Effect of magnetic breakdown on angle-dependent magnetoresistance in a quasi-two-dimensional metal: An analytically solvable model

Abstract

We have developed an analytical model of angle-dependent magnetoresistance oscillations (AMROs) in a quasi-two-dimensional metal in which magnetic breakdown occurs. The model takes account of all the contributions from quasiparticles undergoing both magnetic breakdown and Bragg reflection at each junction and allows extremely efficient simulation of data which can be compared with recent experimental results on the organic metal κ-(BEDT-TTF)2Cu(NCS)2. AMROs resulting from both closed and open orbits emerge naturally at low field, and the model enables the transition to breakdown-AMROs with increasing field to be described in detail.The measurement of angle-dependent magnetoresistance oscillations (AMROs) is a powerful technique in the determination of details of the Fermi surfaces (FSs) in various reduced-dimensionality metals [1,2,3,4]. In many cases the angle-dependence originates in correlations in the time-dependent interplanar velocity of quasiparticles which traverse the FS under the influence of the magnetic field B and hence can be efficiently simulated by integrating up such correlations for all quasiparticle trajectories [5,6,7,8,9,10,11]. In high B, the additional effect of magnetic breakdown (MB) can substantially complicate this picture. This effect occurs in the FSs of quasi-two-dimensional metals such as that illustrated in Fig. 1(a) which is described by the dispersion E(k) =h 2 (k 2 x + k 2 y )/2m * with effective mass m * , Fermi wave vector k F and Brillouin zone edges at k y = ±k F cos ξ. Because of the periodic potential, small gaps in the dispersion open up at the Brillouin zone edge, splitting the FS into distinct open and closed sections. Quasiparticles orbit around the FS with constant k z when B lies along the interlayer direction. In very low B, because of Bragg reflection, only open orbits [ Fig. 1(b)] and small closed orbits [ Fig. 1(c)] occur around the distinct sections of the FS. In high B, mixing between the states on the two FS sections leads to MB at the four filled points shown in Fig. 1(a) which we term MB junctions. At these junctions a quasiparticle "tunnels" in k-space between the FS sections [12], resulting in a single large closed orbit [ Fig. 1(d)].In fact for general values of the magnetic field there should be a superposition of all the orbits in Fig. 1(b)-(d) as well as many other intermediate possibilities in which MB occurs at some of the MB junctions and Bragg reflection occurs at the others. The probability p = exp(−B 0 /B) of MB at each MB junction is parameterized by B 0 , the characteristic breakdown field [12,13,14]. For all finite, non-zero values of B (for which 0 < p < 1) there is a hierarchy of complex trajectories that must be summed to account for all possible contributions to the conductivity in which MB either does or does not occur at each MB junction. If a quasiparticle crosses N MB junctions, one has to consider 2 N possible trajecto- ries with their correct probabilistic weightings, and this complicates a direct computation of AMROs since one has ...

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