Decoupling of the many-body effects from the electron mass in GaAs by means of reduced dimensionality

Abstract

Determining the (bare) electron mass ${m}_{0}$ in crystals is often hindered by many-body effects since Fermi-liquid physics renormalizes the band mass, making the observed effective mass ${m}^{*}$ depend on density. Here, we use a one-dimensional (1D) geometry to amplify the effect of interactions, forcing the electrons to form a nonlinear Luttinger liquid with separate holon and spinon bands, therefore separating the interaction effects from ${m}_{0}$. Measuring the spectral function of gated quantum wires formed in GaAs by means of magnetotunnelling spectroscopy and interpreting them using the 1D Fermi-Hubbard model, we obtain ${m}_{0}=(0.0525\ifmmode\pm\else\textpm\fi{}0.0015){m}_{\text{e}}$ in this material, where ${m}_{\text{e}}$ is the free-electron mass. By varying the density in the wires, we change the interaction parameter ${r}_{\text{s}}$ in the range from $\ensuremath{\sim}1$--4 and show that ${m}_{0}$ remains constant. The determined value of ${m}_{0}$ is $\ensuremath{\sim}22%$ lighter than observed in GaAs in geometries of higher dimensionality $D$ ($D>1$), consistent with the quasiparticle picture of a Fermi liquid that makes electrons heavier in the presence of interactions.