Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene

Abstract

Rhombohedral trilayer graphene has recently emerged as a natural flat-band platform for studying interaction-driven symmetry-breaking phases. The displacement field (D) can further flatten the band to enhance the density of states, thereby controlling the electronic correlation that tips the energy balance between spin and valley degrees of freedom. To characterize the energy competition, chemical potential measurementa direct thermodynamic probe of Fermi surfacesis highly demanding to be conducted under a constant D. In this work, we characterize D-dependent isospin flavor polarization, where electronic states with isospin degeneracies of one and two can be identified. We also developed a method to measure the chemical potential at a fixed D, allowing for the extraction of energy variation during phase transitions. Furthermore, symmetry breaking could also be invoked in Landau levels, manifesting as quantum Hall ferromagnetism. Our work opens more opportunities for the thermodynamic characterization of displacement-field tuned van der Waals heterostructures.

Engineering the Band Topology in a Rhombohedral Trilayer Graphene Moiré Superlattice

“…To keep a constant displacement field penetrating the sample, the gate voltage on the other side of the sample (opposite the detector side) must be adjusted in situ. The detailed relation of adjustment can be found in ref and SI, Note 2. Furthermore, to determine the capacitance in the multilayer heterostructure, the chemical potential of the detector needs to be measured in a similar way (shown in SI, Note 3).…”

“…One is chemical potential (thermodynamic gap, Δ(T)) and the other is temperature dependence of resistance (activation gap, Δ(A)). Figure 3a depicts the measurement scheme of chemical potential, 34 where a bilayer graphene is taken as a detector (see details in SI, Note 2). Here the zero point of chemical potential of ABC-TLG μ ABC is equal to that of the CNP of BLG.…”

“…Here the electric field, as well as magic twist angles, controls the bandwidth and hence correlation of electrons residing in moiré bands. When the gain of exchange energy exceeds the cost of kinetic energy, a Stoner ferromagnetism ,,− of the internal degrees occurs, which may lift the valley degeneracy and results in a finite Chern number. Such an electrical switch of nontrivial topology provides the possibility for advanced engineering of the topological band.…”