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Boundary effects play an essential role in determining the physical properties of semiconductor quantum wires. Additional features come into play when one considers inhomogeneous boundaries, i.e. wires whose widths are functions of distance along the length of the wire. The authors show that, in the adiabatic approximation (which assumes that the boundary potential fluctuation effects, or equivalently, the variations in the wire width, occur on a scale much larger than the inverse of Fermi wavelength), the boundary problem for a quantum wire is equivalent to a one-dimensional Schrodinger equation along the wire with: (i) an effective potential provided by the deviation from the homogeneous boundary and, (ii) a wave function coupled to the lateral direction. In the periodic boundary fluctuation case, the subbands of the system split into many mini-subbands, and become a useful system to test 1D band theory. When the boundary fluctuates randomly, there exists in each of the subbands, a mobility edge, below which the electron states are localized. The localization of the tail states of the top populated subbands makes the conductance drop smoothly whenever the Fermi energy passes the bottom of a new subband. The theory explains the recent experiments of Smith and Craighead (1990).

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Journal of Physics: Condensed Matter

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