One-dimensional rarefactive solitons in electron-hole semiconductor plasmas

We present a theory for linear and nonlinear excitations in semiconductor quantum plasmas consisting of electrons and holes. The system is governed by two coupled nonlinear Schrödinger equations for the collective wave functions of the electrons and holes and Poisson's equation for the electrostatic potential. This gives a closed system including the effects of charge separation between the electrons and holes, quantum tunneling, quantum statistics, and exchange correlation due to electron spin. Three typical semiconductors, GaAs, GaSb, and GaN, are studied. For small-amplitude excitations, the dispersion relation reveals the existence of one high-frequency branch due to charge-separation effects and one low-frequency branch due to the balance between pressure and inertia of the electrons and holes. For the fully nonlinear excitations, the profiles of quasistationary soliton solutions are obtained numerically and show depleted electron and hole densities correlated with a localized potential. The simulation results show that the rarefactive solitons are stable and can withstand perturbations and turbulence for a considerable time.

Figure 1

Wave dispersion curves for GaAs (blue dashed line), GaSb (green solid line), and GaN (red dash-dotted line) semiconductor plasmas.

Figure 2

The spatial profiles of (top) the electron number density $n_e={\left|{\psi }_e\right|}^2$, (middle) the hole number density $n_h={\left|{\psi }_h\right|}^2$, and (bottom) the scalar potential $\varphi$ for rarefactive solitons in GaAs, GaSb, and GaN semiconductor plasmas (left to right columns, respectively).

Figure 3

Nonlinear evolution of solitons in a GaAs semiconductor plasma: (a) the electron number density $n_e={\left|{\psi }_e\right|}^2$, (b) the hole number density $n_h={\left|{\psi }_h\right|}^2$, and (c) the scalar potential $\varphi$.

Figure 4

Nonlinear evolution of solitons in a GaSb semiconductor plasma: (a) the electron number density $n_e={\left|{\psi }_e\right|}^2$, (b) the hole number density $n_h={\left|{\psi }_h\right|}^2$, and (c) the scalar potential $\varphi$.

Figure 5

Nonlinear evolution of solitons in a GaN semiconductor plasma: (a) the electron number density $n_e={\left|{\psi }_e\right|}^2$, (b) the hole number density $n_h={\left|{\psi }_h\right|}^2$, and (c) the scalar potential $\varphi$.