| Özet: | We investigate the competition between the d-wave superconductivity and the nematic order in the high- T _c superconductor and examine the role played by the gapless fermionic degrees of freedom. Apart from the competitive interaction with the superconducting order parameter, the nematic order parameter couples strongly to gapless nodal quasiparticles. The interplay of these two kinds of interactions is analyzed by means of the renormalization group method. In case the fermionic degrees of freedom are entirely neglected, the competitive interaction between the two bosonic order parameters is strongly relevant and can lead to runaway behavior. However, these properties are fundamentally changed once the dynamics of the fermions are taken into account. At the nematic quantum critical point where an extreme fermion velocity anisotropy occurs, the superconducting and nematic order parameters are decoupled from each other. Consequently, the phase transitions are continuous and the d-wave superconductivity can coexist with the nematic order homogeneously. These results indicate that the gapless fermions can play an important role and should be carefully included in the theoretical description of competing orders.
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