Edge State Wave-Functions probed by Tunneling Spectroscopy*

Edge states have recently attracted a lot of attention due to their appearance at surfaces of topological materials and quantum Hall systems. Here we study quantum Hall edge states formed in a GaAs 2D electron gas using a tunnel-coupled quantum wire [1]. We use momentum-conserving tunneling spectroscopy to distinguish spatially overlapping states with different momenta. The tunneling conductance is proportional to the overlap between the edge state and the wire mode wave functions. Because of the varying shape of wire wave functions, their overlaps with edge states will also vary, resulting in a distinct sequence of tunneling conductance intensity patterns for different wire modes. We use self-consistent calculations to obtain the electrostatic potential at zero magnetic field and employ a Schrödinger solver to get the wave functions of the Landau level edge states and wire modes at a finite field. Conductance maps obtained using simulated wave functions agree very well with the measured data, thus confirming the calculated wave functions.

[1] “Evolution of the quantum Hall bulk spectrum into chiral edge states”, T. Patlatiuk, C. P. Scheller et al., Nature Communications 9, 3692, (2018)