Magnetic field switching of Weyl semimetal associated with quantum criticality in one-dimensional extended Su-Schrieffer-Heeger chain

Graphene/silicon nanoribbons (G/SiNRs) provide low-dimensional platforms to engineer the topological characters for carbon/silicon-based electronics. Herein, we propose a one-dimensional (1D) extended Su-Schrieffer-Heeger (SSH) model to describe the G/SiNRs with a superlattice consisting of two interacting dimers, in which the topological quantum phase transition (QPT) and quantum criticality are investigated. The trivial band insulator transition into a nontrivial topological insulator via a critical Dirac semimetal is revealed, the self-duality of which is manifested by the zero value of Grüneisen ratio (GR) irrelevant of temperature. In a magnetic field, the time-reversal symmetry is broken such that the Weyl semimetal appears and is switched by a critical quadratic contact point semimetal with gap closing, at which the quantum criticality is not self-dual with GR Γ∼± T^{− 1}. Furthermore, the quantum critical scaling is done to analyze the quantum criticality, which provides a new clue to detect the QPT. The low-temperature specific heat demonstrates the low-lying excitation of gapped and gapless topological quantum phases explicitly.