Yes it’s old-fashioned, but good manners never go out of style.
Even if it’s not as popular as it once was, following up a job interview with a thank you note is always a good idea. A handwritten note with personalized stationery not only shows you’re courteous, but that you’re taking your job search seriously. And if you’re competing against similarly skilled and experienced candidates, a gesture such as a thank you note might just be the thing to put you over the top when decisions need to be made.
Not acknowledging your interviewer’s time with a quick “thank you” is inexcusable. Even if it’s just an email instead of a handwritten note, something is better than nothing.