Valley splitting in Si/SiGe heterostructures from first principles

We compute valley splitting in Si/SiGe superlattices using density functional theory (DFT). This first-principles approach is expected to provide an excellent description of interfaces, strains, and atomistic disorder without empirically fitted parameters. We benchmark atomistic tight-binding (TB) and the “ <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>2</a:mn> <a:msub> <a:mi>k</a:mi> <a:mn>0</a:mn> </a:msub> </a:mrow> </a:math> ” theory within the effective mass (EM) approximation against DFT. We show that DFT supports the main conclusions of the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>2</b:mn> <b:msub> <b:mi>k</b:mi> <b:mn>0</b:mn> </b:msub> </b:mrow> </b:math> theory, but reveals some limitations of semiempirical methods such as the EM and TB, in particular about the description of atomistic disorder. The DFT calculations also highlight the effects of strong valley-orbit mixing at large valley splitting. Nevertheless, TB and the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>2</c:mn> <c:msub> <c:mi>k</c:mi> <c:mn>0</c:mn> </c:msub> </c:mrow> </c:math> theory shall provide reasonable valley splitting statistics in many heterostructures of interest for spin qubit devices.