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Register a new userInterlayer coherent composite Fermi liquid phase in quantum Hall bilayers
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Composite fermions have played a seminal role in understanding the quantum Hall effect, particularly the formation of a compressible `composite Fermi liquid (CFL) at filling factor nu = 1/2. Here we suggest that in multi-layer systems interlayer Coulomb repulsion can similarly generate `metallic behavior of composite fermions between layers, even if the electrons remain insulating. Specifically, we propose that a quantum Hall bilayer with nu = 1/2 per layer at intermediate layer separation may host such an interlayer coherent CFL, driven by exciton condensation of composite fermions. This phase has a number of remarkable properties: the presence of `bonding and `antibonding composite Fermi seas, compressible behavior with respect to symmetric currents, and fractional quantum Hall behavior in the counterflow channel. Quantum oscillations associated with the Fermi seas give rise to a new series of incompressible states at fillings nu = p/[2(p pm 1)] per layer (p an integer), which is a bilayer analogue of the Jain sequence.
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Half-filled Landau levels admit the theoretically powerful fermion-vortex duality but longstanding puzzles remain in their experimental realization as $ u_T=1$ quantum Hall bilayers, further complicated by Zheng et als recent numerical discovery of an unknown phase at intermediate layer spacing. Here we propose that half-filled quantum Hall bilayers ($ u_T=1$) at intermediate values of the interlayer distance $d/ell_B$ enter a phase with textit{paired exciton condensation}. This phase shows signatures analogous to the condensate of interlayer excitons (electrons bound to opposite-layer holes) well-known for small $d$ but importantly condenses only exciton pairs. To study it theoretically we derive an effective Hamiltonian for bosonic excitons $b_k$ and show that the single-boson condensate suddenly vanishes for $d$ above a critical $d_{c1} approx 0.95 l_B$. The nonzero condensation fraction $n_0=langle b(0) rangle ^2$ at $d_{c1}$ suggests that the phase stiffness remains nonzero for a range of $d>d_{c1}$ via an intermediate phase of paired-exciton condensation, exhibiting $langle bb rangle eq 0$ while $langle b rangle =0$. Motivated by these results we derive a $K$-matrix description of the paired exciton condensates topological properties from composite boson theory. The elementary charged excitation is a half meron with $frac{1}{4}$ charge and fractional self-statistics $theta_s=frac{pi}{16}$. Finally we argue for an equivalent description via the $d=infty$ limit through topological charge-$4e$ pairing of composite fermions. We suggest graphene double layers should access this phase and propose various experimental signatures, including an Ising transition $T_{Ising}$ below the Berezinskii-Kosterlitz-Thouless transition $T_{BKT}$ at $d sim d_{c1}$.
Composite Fermi liquid metals arise at certain special filling fractions in the quantum Hall regime and play an important role as parent states of gapped states with quantized Hall response. They have been successfully described by the Halperin-Lee-Read (HLR) theory of a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with a Chern-Simons term. However, the validity of the HLR description when the microscopic system is restricted to a single Landau has not been clear. Here for the specific case of bosons at filling $ u = 1$, we build on earlier work from the 1990s to formulate a low energy description that takes the form of a {em non-commutative} field theory. This theory has a Fermi surface of composite fermions coupled to a $U(1)$ gauge field with no Chern-Simons term but with the feature that all fields are defined in a non-commutative spacetime. An approximate mapping of the long wavelength, small amplitude gauge fluctuations yields a commutative effective field theory which, remarkably, takes the HLR form but with microscopic parameters correctly determined by the interaction strength. Extensions to some other composite fermi liquids, and to other related states of matter are discussed.
Interlayer tunneling measurements in the strongly correlated bilayer quantized Hall phase at $ u_T=1$ are reported. The maximum, or critical current for tunneling at $ u_T=1$, is shown to be a well-defined global property of the coherent phase, insensitive to extrinsic circuit effects and the precise configuration used to measure it, but also exhibiting a surprising scaling behavior with temperature. Comparisons between the experimentally observed tunneling characteristics and a recent theory are favorable at high temperatures, but not at low temperatures where the tunneling closely resembles the dc Josephson effect. The zero-bias tunneling resistance becomes extremely small at low temperatures, vastly less than that observed at zero magnetic field, but nonetheless remains finite. The temperature dependence of this tunneling resistance is similar to that of the ordinary in-plane resistivity of the quantum Hall phase.
SrRuO$_3$ heterostructures grown in the (111) direction are a rare example of thin film ferromagnets. By means of density functional theory plus dynamical mean field theory we show that the half-metallic ferromagnetic state with an ordered magnetic moment of 2$mu_{B}$/Ru survives the ultimate dimensional confinement down to a bilayer, even at elevated temperatures of 500$,$K. In the minority channel, the spin-orbit coupling opens a gap at the linear band crossing corresponding to $frac34$ filling of the $t_{2g}$ shell. We demonstrate that the respective state is Haldanes quantum anomalous Hall state with Chern number $C$=1, without an external magnetic field or magnetic impurities.
Motivated by the recent proposal of realizing an SU(4) Hubbard model on triangular moire superlattices, we present a DMRG study of an $SU(4)$ spin model obtained in the limit of large repulsion for integer filling $ u_T=1,3$. We retain terms in the $t/U$ expansion up to $O(frac{t^3}{U^2})$ order, that generates nearest-neighbor exchange $J$, as well as an additional three-site ring exchange term, $K$, which is absent in the SU(2) S=1/2 case. For filling $ u_T=3$, when increasing the three-site ring exchange term $K sim frac{t^3}{U^2}$, we identify three different phases: a spin-symmetric crystal, an $SU(4)_1$ chiral spin liquid (CSL) and a decoupled one dimensional chain (DC) phase. The CSL phase exists at intermediate coupling: $U/t in [11.3,,22.9]$. The sign of $K$ is crucial to stabilizing the CSL and the DC phase. For filling $ u_T=1$ with the opposite sign of $K$, the spin-symmetric crystal phase survives to very large $K$. We propose to search for the CSL phase in moire bilayers. For example, in twisted AB stacked transition metal dichalcogenide (TMD) bilayers, the $SU(4)$ spin is formed by layer pseudospin combined with the real spin (locked to valley). The layer pseudospin carries an electric dipole moment in $z$ direction, thus the CSL is really a dipole-spin liquid, with quantum fluctuations in both the electric moment and magnetic moment . The CSL phase spontaneously breaks the time reversal symmetry and shows a quantum anomalous Hall effect in spin transport and dipole transport. Smoking gun evidence for the CSL could be obtained through measurement of the quantized dipole Hall effect in counter-flow transport.
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