Accomidating slow learner
I don't want too know what material I would need just if it could be built within the laws of physics.
Tidal locking happens when one of the bodies in the system is significantly larger (specifically, more massive) than the other, and the distance between them is comparatively small; for example, Earth-Moon, or Sun-Mercury.Then you need to figure out a way to keep the anchor points of the "bridge" from being torn off, but that's an engineering problem, not a physics one.It only becomes a physics problem when you are trying to find a material to build the bridge with. But there's another problem: The elliptical shape of the orbit between the two bodies!Introducing an infinitely strong material but otherwise using physics, I guess it should be possible.But note that I'm not considering at all how you'd build something like this, just whether it would work .That isn't the case, and forcing orbits to be perfectly circular leads to all sorts of problems in the long term.
By realizing that orbits are elliptical, not circular, Kepler was able to derive a model that described the behavior of orbiting bodies much more accurately. When one body is moving away from another, the gravitational attraction between them is reduced, but so is their relative velocity.
Even a small man-made satellite in orbit of the Earth perturbs (tugs at) the Earth ever so slightly.
This is Newton's famous apple pulling the Earth toward it in action.
Tidal locking is a gradual process, but eventually, the smaller body stops rotating relative to the larger body. So there is no good anchor point on the larger body!
The only possible solution I can see to this is to use either rotational pole as the anchor point, on both bodies.
You can solve that by introducing that super-strong material Nobody mentioned, and that I alluded to in the beginning of my answer.