Thermoelectric Transport in a Three-Channel Charge Kondo Circuit

We theoretically investigate the thermoelectric transport through a circuit implementation of the three-channel charge Kondo model quantum simulator [Z. Iftikhar et al., Science 360, 1315 (2018)]. The universal temperature scaling law of the Seebeck coefficient is computed perturbatively approaching the non-Fermi liquid strong coupling fixed point using the Abelian bosonization technique. The predicted $T^{1/3}\log T$ scaling behavior of the thermoelectric power sheds light on the properties of $Z_3$ emerging parafermions and gives access to exploring prefractionalized zero modes in the quantum transport experiments. We discuss a generalization of approach for investigating a multichannel Kondo problem with emergent $Z_N\to Z_M$ crossovers between “weak” non-Fermi liquid regimes corresponding to different low-temperature fixed points.

Figure 1

Schematic of three channel charge Kondo (3CK) setup. A central metallic island, also known as quantum dot (QD), is connected to four electrodes formed by two dimensional electron gas. The state in QD is characterized by the isospin $\sigma =\downarrow$. The states in the electrodes are characterized by the isospin $\sigma =\uparrow$. The left (orange) electrode is heated to the temperature $T+\mathrm{\Delta }T$ and connected to the rest of the setup through a tunnel contact (red dashed lines). The reference temperature of the QD and three blue electrodes is $T$. The yellow plunger gate is used to control a mesoscopic Coulomb blockade in the QD. The setup is fine tuned by an external magnetic field to the integer quantum Hall regime $\nu =2$. The current propagates along spin-polarized edge channels (red solid lines with arrows). Only one relevant (outer) chiral edge channel is shown. The transparencies of the quantum point contacts ${\mathrm{QPC}}_1\text{−}{\mathrm{QPC}}_3$ (narrow blue constrictions) are controlled by the surface split gates (magenta boxes in insert). Black dashed lines depict three independent $x$ axes with origins located in the middle of constrictions (QD boundary). Zoomed in edge state at one of the QPCs and weak backscattering (red dotted lines) are shown in the lower inset. The identical thermovoltages are applied across the tunnel contacts to nullify the net electric current through the device. Upper inset schematically shows a renormalization group flow for 3CK. The unstable strong coupling fixed point at $G_1=G_2=G_3\approx 0.69e^2/h$ corresponds to the 3CK non-Fermi-liquid regime.