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Second-order non-linear conductance of a two-dimensional mesoscopic conductor

We have investigated the weakly non-linear quantum transport properties of a two-dimensional quantum conductor. We have developed a numerical scheme which is very general for this purpose. The second-order non-linear conductance is computed for the first time for a truly two-dimensional structure by explicitly evaluating the various partial densities of states, the sensitivity and the characteristic potential. Interesting spatial structures of these quantities are revealed. We present detailed results concerning the crossover behaviour of the second-order non-linear conductance, occurring when the conductor changes from geometrically symmetrical to asymmetrical. Other issues of interest such as the gauge invariance are also discussed.