Nodal ``ground states'' and orbital textures in semiconductor quantum dots

Unlike the common expectation, theoretical calculations in quantum wires and quantum dots have predicted hole ground state wavefunctions with a node [1-2] that are often associated with the formation of dark excitons [3]. The inversion of the energy level ordering between nodeless (S-like) and nodal (P-like) wavefunction states occurs due to various factors, e.g., confinement size and strength, choice of a material, and spin-orbit interaction. However, the existence of the nodal ground states has been debated and even viewed merely as an artifact of a k\textbullet p model [4]. Using complementary approaches of both k\textbullet 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 theoretical model. Remarkably, the emergence of the nodal ground states can be attributed to the formation of the orbital vortex textures that minimizes ``divergence''. We discuss how our findings and the studies of orbital textures could be also relevant for different materials systems. [1] K. V\'{y}born\'{y} et al., PRB 85, 155312 (2012) [2] A. Bagga et al., PRB 74, 035341 (2006); P. Horodysk\'{a} et al., PRB 81, 045301 (2010); J. Xia and J. Li, PRB 60, 11540 (1999); M. P. Persson and H. Q. Xu, PRB 73, 125346 (2006). [3] M. Nirmal, et al., PRL 75, 3728 (1995); Al. L. Efros, et al., PRB 54, 4843 (1996). [4] L. W. Wang et al., APL 76, 339 (2000)