I strongly recommend the book Murderous Minds: Exploring the Psychopathic Brain: Neurological Imaging and the Manifestation of Evil by Dean Haycock, which happens to be on sale right now for $1.99 (kindle edition). It will tell you what there is to know about the brain of the psychopath, but will also help you understand how to read about scientific studies, generally.
The book purports to be about the latest neurological evidence about psychopaths, and it is. Frankly, all of that information could be put into a magazine article. What makes this book truly worth reading is how Haycock takes apart the state of scientific research, specifically psychology and neurobiology, in order to help us understand the limitations of all these studies we read about in magazines and web blogs. What we come away with is a clearer understanding of how our scientific understanding is limited by ambition, funding, muddy definitions, and avenues that diverged decades ago.
A couple of years ago, I had lunch with one of my grandfather's graduate students*. He told me that what made my grandfather an excellent scientist was his instinctive ability to ask the right question. He added that it was something he'd tried unsuccessfully to teach his own graduate students over the decades. Of course, all of the burgeoning scientists were and are very smart. They can do the math, they can understand complex technical concepts and develop ingenious methodologies for measurements. But none of that really matters if it's not in service to the right question.
Haycock clearly lays all of this out, and it's all in service of helping us to understand what studies have been performed. For example, what is a psychopath, anyway? Is it someone who scores highly on the famous Hare test? Interestingly enough, the brains scans of Hare-defined psychopaths who have never been imprisoned ("successful psychopaths"**) differ from those who have ("unsuccessful psychopaths"). But even that's dodgy because almost all access to psychopaths has been through the prison system, leaving a teeny tiny sample of successful psychopaths to study. Or are they people who are diagnosed with anti-social personality disorder, according to the DSM (which in turns leads to a discussion of the latest edition was put together)? Are psychopathy, sociopathy and anti-social personality the same thing? Depends which researcher you ask, as there is no universal conclusion.
And that's just the tip of the iceberg. Haycock also explores issues like who has access to an MRI machine, and who can you get inside of it. He points to a meta-study that suggests neuro-psychological studies related to psychopathy have a median power of 21 — meaning that the samples are so small, only 21% of variations between subjects and controls are captured. And why are samples so small? Because the pressure to publish means researchers are more inclined to publish short and quick studies over longer and more involved ones...
Yes, you'll also learn about how the brain is structured, not to mention how scientists came to know what they think they know about the brain. You'll hear about a smattering of famous criminals, as it relates directly to the science (for instance, researchers don't think Jeffrey Dahmer was a psychopath! Depending on how you define a psychopath, of course). You'll even learn about how genes work.
I can't recommend this book enough.
*He's in semi-retirement, touring the world to raise awareness about the clear science behind climate change and working on increasing scientific literacy for this very subject. He works with the Bulletin of Atomic Scientists, a group dedicated to warning the public about impending or potential disaster.
** Should researchers even care about successful psychopaths, since there's no measured public cost of their psychopathy?