Following the discovery of the self-sustained current oscillations (SSCOs) in sequential tunneling of superlattices (SLs) under dc bias, a large number of experimental and theoretical studies have focused on the origin of these oscillations and on how they develop. We have established that the generation of a limit cycle, around an unstable steady-state solution caused by the negative differential conductance, is the origin of SSCOs. According to this theory, the SL system moves round and round along the limit cycle, resulting in the SSCOs....[ Read more ]

Following the discovery of the self-sustained current oscillations (SSCOs) in sequential tunneling of superlattices (SLs) under dc bias, a large number of experimental and theoretical studies have focused on the origin of these oscillations and on how they develop. We have established that the generation of a limit cycle, around an unstable steady-state solution caused by the negative differential conductance, is the origin of SSCOs. According to this theory, the SL system moves round and round along the limit cycle, resulting in the SSCOs.

When an extra ac bias is applied to the SSCO, frequency locking into an integer fraction of the ac frequency is obtained in a periodic response in which a limit cycle deforms either with or without a topological change. In brief, the limit cycle deforms in two distinct ways giving rise to the frequency locking. When the frequency of the ac bias, ω_ac = pω_o, where p is an integer, w_o is the SSCO frequency in the dc case, the deformation of the limit cycle occurs via changing its shape. The system moves around the unstable steady-state solu-tion once and returns to its starting point. This results in a periodic response of SSCO with the frequency locking into ω_ac/p (= ω_o). On the other hand, when ω_ac = pω_o/q, where p/q is an irreducible fraction, the limit cycle deforms with topological changes. The system returns to its starting point after q rounds around the unstable steady-state solution. This generates a periodic response of SSCO with the frequency locking into ω_ac/p (= ω_o/q). As the deformation of the limit cycle can adjust itself in some way to sustain a small variation of the extra ac bias, robustness of the frequency locking is expected. All the results are verified both numerically and experimentally, indicating that SSCOs in SLs can be understood within the framework of the general concepts and principles of nonlinear physics.