Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

Abstract

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid. * These two authors contributed equally. arXiv:1712.02357v2 [cond-mat.str-el]

Tunneling density of states, correlation energy, and spin polarization in the fractional quantum Hall regime

“…The experimental I − V curve is not strictly Gaussian of course, since it must vanish at zero bias voltage and is known to be strong suppressed at low bias due to the Coulomb gap effect 11,18,20 and skewed at high bias, possibly due to the influence of disorder. Although the Coulomb gap at low bias has some very interesting 30,31 features also seen in experiment 11 , the sum rule moments on which we focus are dominated by the behavior of the I −V curve near its peak, and are largely uninfluenced by low bias behavior. We attempt to extract physics from the I − V curves by fitting them to the equation…”

Effect of Magnetization on the Tunneling Anomaly in Compressible Quantum Hall States

“…We have arrived at the same results for the tunneling action using a complementary, semi-classical hydrodynamic description for the spreading charge [8] in an accompanying paper [27]. We now consider the various parametric regimes for the tunneling action.…”

“…Optimizing the above action over τ gives an optimal time τ * (V) that characterizes the charge accommodation time, and the tunneling conductivity is given by ∼ exp[−S(τ * (V))/ ]. We have arrived at the same results for the tunneling action using a complementary, semi-classical hydrodynamic description for the spreading charge [8] in an accompanying paper [27]. We now consider the various parametric regimes for the tunneling action.…”

A magnetically-induced Coulomb gap in graphene due to electron-electron interactions

“…4. In the DQW devices, it has been suggested that both inter-and intra-layer e-e interactions can affect the Coulomb gap 29,33,43,44 . In GaAs heterostructures the ratio l B /d ~1 when B = 1 T, so that it is difficult to differentiate between the inter-and intra-layer origin of the Coulomb gap for coherent tunnelling in those devices.…”