Coherent Tunneling in Exciton Condensates of Bilayer Quantum Hall Systems

Abstract

Due to strong interlayer correlations, the bilayer quantum Hall system is a single coherent system as a whole rather than a weakly-coupled set of two independent systems, which makes conventional tunnelling theories inapplicable. In this paper, we develop a theory of interlayer tunnelling in coherent exciton condensates of bilayer quantum Hall systems at total filling factor ${\nu }_T=1$. One of the most important consequences of our theory is that the zero-bias interlayer tunnelling conductance peak is strongly enhanced, but fundamentally finite even at zero temperature. We explicitly compute the height of the conductance peak as a function of interlayer distance, which is compared with experiment. It is emphasized that the interlayer distance dependence of the conductance peak is one of the key properties distinguishing between the spontaneous coherence due to many-body effects of the Coulomb interaction and the induced coherence due to the single-particle tunnelling gap. It is also emphasized that, though the strongly enhanced tunnelling conductance originates from the interlayer phase coherence, it is not the usual Josephson effect. We propose an experimental setup for the true Josephson effect in couterflowing current measurements for a coupled set of two bilayer quantum Hall systems, which is a more precise analogy with the real Josephson effect in superconductivity.

arXiv comment10 pages, 8 figures, Final version published in Phys. Rev. B

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• Coherence and Optical Emission from Bilayer Exciton Condensates
• Charge Imbalance and Bilayer 2D Electron Systems at ${\nu }_T=1$
• Coupling of Josephson Currents in Quantum Hall Bilayers
• Area dependence of interlayer tunneling in strongly correlated bilayer 2D electron systems at ${\nu }_T=1$
• Precursors to Exciton Condensation in Quantum Hall Bilayers
• Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene
• $s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu =1$
• Tunneling at ${\nu }_T=1$ in Quantum Hall Bilayers
• Flux Quantization Due to Monopole and Dipole Currents
• Superconductivity of electron-hole pairs in a bilayer graphene system in a quantizing magnetic field
• Josephson effect as signature of electron-hole superfluidity in bilayers of van der Waals heterostructures
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Pseudospin Transfer Torques in Semiconductor Electron Bilayers
• Quantum Hall bilayer in dipole representation
• Successive electron-vortex binding in quantum Hall bilayers at $\nu =\frac{1}{4}+\frac{3}{4}$
• Single-parameter variational wavefunctions for quantum Hall bilayers
• Designing exciton-condensate Josephson junction in quantum Hall heterostructures
• Role of the compensating current in the weak Josphson coupling regime: An extended study on excitonic Josephson junctions