On the topological characterization of two-dimensional phase transitions

Xiao-Ping Liu, Yuan Zhou, Yi-Fei Wang +1 more

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.

Lucien Gilles Benguigui, Lawrence S. Schulman

M. A. Contínentino

Andrea Kazemi Nava, C. A. Perroni, Reinhold Egger +2 more

We induce and study a topological dynamical phase transition between two planar superconducting phases. Using the Lindblad equation to account for the interactions of Bogoliubov quasiparticles among themselves and with the fluctuations of the superconducting order parameter, we derive the relaxation dynamics of the order parameter. To characterize the phase transition, we compute the fidelity and the spin-Hall conductance of the open system. Our approach provides crucial information for experimental implementations, such as the dependence of the critical time on the system-bath coupling.

Xuebing Luo, Kezhao Zhou, Wu‐Ming Liu +2 more

We investigate the fidelity susceptibility (FS) of a two-dimensional spin-orbit-coupled (SOC) Fermi superfluid and the topological phase transition driven by a Zeeman field in the perspective of its ground state wave function. Without Zeeman coupling, FS shows additional features characterizing the BCS-BEC crossover induced by SOC. In the presence of a Zeeman field, the topological phase transition is explored using both FS and the topological invariant. In particular, we obtain the analytical result of the topological invariant which explicitly demonstrates that the topological phase transition corresponds to a sudden change of the ground state wave function. Consequently, FS diverges at the phase transition point with its critical behavior being $\ensuremath{\chi}\ensuremath{\propto}\text{ln}|h\ensuremath{-}{h}_{c}|$ . Based on this observation, we conclude that the topological phase transition can be detected by measuring the momentum distribution in cold atom experiments.

Robert-Jan Slager