A Holographic Weyl Semimetal in an Effective Gauss--Bonnet Geometry
We study how an effective Gauss--Bonnet deformation of the thermal geometry changes the competition between the conducting Weyl-semimetal and insulating flavour phases of the probe D3/D7 model. The phases are represented by horizon-reaching and smoothly capped D7 embeddings, respectively, whose free energies exhibit a first-order transition. At the temperatures examined, positive Gauss--Bonnet coupling shifts coexistence toward larger flavour mass and expands the thermodynamically preferred Weyl-semimetal region, while negative coupling shifts the boundary in the opposite direction. The normalized zero-temperature transition remains unchanged. An on-shell analysis shows that the leading finite-temperature shift is largely explained by an effective rescaling of the thermal scale, opposed by an intrinsic fixed-horizon geometric contribution. The enlargement of the conducting phase does not imply stronger electrical response: the longitudinal and anomalous Hall conductivity jumps at coexistence can decrease, and the coupling response of the longitudinal jump reverses with temperature. The mass-dependent maximum of the longitudinal DC conductivity can also cease to occur on the thermodynamically preferred branch. Thus the geometric deformation changes both which phase is favored and how the Weyl-semimetal phase conducts.