  Conventional understanding implies that the ground state of a nonmagnetic
quantum mechanical system should be nodeless. While this notion also provides a
valuable guidance in understanding the ordering of energy levels in
semiconductor nanostructures, there are reports that $\textit{nodal}$ ground
states for holes are possible. However, the existence of such nodal states has
been debated and even viewed merely as an artifact of a
$\boldsymbol{k{\cdot}p}$ model. Using complementary approaches of both
$\boldsymbol{k{\cdot}p}$ and tight-binding models, further supported by an
effective Hamiltonian for a continuum model, we reveal that the nodal ground
states in quantum dots are not limited to a specific approach. Remarkably, the
emergence of the nodal hole states at the top of the valence band can be
attributed to the formation of the orbital vortex textures through competition
between the hole kinetic energy and the coupling to the conduction band states.
We suggest an experimental test for our predictions of the reversed energy
ordering and the existence of nodal ground states. We discuss how our findings
and the studies of orbital textures could be also relevant for other materials
systems.
