Cascades in transport and optical conductivity of Twisted Bilayer Graphene

Abstract

Using a combined Dynamical Mean Field Theory and Hartree (DMFT+H) calculation we study the transport and optical properties of the 8-band heavy fermion model for Twisted Bilayer Graphene (TBG) in the normal state. We find resistive states around integer fillings which resemble the ones observed in transport experiments. From a Drude fitting of the low frequency optical conductivity, we extract a very strongly doping-dependent Drude weight and scattering rate, resetting at the integers. For most dopings, particularly above the integers, the Drude scattering rate is high but notably smaller than that of the local electrons. This highlights the important role of itinerant electrons in the transport properties, despite their limited spectral weight on the flat bands. At far infrared frequencies, the optical conductivity exhibits cascades characterized by highly asymmetric resets of the intensity and oscillations in the interband peak frequencies.

Figures (8)

• Figure 1: (a) Doping and energy dependent DOS, (b) inverse compressibility and (c) dc conductivity of TBG versus doping $\nu$. (d) Spectral weight at the Fermi level at CNP within the first Brillouin zone showing small pockets close to $\Gamma$. We highlight momenta $\Gamma$, M, K and k$_{\Gamma-K}$ at which the doping dependence spectral weight is plotted in Fig. \ref{['fig:Fig3']}(e). (e) Zoom of the low energy DOS for $\nu=1$ at temperatures T=5.8 K and T=0.7 K. (f) DOS at the Fermi level versus doping, including the total DOS (black), the AA$_p$ DOS (orange) and the itinerant orbitals DOS (blue). The quantities displayed in (a)-(f) have been obtained within the DMFT+H calculations. (g) Non-interacting band structure corresponding to the 1.08$^o$ TBG studied.
• Figure 2: (a) Low frequency DMFT+H optical conductivity versus doping and energy. (b) Drude weight and (c) scattering rate obtained from the fitting of the optical conductivity to a Drude model. In (c) the Drude scattering rate is compared to the one obtained from the real frequency DMFT self-energy of the local AAp electrons $\hbar \Gamma_{\rm{AAp}}=-2\Sigma(\omega=0)$.
• Figure 3: (a) DMFT+H optical conductivity showing resets in the intensity at integer fillings, oscillations in the frequency at which the intensity peaks. (b)-(c) Optical spectrum respectively in the absence of interactions and in the Hartree approximation.(d) Spectral weight $A({\bf{k}},w)$ from the DMFT+H calculations at doping $\nu=0, 0.21, 0.5, 1.05, 1.88 ~\rm{and}~3.5$ as a function of momentum; and (e) Spectral weight $A({\bf{k}},w)$ as a function of doping $\nu$ at fixed momenta. From left to right: $K$, the k$_{k-\Gamma}$ point situated along the $K-\Gamma$ direction, $\Gamma$, and $M$, all of them marked in Fig. \ref{['fig:Fig1']}(d). The colorbar in (d) is also valid for (e).
• Figure S1: (a) Non-interacting band structure obtained from the continuum model (black) and the 8 orbital fitting (blue). (b) Density-density interactions between the orbitals of the effective 8-orbital model used in the calculation as a function of the distance between their centers. (c) Orbital decomposition of the non-interacting bands, distinguishing the four types of orbitals in the model. (d) Decomposition of the non- interacting bands into strongly correlated AA$_p$ orbitals and less correlated lc orbitals.
• Figure S2: (a) and (b) Band structure for the 1.08$^\circ$ and $w_0/w_1=0.7$ twist angle TBG in the Hartree approximation corresponding to $\nu$=1.0 and $\nu$=3.5 calculated using the same interactions as in the DMFT+H calculations. (c), (e) and (g) Orbital resolved density of states for AA$_p$ and $\it lc$ orbitals, dc conductivity and low frequency optical conductivity, respectively, as a function of doping $\nu$ in the absence of interactions. (d), (f) and (h) Same in the Hartree approximation.