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We consider D-dimensional Einstein gravity coupled to two U(1) fields and adilaton with a scalar potential. We derive the condition that the analyticalAdS black holes with two independent charges can be constructed. Turning offthe cosmological constant, the extremal Reissner-Nordstrom black hole emergesas the harmonic superposition of the two U(1) building blocks. With thenon-vanishing cosmological constant, our extremal solutions contain thenear-horizon geometry of AdS_2 x R^{D-2} with or without a hyperscaling. Wealso obtain the magnetic AdS_{D-2} x Y^2 vacua where Y^2 can be R^2, S^2 orhyperbolic 2-space. These vacua arise as the fix points of some superpotentials and recover the known supersymmetric vacua when the theory can beembedded in gauged supergravities. The AdS_{D-2} x R^2 vacua are of particularinterest since they are dual to some quantum field theories at the lowestLandau level. By studying the embedding of some of these solutions in thestring and M-theory, we find that the M2/M5-system with the equal M2 and M5charges can intersect with another such M2/M5 on to a dyonic black hole.Analogous intersection rule applies also to the D1/D5-system. The intersectionsare non-supersymmetric but in the manner of harmonic superpositions.

Charged Dilatonic AdS Black Holes and Magnetic AdS_{D-2} x R^2 Vacua