Zero-Field Composite Fermi Liquid in Twisted Semiconductor Bilayers

Recent experiments have produced evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in the semiconductor moiré superlattice system $t{\mathrm{MoTe}}_2$. Here, we argue that a composite fermion description, already a unifying framework for the phenomenology of 2D electron gases at high magnetic fields, provides a similarly powerful perspective in this new context. To this end, we present exact diagonalization evidence for composite Fermi liquid states at zero magnetic field in $t{\mathrm{MoTe}}_2$ at fillings $n=\frac{1}{2}$ and $n=\frac{3}{4}$. We dub these non-Fermi liquid metals anomalous composite Fermi liquids (ACFLs), and we argue that they play a central organizing role in the FQAH phase diagram. We proceed to develop a long wavelength theory for this ACFL state that offers concrete experimental predictions upon doping the composite Fermi sea, including a Jain sequence of FQAH states and a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system.

Figure 1

Anomalous composite Fermi liquid and and ferromagnetic Fermi liquid in semiconductor moiré bands. Low-lying spectrum as a function of many-body crystal momentum (see the Supplemental Material [49] for elaboration) of the (a) half-filled LLL and (b) lowest moiré band at a twist angle $\theta =2°$ with a Coulomb interaction. Occupation numbers of the Bloch states averaged over the degenerate ground state manifolds denoted GS, (see main text), $n(\mathit{k})\equiv {\sum }_{i\in \text{GS}}⟨{\mathrm{\Psi }}_i|c_{\mathit{k}}^{†}{c}_{\mathit{k}}|{\mathrm{\Psi }}_i⟩/N_{\text{GS}}$, are also shown. Full spin polarization is assumed in the LLL whereas all possible $S_z$ sectors are considered in the moiré band. Analogous data at (c) $\theta =2°$, $n=\frac{3}{4}$ and (d) $\theta =4.5°$, $n=\frac{1}{2}$. In each case the lowest 20 energy levels within each $(\mathit{k},S_z)$ sector are shown. In (b)–(d) a dielectric constant $\epsilon =10$ is used.

Figure 2

Jain sequence states at $n=\frac{2}{5}$, $\frac{3}{5}$. (a) Low-lying spectrum of the LLL with Coulomb interaction on a torus with 30 flux quanta at $\nu =\frac{2}{5}$ and $\frac{3}{5}$. (b) Corresponding data for the lowest moiré band at $\theta =2°$, $\epsilon =10$. The moiré ground state manifold has the same momentum quantum numbers and approximate fivefold topological ground state degeneracy as the LLL. In each case the lowest three fully spin polarized states in each momentum sector are shown.

Figure 3

Commensurability oscillations. Schematic of cyclotron orbits at special commensurate values. For $j\ge 5$, $\frac{1}{2}<{\rho }_e<\frac{3}{5}$.