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Register a new userMagneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping
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We investigate the magneto-conductance (MC) anisotropy in the variable range hopping regime, caused by quantum interference effects in three dimensions. When no spin-orbit scattering is included, there is an increase in the localization length (as in two dimensions), producing a large positive MC. By contrast, with spin-orbit scattering present, there is no change in the localization length, and only a small increase in the overall tunneling amplitude. The numerical data for small magnetic fields $B$, and hopping lengths $t$, can be collapsed by using scaling variables $B_perp t^{3/2}$, and $B_parallel t$ in the perpendicular and parallel field orientations respectively. This is in agreement with the flux through a `cigar--shaped region with a diffusive transverse dimension proportional to $sqrt{t}$. If a single hop dominates the conductivity of the sample, this leads to a characteristic orientational `finger print for the MC anisotropy. However, we estimate that many hops contribute to conductivity of typical samples, and thus averaging over critical hop orientations renders the bulk sample isotropic, as seen experimentally. Anisotropy appears for thin films, when the length of the hop is comparable to the thickness. The hops are then restricted to align with the sample plane, leading to different MC behaviors parallel and perpendicular to it, even after averaging over many hops. We predict the variations of such anisotropy with both the hop size and the magnetic field strength. An orientational bias produced by strong electric fields will also lead to MC anisotropy.
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We show that the spin chain/ladder compound La_3Sr_3Ca_8Cu_24O_41 is an insulator with hopping transport along the chains. In the temperature range 35 - 280 K, DC conductivity sigma_{DC}(T) follows Motts law of variable-range hopping conduction; the frequency dependence has the form sigma( u, T) = sigma_{DC}(T) + A(T) u^{s}, where s approx 1. The conduction mechanism changes from variable-range hopping to nearest-neighbor hopping around T_{c} =300 K. The chain array thus behaves like a one-dimensional disordered system. Disorder is due to random structural distortions of chains induced by irregular coordination of the La/Sr/Ca ions.
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