  Super-Eddington mass accretion has been suggested as an efficient mechanism
to grow supermassive black holes (SMBHs). We investigate the imprint left by
the radiative efficiency of the super-Eddington accretion process on the
clustering of quasars using a new semi-analytic model of galaxy and quasar
formation based on large-volume cosmological $N$-body simulations. Our model
includes a simple model for the radiative efficiency of a quasar, which
imitates the effect of photon trapping for a high mass accretion rate. We find
that the model of radiative efficiency affects the relation between the quasar
luminosity and the quasar host halo mass. The quasar host halo mass has only
weak dependence on quasar luminosity when there is no upper limit for quasar
luminosity. On the other hand, it has significant dependence on quasar
luminosity when the quasar luminosity is limited by its Eddington luminosity.
In the latter case, the quasar bias also depends on the quasar luminosity, and
the quasar bias of bright quasars is in agreement with observations. Our
results suggest that the quasar clustering studies can provide a constraint on
the accretion disc model.
