Tunneling into and between helical edge states - fermionic approach

Abstract

We study four-terminal junction of spinless Luttinger liquid wires, which describes either a corner junction of two helical edges states of topological insulators or the tunneling from the spinful wire into the helical edge state. We use the fermionic representation and the scattering state formalism, in order to compute the renormalization group (RG) equations for the linear response conductances. We establish our approach by considering a junction between two possibly non-equivalent helical edge states and find an agreement with the earlier analysis of this situation. Tunneling from the tip of the spinful wire to the edge state is further analyzed which requires some modification of our formalism. In the latter case we demonstrate i) the existence of both fixed lines and conventional fixed points of RG equations, and ii) certain proportionality relations holding for conductances during renormalization. The scaling exponents and phase portraits are obtained in all cases.

10 pages, 6 figures

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Cited by in corpus (6)

• Tunneling Aharonov-Bohm interferometer on helical edge states
• Spin-polarized tunneling into helical edge states: asymmetry and conductances
• Tunable helical crystals
• Effective Hamiltonian of topologically protected qubit in a helical crystal
• Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium
• A non-magnetic mechanism of backscattering in helical edge states