Detecting Symmetry Breaking in Magic Angle Graphene Using Scanning Tunneling Microscopy

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a “cascade” of spontaneous symmetry-breaking transitions, sparking interest in the potential relationship between symmetry breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here, we show how atomically resolved scanning tunneling microscopy can be used as a fingerprint of symmetry-breaking order. By analyzing the pattern of sublattice polarization and “Kekulé” distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the “Kramers intervalley coherent state,” which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.

Figure 1

Spectroscopy calculation results for the self-consistent HF solutions of spinless NSM, ${\mathrm{KIVC}}_0$, and ${\mathrm{KIVC}}_B$ states at the CNP ($\nu =0$) and IKS states at $\nu =-1$. We present (a) total LDOS $\rho (\mathbf{r};z)$ (b) total FTLDOS $\rho (\mathbf{q};z)$, and (c) total and Kekulé DOS $\rho (z=E+i\eta )$ signals for the bottom layer $AA$ region of MATBG. The signals are normalized by their maximum. For FTLDOS, logarithm is taken on the normalized signals. Cyan lines in (c) indicate the scanning energy, and the energy range was chosen to show the occupied states. White dots in (a) denote carbon lattice sites.

Figure 2

(a) Total current density of KIVC eigenstates [Eq. (5)] $|\mathbf{k}=M_m,n=\pm 1⟩$. $M_m$ is the $M$ point of the mini-BZ. Lime (pink) dots are the $A$ ($B$) sublattice sites. (b) Schematic representation of the energy levels of KIVC. From left to right: the basis states; KIVC eigenstates; and perturbation eigenstates [Eq. (4)]. Red (blue) corresponds to superposed states with predominantly $\mathrm{Chern}+1$ ($-1$) character. (c) Kekulé charge density of $|\mathbf{k}=M_m,\mathrm{occ},n=\pm 1⟩$.

Figure 3

(a) and (b) Self-consistent HF band structure and DOS of ${\mathrm{KIVC}}_0$ at CNP and $\eta =0.5\mathrm{meV}$. The yellow patch denotes the spectrum within valence bands probed at $\eta =0.1\mathrm{meV}$ in (c) and (d). (c) Band structure of ${\mathrm{KIVC}}_B$ at $E_B=0.1\mathrm{meV}$. The area of the blue (red) dots corresponds to the degree of positive (negative) Chern polarization of the wave function. (d) Total and Kekulé DOS of ${\mathrm{KIVC}}_0$ and ${\mathrm{KIVC}}_B$ along with Chern polarization-weighted total DOS.