Novel Quantum Criticality in Two Dimensional Topological Phase transitions.

Gil Young Cho,Eun-Gook Moon

doi:10.1038/srep19198

Gil Young Cho, Eun-Gook Moon

Open Access

https://doi.org/10.1038/srep19198

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Abstract

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.

Highlights

Unique interplay between the Coulomb interaction and electronic critical modes enforces the anisotropic renormalization of the Coulomb interaction and marginally modified electronic excitation
Since correlation and fluctuation are enhanced in lower dimensions, one may expect stronger interplay between the Coulomb interaction and critical modes in a topological phase transition, and we find the novel quantum criticality in a class of 2d topological quantum phase transitions
The topological nature of the transition is captured by the change in the Berry curvature of the wave-function depending on the sign of M, and different patterns of opening up band gaps at separate Dirac points represent different topological insulator phases when supplemented with proper symmetries

Summary

OPEN Novel Quantum Criticality in Two

Dimensional Topological Phase transitions received: 02 September 2015 accepted: 08 December 2015. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. We discover a novel quantum criticality at the phase transition by incorporating the 1 long range Coulomb interaction. Long-range 1 Coulomb interaction between electrons induces striking screening effects near the topological phase transitiorns. Quasi-particles lose their stability due to the Coulomb interaction and the ground state becomes quantum critical non-Fermi liquid with emergent full rotational symmetry in quadratic band touching semimetals, which is near three dimensional (3d) topological insulator[8]. The anisotropic marginal quantum criticality is out of intricate interplay between the long range Coulomb interaction in 2d and the critical electron modes, and we emphasize its striking properties by calculating physical observables

Models with Coulomb Interaction

The beta functions around the novel fixed point are dα dl

Experimental Signatures

Following the straightforward calculation in supplementary information

Discussion and Conclusion

Additional Information