The effect of incoherent interlayer transport on the interlayer resistance of a layered metal is considered. We find that for both quasi-one-dimensional and quasi-two-dimensional Fermi liquids the angular dependence of the magnetoresistance is essentially the same for coherent and incoherent transport. Consequently, the existence of a three-dimensional Fermi surface is not necessary to explain the oscillations in the magnetoresistance that are seen in many organic conductors as the field direction is varied. [S0031-9007(98)

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport, and makes use of results of semiclassical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations ͑AMRO͒ in quasi-one-and quasi-two-dimensional organic metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two-and quasi-onedimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time ͑and thus the temperature͒. We point out three distinctive features of coherent interlayer transport: ͑i͒ a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, ͑ii͒ a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and ͑iii͒ a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties ͑i͒ and ͑ii͒ are compared with published experimental data for a range of quasi-two-dimensional organic metals. ͓S0163-1829͑99͒02236-5͔

The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field that is tilted away from the normal to the layers is considered. For both quasi-one-and quasi-two-dimensional systems resonances occur when the frequency is a harmonic of the frequency at which the magnetic field causes the electrons to oscillate on the Fermi surface within the layers. The intensity of the different harmonic resonances varies significantly with the direction of the field. The resonances occur for both coherent and weakly incoherent interlayer transport and so their observation does not imply the existence of a threedimensional Fermi surface. ͓S0163-1829͑99͒51240-X͔ There is considerable interest in performing frequencydependent transport measurements on strongly correlated metals in the hope that they will provide information about the metallic state such as a direct determination of the scattering rate. Layered organic metals 1,2 are ideal for such experiments due to their high purity and a number of experiments have been performed. 3,4 In this paper, we show that when the magnetic field is tilted away from the normal to the layers that there are well-defined resonances in the interlayer conductivity when the frequency equals a harmonic of the frequency at which the magnetic field causes electrons to traverse the Fermi surface within the layers. This occurs for both quasi-two and quasi-one-dimensional systems. The intensity of the resonances at different harmonics varies significantly with the direction of the field. For example, it is possible to choose the field direction so one will see predominantly only odd or even harmonic resonances. In general, a three-dimensional Fermi surface is not necessary for the observation of the resonances. We also compare our results to previous theoretical work, 5,6 which has involved more complicated band structures.We assume a Fermi liquid within the layers with the simplest possible dispersion relation ⑀(k x ,k y ). For quasi-onedimensional systems we takewhere v F is the Fermi velocity, k F is the Fermi wave vector, t b the interchain hopping integral, and b the interchain distance. For the quasi-two-dimensional case, ⑀(k x ,k y ) ϭប 2 /2m*(k x 2 ϩk y 2 ) where m* is the effective mass. Solution of the semi-classical equations of motion shows that in a magnetic field B normal to the layers electrons move across the Fermi surface within the layers at a periodic orbit frequency 0 , which equals ev F bB/ប or eB/m* for the quasione-and quasi-two-dimensional cases, respectively.We consider a magnetic field tilted at an angle away from the normal to the layers. For the quasi-one-dimensional case, we at first only consider the case where the field is confined to the xϪz plane, i.e., the plane containing the most and least-conducting directions. This is done for reasons of simplicity; later in the paper, we consider more general field directions for the quasi-one-dimensional case. We have calculated the frequency-dependent interlayer conductivity for two differen...

In a number of quasi-one-dimensional organic metals the dependence of the magnetoresistance on the direction of the magnetic field is quite different from the predictions of the Boltzmann transport theory for a Fermi liquid with a scattering rate that is independent of momentum. We consider a model in which there are large variations in the scattering rate over the Fermi surface. The model is the quasi-one-dimensional version of the ''cold spots'' model introduced by Ioffe and Millis to explain anomalous transport properties of the metallic phase of the cuprate superconductors. The dependence of the resistance, in the most-and leastconducting directions, on the direction and magnitude of the magnetic field is calculated. The calculated magnetoresistance has a number of properties that are quite distinct from conventional transport theory, such as magic angle effects and a significant magnetoresistance when the field and current are both in the leastconducting direction. However, the model cannot give a complete description of the unusual properties of (TMTSF) 2 PF 6 at pressures of 8-11 kbar.

The interlayer magnetoresistance of a quasi-one-dimensional Fermi liquid is considered for the case of a magnetic field that is rotated within the plane perpendicular to the most-conducting direction. Within semi-classical transport theory dips in the magnetoresistance occur at integer "magic angles" only when the electronic dispersion parallel to chains is nonlinear. If the field direction is fixed at one of the magic angles and the temperature is varied then the resulting variation of the scattering rate can lead to a non-monotonic variation of the interlayer magnetoresistance with temperature. Although the model considered here gives a good description of some of the properties of the Bechgaard salts, (TMTSF)2PF6 for pressures less than 8 kbar and (TMTSF)2ClO4 it gives a poor description of their properties when the field is parallel to the layers and of the intralayer transport.