperature as xy = 2Ne 2 =h; (1) where e is the electron charge, h = 2 h is the Planck constant, and N is an integer that characterizes the FISDW. However, at a nite temperature, because electrons are thermally excited above the FISDW energy gap, the Hall conductivity is not quantized. In this paper , we calculate temperature dependence of the Hall conductivity in the FISDW state. To model (TMTSF) 2 X, let us consider a 2D system that consists of many chains, parallel to the x axis and equally spaced along the y-axis with the distance b. 1) The chains are coupled through the electron tunneling of the amplitude t b. To calculate the Hall conductivity, suppose that a magnetic eld H is applied along the z axis perpendicular to the (x; y) plane, and an electric eld E y is applied perpendicular to the chains. The electron Hamiltonian in the FISDW state is: 2) ^ H = ? h 2 2m @ 2 @x 2 +22 …