Conductance of a quantum point contact based on spin-density-functional theory

Abstract

We present full quantum mechanical conductance calculations of a quantum point contact (QPC) performed in the framework of the density functional theory (DFT) in the local spin-density approximation (LDA). We start from a lithographical layout of the device, and the whole structure, including semi-infinitive leads, is treated on the same footing (i.e., the electron-electron interaction is accounted for in both the leads and the central device region). We show that the spin degeneracy of the conductance channels is lifted and the total conductance exhibits a broad plateaulike feature at $\ensuremath{\sim}0.5\ifmmode\times\else\texttimes\fi{}2{e}^{2}∕h$. The lifting of the spin degeneracy is a generic feature of all studied QPC structures (both very short and very long ones, with lengths in the range $40\ensuremath{\lesssim}l\ensuremath{\lesssim}500\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$). The calculated conductance also shows a hysteresis for forward and backward sweeps of the gate voltage. These features in the conductance can be traced to the formation of weakly coupled quasibound states (magnetic impurities) inside the QPC (also predicted in previous DFT-based studies). A comparison of the results obtained with the experimental data shows, however, that while the spin-DFT-based ``first-principles'' calculations exhibit spin polarization in the QPC, the calculated conductance clearly does not reproduce the 0.7 anomaly observed in almost all QPCs of various geometries. We critically examine the major features of the standard DFT-based approach to the conductance calculations and argue that its inability to reproduce the 0.7 anomaly might be related to the infamous derivative discontinuity problem of the DFT, leading to spurious self-interaction errors not corrected in the standard LDA. Our results indicate that the formation of magnetic impurities in the QPC might be an artifact of the LDA when localization of charge is expected to occur. We thus argue that an accurate description of the QPC structure would require approaches that go beyond the standard $\mathrm{DFT}+\mathrm{LDA}$ schemes.