So far, the longest reach 'native' E-mount lens is the upcoming FE70-300mm F4.5-5.6 G OSS lens...it debuts in a few weeks (May 4) and will give you a respectable 450mm equivalent reach. If you need more, you'll have to switch over to using adapters, which on the A6000 will render the focus pretty slow with just about all adapters except the LA-EA2 and LA-EA4 from Sony, which have their own focus systems built in and doesn't use the camera's focus system...those adapters can be paired with any Alpha A-mount lens like the 70-400mm G, Minolta 300, 400, or 600mm, Sony 500mm, Tamron 150-600mm, etc.
I recently replaced my A6000 with the newer A6300 - on the A6000 I used the FE70-200mm F4 as a primary birding and wildlife lens to back up my DSLR...I've got the 70-300mm lens on order as soon as it comes out, and I've also been using the lighter and smaller LA-EA3 adapter on the A6300 with the Tamron 150-600mm lens and it works pretty well too - but that adapter and lens doesn't work well on the A6000, only on the A6300.
Hope that helps!
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses