Optical Conductivity as a Probe of the Interaction-Driven Metal in Rhombohedral Trilayer Graphene

Abstract

Study of the strongly correlated states in van der Waals heterostructures is one of the central topics in modern condensed matter physics. Among these, the rhombohedral trilayer graphene (RTG) occupies a prominent place since it hosts a variety of interaction-driven phases, with the metallic ones yielding exotic superconducting orders upon doping. Motivated by these experimental findings, we show within the framework of the low-energy Dirac theory that the optical conductivity can distinguish different candidates for a paramagnetic metallic ground state in this system. In particular, this observable shows a single peak in the fully gapped valence-bond state. On the other hand, the bond-current state features two pronounced peaks in the optical conductivity as the probing frequency increases. Finally, the rotational symmetry breaking charge-density wave exhibits a minimal conductivity with the value independent of the amplitude of the order parameter, which corresponds precisely to the splitting of the two cubic nodal points at the two valleys into two triplets of the band touching points featuring linearly dispersing quasiparticles. These features represent the smoking gun signatures of different candidate order parameters for the paramagnetic metallic ground state, which should motivate further experimental studies of the RTG.

Keywords: electron-electron interactions; optical conductivity; trilayer graphene.

Figure 1

Real part of the optical conductivity (in units of $e^2/\hslash$) in the collisionless regime for: (a) the valence-bond order (VBO); (b) the bond-current order (BCO); (c) smectic charge-density wave (sCDW), respectively, given by Equations (6), (8), and (13), at the neutrality point $\mu =0$ and at $T=0$. u and $\Delta$ are given in units of the bandwidth scale t, see also the discussion after Equation (1). In panels (a,b), the green dashed line corresponds to the universal optical conductivity for the non-interacting spinless RTG in the collisionless regime, ${\sigma }_0=3/8$.

Figure 2

The density of states (DOS) in the candidate paramagnetic states. (a) valence-bond order (VBO); (b) bond-current order (BCO); (c) smectic charge-density wave (sCDW). The DOS in the three phases is given in Equations (7), (11), and (S69) in the SI. The energy (E) is in units of the bandwidth (t), see also Figure 1. u and $\Delta$ are given in units of t. The inset in (c) corresponds to the DOS for the noninteracting case, where the low-energy DOS scales as ${\left|E\right|}^{-1/3}$.

Figure 3

The band structure for the noninteracting Hamiltonian given by Equation (1) (left panel), where the pairs of degenerate bands corresponding to the same valley are superimposed. In the smectic charge-density wave with the order parameter ${\mathsf{\Gamma }}_{\rho 0}$, $\rho =1,2$, the two cubic band touching points split into six points, with the triplets featuring opposite vorticities $\pm \pi$ (right panel). Notice that the smectic charge-density wave order parameter mixes the two valleys and, therefore, also breaks the original lattice translation symmetry, besides the rotational one. The rotational symmetry is, however, restored close to each of the new band touching points.