Negative quasiparticle shifts in phosphorene quantum dots

It is commonly believed that electron correlations would open up a quasiparticle gap in semiconductors. Contrary to this intuitive expectation, here we reveal that phosphorene quantum dots (PQDs) may exhibit just the opposite effect. By using a configuration interaction approach beyond the conventional double-excitation scheme, quasiparticle energies are calculated for hexagonal and rectangular PQDs in various dielectric environments. For the hexagonal PQD with a nominal gap of 2.26 eV, it is found that the quasiparticle shift decreases by more than 500 meV and eventually becomes negative when the effective dielectric constant is reduced from 20.0 to 5.0. For other trapezoidal, triangular, and rectangular PQDs, the quasiparticle shift exhibits a similar amount of decrement after the same change in the dielectric environment. Furthermore, the calculation by adopting the Rytova-Keldysh potential, which may be more suitable to describe two-dimensional screening, also shows a very similar result, although with smaller decrement of the quasiparticle shift. The origin of this anomalous quasiparticle shift is believed to be related to the long-range electron-electron interactions in the distinctive lattice structure of PQDs, as a similar phenomenon has never been found in graphene quantum dots.

Figure 1

Quasiparticle shifts calculated as a function of the inverse of the effective dielectric constant by using the Rytova-Keldysh potential (circular dots) or the conventional Coulomb interaction potential (diamond dots) for a hexagonal phosphorene quantum dot as depicted in the inset. The nominal gap of the PQD is 2.26 eV.

Figure 2

Quasiparticle shifts calculated as a function of the inverse of the effective dielectric constant for a trapezoidal phosphorene quantum dot as depicted in the inset. The nominal gap of the PQD is 2.1 eV.

Figure 3

Quasiparticle shifts calculated as a function of the inverse of the effective dielectric constant for a triangular phosphorene quantum dot as depicted in the inset. The nominal gap of the PQD is 2.44 eV.

Figure 4

Quasiparticle shifts calculated as a function of the inverse of the effective dielectric constant for a rectangular phosphorene quantum dot as depicted in the inset. The nominal gap of the PQD is 2.48 eV.

Figure 5

Quasiparticle shifts calculated as a function of the size of triangular phosphorene quantum dot for the effective dielectric constant set as 5.0. The total number of atoms starts from 30 in the smallest PQD to 200 in the largest one. Correspondingly, the nominal gap of PQDs decreases from 3.28 to 1.99 eV. The lines depicted are only to guide the eye.

Figure 6

The relative change of the quasiparticle shift calculated as a function of the on-site Coulomb energy when ${\kappa }^{-1}=0.12$ for the rectangular phosphorene quantum dot, as depicted in Fig. 4. The nominal gap of the PQD is 2.48 eV.

Figure 7

At various values of the cut-off distance in the RK interaction potential, quasiparticle shifts calculated as a function of the inverse of the effective dielectric constant for the rectangular phosphorene quantum dot with a nominal gap of 2.48 eV.

Figure 8

Quasiparticle shifts calculated as a function of the cutoff distance in the RK interaction potential at $\kappa =5.0$ for the rectangular phosphorene quantum dot with a nominal gap of 2.48 eV. The lines depicted are only to guide the eye.