Under nonequilibrium conditions, bosonic modes can become dynamically unstable with an exponentially growing occupation. On the other hand, topological band structures give rise to symmetry protected midgap states. In this Letter, we investigate the interplay of instability and topology. Thereby, we establish a general relation between topology and instability under ac driving. We apply our findings to create dynamical instabilities which are strongly localized at the boundaries of a finite-size system. As these localized instabilities are protected by symmetry, they can be considered as topological instabilities.
Phys. Rev. Lett. 117, 2016
a) Topological phase diagram. The parameters are as in Fig. 1. In the green (dark gray) areas, the system is not globally stable, so the topological invariant WS in Eq. (9) is not defined there. In the white and yellow (light gray) areas, we find that WS=0 and WS=2 , respectively. The topological phases are separated by instability areas (green). Dashed lines are obtained by using an effective Hamiltonian . (b) Stability diagram as a function of hx,1 and hy,1 corresponding to (a). The parameters of the curves &gammna;a,b,c are depicted in (a) by the points p=a , b , c . The parameters p=a and p=b correspond to Figs. 1 and 1. Curve γc can be contracted to point P , so that it is topologically trivial according to the explanations in the main text.