Hi yrresnik,
In general, the top six schools are not necessarily going to give more weight to an applicant who simply expresses an interest in teaching/research in law (i.e. becoming a law professor).
However, applicants who can convincingly demonstrate (1) that they've done significant scholarly research in a law-related field, and (2) that they have a desire to use a legal education to expand their research into a specific area of interest that requires legal expertise, could certainly gain a leg up at any school (including the top six). NYU, for example, has a specific scholarship program geared toward applicants interested in legal academia. Yale, as another example, is well known for placing large numbers of its graduates into law teaching (upon completion of judicial clerkships and other academic fellowship programs). Chicago almost always has a few students who complete Ph.D. work in related fields at the school, alongside their J.D. programs.
The key to getting on these schools' radars for these purposes is not simply expression of interest, though. They're going to be looking for
demonstrated potential to become an academic: some significant scholarly research history, plus a demonstration of specific interest in an academic area that could launch a (legal) scholarly career. If you can identify and correspond with a professor at the school who shares an area of scholarly interest, that person could serve as a mentor during your law school years, helping you shape research projects and putting you in touch with opportunities to develop your teaching and research skills.
For additional help with the process of shaping your application to express your potential and interest in teaching and research, consider reaching out to one of our admission counselors:
https://www.powerscore.com/lsat/law-school-admissions/.
And do let us know if this triggers further questions. For now, I hope this helps!
Jeremy
Jeremy Press
LSAT Instructor and law school admissions consultant
Follow me on Twitter at:
https://twitter.com/JeremyLSAT