Two-dimensional Dirac semimetal with tilted Dirac cone has recently attracted increasing interest. Tilt of Dirac cone can be realized in a number of materials, including deformed graphene, surface state of topological crystalline insulator, and certain organic compound. We study how Dirac cone tilting affects the low-energy properties by presenting a renormalization group analysis of the Coulomb interaction and quenched disorder. Random scalar potential or random vector potential along the tilting direction cannot exist on its own as it always dynamically generates a new type of disorder, which dominates at low energies and turns the system into a compressible diffusive metal. Consequently, the fermions acquire a finite disorder scattering rate. Moreover, the isolated band-touching point is replaced by a bulk Fermi arc in the Brillouin zone. These results are not qualitatively changed when the Coulomb interaction is incorporated. In comparison, random mass and random vector potential along the non-tilting direction can exist individually, without generating other types of disorder. They both suppress tilt at low energies, and do not produce bulk Fermi arc. Upon taking the Coulomb interaction into account, the system enters into a stable quantum critical state, in which the fermion field acquires a finite anomalous dimension but the dynamical exponent z = 1. These results indicate that Dirac cone tilt does lead to some qualitatively different low-energy properties comparing to the untilted system.

No abstract

No abstract

In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the Dyson-Schwinger equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.

In previous theoretical studies of phonon-mediated superconductors, the electron-phonon coupling is treated by solving the Migdal-Eliashberg equations under the bare vertex approximation, whereas the effect of Coulomb repulsion is incorporated by introducing one single pseudopotential parameter. These two approximations become unreliable in low carrier-density superconductors in which the vertex corrections are not small and the Coulomb interaction is poorly screened. Here, we shall go beyond these two approximations and employ the Dyson-Schwinger equation approach to handle the interplay of electron-phonon interaction and Coulomb interaction in a self-consistent way. We first derive the exact Dyson-Schwinger integral equation of the full electron propagator. Such an equation contains several unknown single-particle propagators and fermion-boson vertex functions, and thus seems to be intractable. To solve this difficulty, we further derive a number of identities satisfied by all the relevant propagators and vertex functions and then use these identities to show that the exact Dyson-Schwinger equation of electron propagator is actually self-closed. This selfclosed equation takes into account not only all the vertex corrections, but also the mutual influence between electron-phonon interaction and Coulomb interaction. Solving it by using proper numerical methods leads to the superconducting temperature Tc and other quantities. As an application of the approach, we compute the Tc of the interfacial superconductivity realized in the one-unit-cell FeSe/SrTiO3 system. We find that Tc can be strongly influenced by the vertex corrections and the competition between phonon-mediated attraction and Coulomb repulsion.