Monolayer phosphorene under time-dependent magnetic field

TL;DR

This paper derives exact solutions for monolayer phosphorene in time-dependent magnetic fields, analyzing energy levels and transition probabilities, revealing linear and oscillatory behaviors depending on the magnetic field type.

Contribution

It provides an exact wave function solution for phosphorene under time-dependent magnetic fields using the dynamical invariant method, a novel approach in this context.

Findings

Landau levels vary linearly with quantum numbers and magnetic field in constant fields.

Energy oscillates over time under oscillatory magnetic fields.

Transitions occur only when quantum numbers satisfy specific conditions.

Abstract

We obtain the exact wave function of a monolayer phosphorene under a low- intensity time-dependent magnetic field using the dynamical invariant method. We calculate the quantum-mechanical energy expectation value and the transition probability for a constant and an oscillatory magnetic field. For the former we observe that the Landau level energy varies linearly with the quantum numbers n and m and the magnetic field intensity B_0. No transition takes place. For the latter, we observe that the energy oscillates in time, increasing linearly with the Landau level n and m and nonlinearly with the magnetic field. The (k,l) to (n,m) transitions take place only for l=m. We investigate the (0,0) to (n,0) and (1,l) and (2,l) probability transitions.