Some time ago I read 'I am a Strange Loop' by Douglas Hofstadter.
His style can appear pedantic but there is a core of succinct truth in his work. Hofstadter clearly accepts himself as a purely material being. He attempts to put his finger on what "I" means within this context.
The core of his explanation is that the Self must be generated within the atomic structure of the brain. "I" is a "loop" generated by the brain feeding its own output back into its own input. But it's no ordinary type of loop; not one that is constrained to repetitive, mundane processes. The complex and chaotic nature of the feeds creates something unique within the system: that which we call "me".
The unpredictable output of "loopy" systems is demonstrated in video feedback experiments, on which Hofstadter is keen. He gives other examples including Godelian mathematical anomalies and language experiments, which can be made to exhibit a similar type of capricious behaviour.
I picked up an older book in a charity shop some time after I had read "I am a Strange Loop" - "The Creative Loop" by Erich Harth. His theme is similar but perhaps easier to understand and I think he may have been influenced by Hofstadter's earlier work. Harth uses the analogy of a hall of mirrors to describe the Self. We're not always directly responding to the input of our senses, we're responding to our inner reflections of those inputs chaotically mixed with all the other inputs we have ever had, and all of their component reflections.
I like this explanation. All Hail the careenium. I accept my loopiness and revel in it.