Tunneling of correlated electrons in an ultrahigh magnetic field

Effects of the electron-electron interaction on tunneling into a metal in an ultrahigh magnetic field (ultraquantum limit) are studied. The range of the interaction is found to have a decisive effect both on the nature of the field-induced instability of the ground state and on the properties of the system at energies above the corresponding gap. For a short-range repulsive interaction, tunneling is dominated by the renormalization of the coupling constant, which leads eventually to the charge-density wave instability. For a long-range interaction, there exists an intermediate energy range in which the conductance obeys a power-law scaling form, similar to that of a one-dimensional Luttinger liquid. The exponent is magnetic-field dependent, and more surprisingly, may be positive or negative, i.e., interactions may either suppress or enhance the tunneling conductance compared to its noninteracting value. At energies near the gap, scaling breaks down and tunneling is again dominated by the instability, which in this case is an (anisotropic) Wigner-crystal instability.