Interlayer Tunneling in Double-Layer Quantum Hall Pseudoferromagnets

We show that the interlayer tunneling $I-V$ in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder, and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a “derivative” feature at $V_B\left(B_{\parallel }\right)=2\mathrm{}\pi ħ{\mathrm{vB}}_{\parallel }d/e{\phi }_0$, which gives a direct measurement of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state.