Noise in the Helical Edge Channel Anisotropically Coupled to a Local Spin

Abstract

We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin S = 1/2 of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poisson noise of the full current I at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages eV ≫ T is frequency-independent. Both the noise and the backscattering current I_bs saturate at voltageindependent values. Finally, if the Hamiltonian contains all types of non-spin-conserving scattering, the noise at high voltages becomes frequency-dependent again. At low frequencies, its ratio to 2eI_bs is larger than 1 and may reach 2 in the limit I_bs→0. At high frequencies, it tends to 1.