Emergent chirality in multi-lead Luttinger-liquid junctions out of equilibrium

Abstract

We study charge transport through $N$-lead junctions ($N\ge 3$) of spinless Luttinger liquid wires with bias voltages applied to Fermi-liquid reservoirs. In particular, we consider a Y junction, which is a setup characteristic of the tunneling experiment. In this setup, the strength of electron-electron interactions in one of the arms ("tunneling tip") is different from that in the other two arms (which form together the "main wire"). For a generic single-particle $S$ matrix of the junction, we find that the bias voltage $V$ applied---even symmetrically---to the main wire generates a current proportional to $|V|$ in the tip wire. We identify two mechanisms of this nonequilibrium-induced "emergent chirality" in a setup characterized by the time-reversal and parity symmetric Hamiltonian of the junction. These are: (i) the emergence of an effective magnetic flux, which breaks time-reversal symmetry, and (ii) the emergence of parity-breaking asymmetry of the setup, both proportional to the interaction strength and the sign of the voltage. The current in the tip wire generated by mechanism (i) is reminiscent of the Hall current in the linear response of a system the Hamiltonian of which breaks time-reversal symmetry; however, in the absence of any magnetic field or a local magnetic moment. Similarly, mechanism (ii) can be thought of as an emergent "photogalvanic effect"; however, in the presence of inversion symmetry within the main wire. The nonequilibrium chirality implies a rectification of the current in the tip when the main wire is biased by $ac$ voltage.

16 pages, 3 figures, comments and references added

References in corpus (12)

• Conductance through a potential barrier embedded in a Luttinger liquid: nonuniversal scaling at strong coupling
• Tunneling into a Luttinger liquid revisited
• Oscillatory non-linear conductance of an interacting quantum wire with an impurity
• Signature of the electron-electron interaction in the magnetic field dependence of nonlinear I-V characteristics in mesoscopic conductors
• Chiral Y junction of quantum spin chains
• Quantum spin circulator in Y junctions of Heisenberg chains
• Transport properties of a two-lead Luttinger liquid junction out of equilibrium: fermionic representation
• A fermionic approach to tunneling through junctions of multiple quantum wires
• Rectification in Y-junctions of Luttinger liquid wires
• Y-junction of Luttinger-liquid wires out of equilibrium
• Impurity entropy of junctions of multiple quantum wires
• Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

Cited by in corpus (1)

• Quantum wires with local particle loss: Transport manifestations of fluctuation-induced effects