Thermodynamic topology of dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity

In this study, we investigate the thermodynamic topology of the high-dimensional dyonic AdS black holes with quasitopological electromagnetism in the Einstein-Gauss-Bonnet background. We first examine the topological charge connected to the critical point and find that the two conventional critical points $CP_{1},CP_{2}$ of the black hole are physical critical point, and the novel critical point $CP_{3}$ that lacks the capability to minimize the Gibbs free energy ($\alpha=0.5$). The critical points $CP_{1}$ and $CP_{2}$ are observed to occur at the maximum extreme points of temperature in the isobaric curve, while the critical point $CP_{3}$, emerges at the minimum extreme points of temperature. Furthermore, the number of phases at the novel critical point exhibits an upward trend, followed by a subsequent decline at the conventional critical points. With the increase of the coupling constant ($\alpha = 1$), although the system has three critical points, only the conventional $CP_{1}$ is a (physical) critical point, and the conventional $CP_{2}$ serves as the phase annihilation point. This means that the coupling constant $\alpha$ has significant impact on the phase structure. Additionally, we regard dyonic AdS black holes as a topological defect within the thermodynamic space, our findings indicate that alterations in pressure can result in the system exhibiting distinct points of generation and annihilation. However, the total topological number of black holes in different dimensions is $1$, the system shares a similar topological classification as the charged RN-AdS black holes. The discovery we have made provides a crucial component in understanding the thermodynamic topology of dyonic AdS black holes.