Quantum phase transitions and critical phenomena in graphene
Final Report Abstract
We have investigated phase transitions and critical phenomena in Fermi systems in which the conduction and valence bands touch or cross at isolated points in the Brillouin zone. The most prominent two-dimensional example of such a system is given by graphene with its two linear band crossing points. Using a symmetry classification and effective field theory methods, we have studied the phase diagram of such Dirac systems and were able to quantify the critical behavior of the continuous transitions from the semimetallic to the charge-density-wave and antiferromagnetic phases, respectively, in terms of the critical exponents and v, and the corrections-to-scaling exponent w. We have also examined the transition between the two insulating phases, the nature of which turned out to decisively depend on the number of Dirac cones in the spectrum and can be either discontinuous or continuous, with a universal multicritical behavior in the latter case. A second class of such zero-gap semiconductors we investigated is given by the threedimensional systems with quadratic band touching points. Examples are given by HgTe, a-Sn, and the pyrochlore iridate Pr2lr207. We were able to show that the non-Fermi liquid state that was previously theoretically predicted to govern the low-temperature behavior in these systems becomes unstable towards a nematic state in which a topologically nontrivial band gap opens up. At low temperatures, very pure HgTe and a-Sn, and possibly also Pr2Ir207, should hence display a transition towards a topological insulator state with dynamically-induced band gap—a topological Mott insulator phase. Experimentally, the transition should reveal itself through a singularity in the thermodynamic observables, the emergence of the Dirac-like surface states together with their characteristic quantum Hall effect, as well as through anisotropic transport properties.
Publications
- Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach, Phys. Rev. B 89, 205403 (2014)
L. Janssen and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.89.205403) - Topological Mott Insulator in Three-Dimensional Systems with Quadratic Band Touching, Phys. Rev. Lett. 113, 106401 (2014)
I. F. Herbut and L. Janssen
(See online at https://doi.org/10.1103/PhysRevLett.113.106401) - Mott multicriticality of Dirac electrons in graphene, Phys. Rev. B 92, 035429 (2015)
L. Glassen, I. F. Herbut, L. Janssen, and M. M. Scherer
(See online at https://doi.org/10.1103/PhysRevB.92.035429) - Nematic quantum criticality in three-dimensional Fermi system with quadratic band touching, Phys. Rev. B 92, 045117 (2015)
L. Janssen and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.92.045117)
