Prediction that Uniaxial Tension along ⟨111⟩ Produces a Direct Band Gap in Germanium

We predict a new way to achieve a direct band gap in germanium, and hence optical emission in this technologically important group-IV element: tensile strain along the < 111 > direction in Ge nanowires. Although a symmetry-breaking band splitting lowers the conduction band at the corner of the Brillouin zone (at the L point), a direct gap of 0.34 eV in the center of the Brillouin zone (at Gamma) can still be achieved at 4.2% longitudinal strain, through an unexpectedly strong nonlinear drop in the conduction band edge at Gamma for strain along this axis. These strains are well within the experimentally demonstrated mechanical limits of single-crystal Ge (or GexSi1-x) nanowires, thereby opening a new material system for fundamental optical studies and applications.