The number 1, 2, 3 etc. application of nanotechnology is in semiconductors. It is absolutely impossible to conduct nanotechnology research without semiconductor processing and characterization equipment. Nanotechnology applications such as photovoltaics, power transmission, memory, etc. all deal with semiconductor materials. The non-IT related part of nanotechnology (i.e. sensors, power, light emission or transmission, basically stuff unrelated to shuffling electrons as 1's and 0's) is the OSD part of the semiconductor market; the IT part is everything else. Non-semiconductor applications of nanotechnology are a very small market. A possible breakthrough is the replacement of Si as the gated conduction material in transistors with a low dimensional crystal like MoS2 or graphene. However, that is still a semiconductor application, even though the papers are all published as "nanotechnology".
This is why I am confident of catchup in the semiconductor industry - Chinese universities and institutes publish a vast amount of papers on nanotechnology, every province has at least 1 research level foundry and the country has the 5th largest commercial foundry in the world at SMIC. Once you have the hardware (the foundry), the software (the papers and the scientific momentum) and the people, catchup or even finding a technological breakthrough, even for niche applications, is very likely. Even if there is no catchup commercially, there will be a vast storage of intellectual property and experience at national labs, universities and partnered foundries, which allows for a quick industry buildup and the creation of competitors in case of any supply disruptions.
The main problem is, of course, the great wall of patents protecting certain chip architectures, making catchup in the materials, foundry and test/assembly fields much more likely than in design. However, even in design, Huawei has already begun to move all chip development in-house and other companies such as Lenovo and ZTE are likely to follow; this is all in addition to independent chip designers like.
Life sciences is even more dominated by the West than semiconductors, and since it supplies consumers directly, there is absolutely zero chance of catchup even with a major technological breakthrough due to media. In fact, semiconductors are the #1 potential field for catchup, especially foundry services and assembly/test, simply by volume of research papers coming out of China vs. the volume of research papers in life sciences. No technological breakthrough is required, merely parity.