By my reading, the bark is photosynthetic in virtually any woody plant with smooth bark. A contrary example would be interesting.
The benefits of recycling: how photosynthetic bark can increase drought tolerance
[quote]In this issue of New Phytologist, Vandegehuchte et al. (pp. 998–1002) bring this process into the spotlight, and provide a compelling argument for why we should take more notice of that often-hidden, green layer of tissue that is ubiquitous beneath the smooth-bark surfaces of woody plants (Scott, 1907; Pfanz et al., 2002; Dima et al., 2006; Rosell et al., 2015).
...
The far more common stem photosynthetic syndrome is one in which chlorophyllous cells in the bark cortex refix a portion of the CO2 respired by the underlying tissues or carried into the stem segment by the transpiration stream as it diffuses from inside the stem to the atmosphere. This kind of stem photosynthetic activity likely takes place in all shrub and tree species that have smooth bark surfaces. In some of these species, smooth bark will be found on only the youngest stems, whereas in others (e.g. some Eucalyptus species) smooth bark will be maintained as the stems age and increase in diameter through successive shedding of dead bark layers (Pfanz et al., 2002; Cernusak & Hutley, 2011). [/quote]
In the case of Madrone that Richard mentions, the shedding of the bark may be sufficient to discourage lichens. ? I have seen lichens growing on dead branches of Madrone at Limestone Kiln Lighthouse on San Juan Is.
Adding 'scratch through bark' to my remember-to-do-in-the-field list. :)