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We define the notion of a knot type having Legendrian large cables and showthat having this property implies that the knot type is not uniformly thick.Moreover, there are solid tori in this knot type that do not thicken to a solidtorus with integer sloped boundary torus, and that exhibit new phenomena;specifically, they have virtually overtwisted contact structures. We then showthat there exists an infinite family of ribbon knots that have Legendrian largecables. These knots fail to be uniformly thick in several ways not previouslyseen. We also give a general construction of ribbon knots, and show when theygive similar such examples.

Legendrian Large Cables And New Phenomenon For Non-Uniformly Thick Knots