The inhomogeneous distribution of excess or deficient silver atoms lies behind the large and linear transverse magnetoresistance displayed by Ag 2 Se and Ag 2 Te, introducing spatial conductivity fluctuations with length scales independent of the cyclotron radius. We report a negative, nonsaturating longitudinal magnetoresistance up to at least 60 T, which becomes most negative where the bands cross and the effect of conductivity fluctuations is most acute. Thinning samples down to 10 m suppresses the negative response, revealing the essential length scale in the problem and paving the way for designer magnetoresistive devices. DOI: 10.1103/PhysRevLett.95.186603 PACS numbers: 72.20.My, 72.15.Gd, 72.80.Jc The silver chalcogenides provide a striking example of the benefits of imperfection. Perfectly stoichiometric Ag 2 Se and Ag 2 Te are nonmagnetic, narrow-gap semiconductors whose electron and hole bands cross at liquid nitrogen temperatures. They exhibit negligible magnetoresistance [1], as predicted from conventional theories [2]. By contrast, minute amounts of excess Ag or Se=Te-at levels as small as 1 part in 10 000 -lead to a huge and linear magnetoresistance over a broad temperature range [3][4][5][6][7][8]. The unusual linear dependence on magnetic field down to 100 G indicates a particularly long length scale associated with the underlying physics, while, at high field, a nonsaturating response up to at least 0.5 MG exceeds by a factor of 50 to 100 the expected cutoff where the product of the cyclotron frequency and the scattering rate ! 1 [9]. This remarkably robust linear magnetoresistive response makes the silver chalcogenides promising candidates for high field sensors. Missing at present, however, is experimental evidence for the pertinent length scales of the inhomogeneities that determine the unusual physics and that are essential to the materials' usefulness.Abrikosov was the first to stress the importance of the inhomogeneous distribution of the excess or deficient silver ions. In his effective medium theory of quantum linear magnetoresistance [10], disorder and a linear dispersion relation at band crossing [11] combine to produce a linear, rather than a quadratic, magnetic field dependence for the electrical conductivity. As pointed out by Parish and Littlewood [12], fluctuations in the mobility are particularly acute when the gap goes to zero and both positive and negative values can be sampled. Their simulations of large spatial conductivity fluctuations in strongly inhomogeneous semiconductors derive a linear magnetoresistance from the Hall voltage picked up from macroscopically distorted current paths caused by variations in the stoichiometry. The spatial fluctuations in the conductivity are caused by the random distribution of Ag ions, which may take the form of highly conducting nanothreads or lamellae along the grain boundaries of polycrystalline material [13]. The distorted current paths seen in the simulations lead to the emergence of a characteristic length scale that can be associ...