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Dynamical quantum phase transitions occur in dynamically evolving quantumsystems when non-analyticities occur at critical times in the return rate, adynamical analogue of the free energy. This extension of the concept of phasetransitions can be brought into contact with another, namely that oftopological phase transitions in which the phase transition is marked by achange in a topological invariant. Following a quantum quench dynamical quantumphase transitions can happen in topological matter, a fact which has alreadybeen explored in one dimensional topological insulators and in two dimensionalChern insulators. Additionally in one dimensional systems a dynamical bulkboundary correspondence has been seen, related to the periodic appearance ofzero modes of the Loschmidt echo itself. Here we extend both of these conceptsto two dimensional higher order topological matter, in which the topologicallyprotected boundary modes are corner modes. We consider a minimal model whichencompasses all possible forms of higher order topology in two dimensionaltopological band structures. We find that DQPTs can still occur, and can occurfor quenches which cross both bulk and boundary gap closings. Furthermore adynamical bulk boundary correspondence is also found, which takes a differentform to that in one dimension.

Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators