Theory of Topological Quantum Phase Transitions in 3D Noncentrosymmetric Systems

We construct a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system’s codimension generally predicts the appearance of a stable metallic phase between the normal and topological insulators, it is shown that a direct topological phase transition between two insulators is also possible when an accidental band crossing occurs along directions with high crystalline symmetry. At the quantum critical point, the energy dispersion becomes quadratic along one direction while the dispersions along the other two orthogonal directions are linear, which manifests the zero chirality of the band touching point. Because of the anisotropic dispersion at quantum critical point, various thermodynamic and transport properties show unusual temperature dependence and anisotropic behaviors.

Figure 1

Generic phase diagrams, resulting from the ABC between the conduction and valence bands in 3D noncentrosymmetric systems. Here, $m$ indicates an external control parameter.

Figure 2

Evolution of the band structure, obtained from first-principles calculations, across the topological PT in BiTeI under pressure $P$. The energy dispersion of the conduction or valence bands near one of the BTPs in the ($p_1$, $p_2$) plane, which is normal to the high symmetry line embracing QCPs, is shown for (a) $P<P_c$, (b) $P=P_c$, and (c) $P>P_c$, respectively. Energy dispersions along the $p_1$ (red solid line), $p_2$ (green dash-dotted line), and $p_3$ (blue dashed line) directions are shown for (d) $P<P_c$, (e) $P=P_c$, and (f) $P>P_c$, respectively.

Figure 3

The trajectory of BTPs in 3D space and its 2D projections. (a) The curve is lying on a 2D plane leading to Fig. 1b. (b) The curve is moving in 3D space leading to Fig. 1c.