Correlation and transport phenomena in topological nodal-loop semimetals

Abstract

We study the unique physical properties of topological nodal-loop semimetals protected by the coexistence of time-reversal and inversion symmetries with negligible spin-orbit coupling. We argue that strong correlation effects occur at the surface of such systems for relatively small Hubbard interaction $U$, due to the narrow bandwidth of the "drumhead" surface states. In the Hartree-Fock approximation, at small $U$ we obtain a surface ferromagnetic phase through a continuous quantum phase transition characterized by the surface-mode divergence of the spin susceptibility, while the bulk states remain very robust against local interactions and remain non-ordered. At slightly increased interaction strength, the system quickly changes from a surface ferromagnetic phase to a surface charge-ordered phase through a first-order transition. When Rashba-type spin-orbit coupling is applied to the surface states, a canted ferromagnetic phase occurs at the surface for intermediate values of $U$. The quantum critical behavior of the surface ferromagnetic transition is nontrivial in the sense that the surface spin order parameter couple to Fermi-surface excitations from both surface and bulk states. This leads to unconventional Landau damping and consequently a naïve dynamical critical exponent $z\approx 1$ when the Fermi level is close to the bulk nodal energy. We also show that, already without interactions, quantum oscillations arise due to bulk states, despite the absence of a Fermi surface when the chemical potential is tuned to the energy of the nodal loop. The bulk magnetic susceptibility diverges logarithmically whenever the nodal loop exactly overlaps with a quantized magnetic orbit in the bulk Brillouin zone. These correlation and transport phenomena are unique signatures of nodal loop states.

8+7 pages, 7 figures, submitted to PRB

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• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Strong spin-orbit splitting on Bi surfaces
• Low energy effective theory of Fermi surface coupled with U(1) gauge field in 2+1 dimensions
• Weyl semimetals from noncentrosymmetric topological insulators
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Universal phase diagrams for the quantum spin Hall systems

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