Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions

摘要

HgTe quantum wells and surfaces of three-dimensional topological insulatorssupport Dirac fermions with a single-valley band dispersion. In the presence ofdisorder they experience weak antilocalization, which has been observed inrecent transport experiments. In this work we conduct a comparative theoreticalstudy of the weak antilocalization in HgTe quantum wells and topologicalsurface states. The difference between these two single-valley systems comesfrom a finite band gap (effective Dirac mass) in HgTe quantum wells in contrastto gapless (massless) surface states in topological insulators. The finiteeffective Dirac mass implies a broken internal symmetry, leading to suppressionof the weak antilocalization in HgTe quantum wells at times larger than certaint_M, inversely proportional to the Dirac mass. This corresponds to the openingof a relaxation gap 1/t_M in the Cooperon diffusion mode which we obtain fromthe Bethe-Salpeter equation including relevant spin degrees of freedom. Wedemonstrate that the relaxation gap exhibits an interesting nonmonotonicdependence on both carrier density and band gap, vanishing at a certaincombination of these parameters. The weak-antilocalization conductivityreflects this nonmonotonic behavior which is unique to HgTe QWs and absent fortopological surface states. On the other hand, the topological surface statesexhibit specific weak-antilocalization magnetoconductivity in a parallelmagnetic field due to their exponential decay in the bulk.