Stopping power of two-dimensional spin quantum electron gases

Quantum effects can contribute significantly to the electronic stopping powers in the interactions between the fast moving beams and the degenerate electron gases. From the Pauli equation, the spin quantum hydrodynamic (SQHD) model is derived and used to calculate the stopping power and the induced electron density for protons moving above a two-dimensional (2D) electron gas with considering spin effect under an external in-plane magnetic field. In our calculation, the stopping power is not only modulated by the spin direction, but also varied with the strength of the spin effect. It is demonstrated that the spin effect can obviously enhance or reduce the stopping power of a 2D electron gas within a laboratory magnetic field condition (several tens of Tesla), thus a negative stopping power appears at some specific proton velocity, which implies the protons drain energy from the Pauli gas, showing another significant example of the low-dimensional physics.