Citationjet (C525/C526) - CJ I / II / III / IV
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 200; Flight Crew Total 8000; Flight Crew Type 1500
Fatigue; Situational Awareness
Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Unstabilized Approach; Inflight Event / Encounter CFTT / CFIT
Flight Crew Returned To Clearance; Flight Crew Became Reoriented
Human Factors
I was the pilot flying on this empty leg; Part 135 repositioning flight to ZZZ.  I was flying with a XX-year Part 121 pilot who was a recent upgrade and very new to Part 135 flying.  We were on our second week-long rotation together and had been working exceptionally well together on all our previous flights.  Because I had been to ZZZ before; i was pointing out all the important details of the area and what I knew of the airport and local ops prior to descending for the approach.  On this morning; we arrived over the ZZZ area to find a thick morning fog/haze layer over the entire area.  We were in hopes of visually acquiring the airport and making a visual approach; but were unable to see the airport until just before passing overhead; so we elected to shoot the RNAV (GPS) XX.  We had been cleared down to 10;000 feet or 11;000 feet before requesting the RNAV approach; but were instructed to climb and maintain 12;000 feet for the approach.  We were kept at 12;000 feet until crossing ZZZZZ intersection (the IAF).  Twelve thousand feet was significantly higher than the 10;600 feet the procedure calls for prior to ZZZZZ (from that direction) and the 7;500 foot minimum on the leg immediately to follow.  The MSA in the area is 12;400 feet; however.  We initiated a 2;000 FPM descent from 12;000 feet to get established.  I believe we crossed ZZZZZ1 at (or near) the published 7;500 feet. Because we picked up the field visually when crossing overhead and I knew the area (once established inbound) was flat and free of obstructions; coupled with the relatively good visibility near ZZZZZ2 intersection (GS intercept at 6;800 feet); I suppose I transitioned (erroneously) into a 'visual approach; backed up with the RNAV' mentality and; as a result; continued the steeper descent beyond ZZZZZ2 and wound up at least 500 feet low.  I believe the early morning hour; featureless terrain; relatively good (though reduced) visibility and knowledge that the mountainous areas were now behind us lulled me into a more relaxed; visual approach mindset.  The PM was heads-down and neither of us recognized how low we really were until we got an altitude alert from the aircraft.  At that point; I leveled off; recognized the fact we were just under 1;000 feet AGL at approximately 4 NM from the field climbed to correct the deficiency and elected to continue the approach; as we were now re-established with the field clearly in sight.  We immediately called the field and continued visually.  We waited until we were parked at the FBO before debriefing the flight.
Air Taxi First Officer reported not recognizing they had descended below final approach altitude. The flight crew returned to the correct altitude and continuing to landing.