  Discrete time quantum walks (DTQWs) are nontrivial generalizations of random
walks with a broad scope of applications. In particular, they can be used as
computational primitives, and they are suitable tools for simulating other
quantum systems. DTQWs usually spread ballistically due to their quantumness.
In some cases, however, they can remain localized at their initial state
(trapping). The trapping and other fundamental properties of DTQWs are
determined by the choice of the coin operator. We introduce and analyze an up
to now uncharted type of walks driven by a coin class leading to strong
trapping, complementing the known list of walks. This class of walks exhibit a
number of exciting properties with the possible applications ranging from light
pulse trapping in a medium to topological effects and quantum search.
