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Conventional understanding implies that the ground state of a nonmagneticquantum mechanical system should be nodeless. While this notion also provides avaluable guidance in understanding the ordering of energy levels insemiconductor nanostructures, there are reports that $\textit{nodal}$ groundstates for holes are possible. However, the existence of such nodal states hasbeen 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 aneffective Hamiltonian for a continuum model, we reveal that the nodal groundstates in quantum dots are not limited to a specific approach. Remarkably, theemergence of the nodal hole states at the top of the valence band can beattributed to the formation of the orbital vortex textures through competitionbetween the hole kinetic energy and the coupling to the conduction band states.We suggest an experimental test for our predictions of the reversed energyordering and the existence of nodal ground states. We discuss how our findingsand the studies of orbital textures could be also relevant for other materialssystems.

Nodal "ground states" and orbital textures in semiconductor quantum dots