I'm an undergraduate student majoring in physics and mathematics, who is preparing to begin applying to graduate programs in physics. In doing so, I've reached out to a few people for advice, and I've received a lot of conflicting opinions on various topics. Among them is the importance of reaching out to potential PI's, and how much doing so potentially affects my admissions odds.
Firstly, how and when should one reach out to a potential PI? I've "cold-called" professors plenty of times under other circumstances, however I'm not sure what the etiquette here is. Should I write multiple faculty members in the department? What and how much information should I provide about myself? Does it make sense to reach out to faculty at highly-competitive "reach" schools (I'm planning to apply to Columbia, for instance, and I imagine they receive tons of emails, so it seems a bit silly to "cold-call" random Ivy-league faculty)?
Secondly, how much does it affect my odds of admission? I've read and been told that communicating with a faculty member can effectively guarantee admission, if you can "sell yourself" such that they are interested in taking you on as (and presumably funding you as) a student. Is this true? Does not reaching out to potential PI's put me at a significant disadvantage?
I'm not sure what the etiquette is here, nor how much effort I should be putting into this.