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Register a new userInterlayer Interactions and the Fermi Energy of Bilayer Composite Fermion Metals
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James P. Eisenstein
Publication date
2018
fields
Physics
and research's language is
English
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When two 2D electron gas layers, each at Landau level filling factor $ u=1/2$, are close together a condensate of interlayer excitons emerges at low temperature. Although the excitonic phase is qualitatively well understood, the incoherent phase just above the critical layer separation is not. Using a combination of interlayer tunneling spectroscopy and conventional transport, we explore the incoherent phase in samples both near the phase boundary and further from it. In the more closely spaced bilayers we find the electronic spectral functions narrower and the Fermi energy of the $ u = 1/2$ composite fermion metal smaller than in the more widely separated bilayers. We attribute these effects to a softening of the intralayer Coulomb interaction due to interlayer screening.
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We study the effect of the Chern-Simons gauge fields on the possible transition from two decoupled composite fermion metals to the interlayer coherent composite fermion state proposed by Alicea et al. [Phys. Rev. Lett. 103, 256403 (2009)] in a symmetrically doped quantum Hall bilayer with total Landau level filling fraction $ u_{tot} = 1$. In this transition, interlayer Coulomb repulsion leads to excitonic condensation of composite fermions which are then free to tunnel coherently between layers. We find that this coherent tunneling is strongly suppressed by the layer-dependent Aharonov-Bohm phases experienced by composite fermions as they propagate through the fluctuating gauge fields in the system. This suppression is analyzed by treating these gauge fluctuations within the random-phase approximation and calculating their contribution to the energy cost for forming an exciton condensate of composite fermions. This energy cost leads to (1) an increase in the critical interlayer repulsion needed to drive the transition; and (2) a discontinuous jump in the energy gaps to out-of-phase excitations (i.e., excitations involving currents with opposite signs in the two layers) at the transition.
Composite fermion metal states emerge in quantum Hall bilayers at total Landau level filling factor $ u_T$=1 when the tunneling gap collapses by application of in-plane components of the external magnetic field. Evidence of this transformation is found in the continua of spin excitations observed by inelastic light scattering below the spin-wave mode at the Zeeman energy. The low-lying spin modes are interpreted as quasiparticle excitations with simultaneous changes in spin orientation and composite fermion Landau level index.
The Hall viscosity has been proposed as a topological property of incompressible fractional quantum Hall states and can be evaluated as Berry curvature. This paper reports on the Hall viscosities of composite-fermion Fermi seas at $ u=1/m$, where $m$ is even for fermions and odd for bosons. A well-defined value for the Hall viscosity is not obtained by viewing the $1/m$ composite-fermion Fermi seas as the $nrightarrow infty$ limit of the Jain $ u=n/(nmpm 1)$ states, whose Hall viscosities $(pm n+m)hbar rho/4$ ($rho$ is the two-dimensional density) approach $pm infty$ in the limit $nrightarrow infty$. A direct calculation shows that the Hall viscosities of the composite-fermion Fermi sea states are finite, and also relatively stable with system size variation, although they are not topologically quantized in the entire $tau$ space. I find that the $ u=1/2$ composite-fermion Fermi sea wave function for a square torus yields a Hall viscosity that is expected from particle-hole symmetry and is also consistent with the orbital spin of $1/2$ for Dirac composite fermions. I compare my numerical results with some theoretical conjectures.
The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sublattice symmetry, or both.
The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high field regime, the eight-fold degeneracy in the zero energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding filling factors $ u=$0, 1, 2, & 3. Measurements of the activation energy gap in tilted magnetic fields suggest that the Landau level splitting at the newly formed $ u=$1, 2, & 3 filling factors are independent of spin, consistent with the formation of a quantum Hall ferromagnet. In addition, measurements taken at the $ u$ = 0 charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.
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