Seebeck effect on a weak link between Fermi and non-Fermi liquids

We propose a model describing Seebeck effect on a weak link between two quantum systems with fine-tunable ground states of Fermi and non-Fermi liquid origin. The experimental realization of the model can be achieved by utilizing the quantum devices operating in the integer quantum Hall regime [Z. Iftikhar et al., Nature (London) 526, 233 (2015)] designed for detection of macroscopic quantum charged states in multichannel Kondo systems. We present a theory of thermoelectric transport through hybrid quantum devices constructed from quantum-dot–quantum-point-contact building blocks. We discuss pronounced effects in the temperature and gate voltage dependence of thermoelectric power associated with a competition between Fermi and non-Fermi liquid behaviors. High controllability of the device allows to fine tune the system to different regimes described by multichannel and multi-impurity Kondo models.

Figure 1

Schematic representation of a hybrid metal-semi- conductor single electron transistor quantum device: two quantum dots QD1 and QD2 (cross-hatched areas) are connected through a tunnel barrier (blue dashed lines) controlled by a split gate (light green boxes). Each QD being a metallic island with continuous electron density of states is electrically coupled to a two-dimensional electron gas (2DEG) denoted by pink and gray areas inside circles and strongly coupled to large electrodes through the quantum point contacts (QPC) labeled by A, B, C, and D. The QPCs are fine tuned by field effects in split gates (not shown) to different regimes to provide a weak coupling between (i) two coupled Fermi liquids; (ii) a Fermi liquid coupled to a non-Fermi liquid; (iii) two coupled non-Fermi liquids (see Sec. 4). The QPCs are formed by the 2DEG (pink and gray areas inside parabolas) placed in a perpendicular magnetic field to achieve a regime of the integer quantum Hall with $\nu =2$ [27]. The current flows along two spin-polarized chiral spin edge channels. The inner edge channel (not shown) is fully reflected and the outer edge channel (shown by red dashed line with arrow) is partially transmitted through almost transparent QPCs (see insert showing zoomed in area of QPC). The pink color stands for the higher temperature $T+\mathrm{\Delta }T$ compared to the reference temperature $T$ of the gray electrode.

Figure 2

(Left) Plots of thermopower $eS$ as a function of $N=N_1=N_2$ and temperature $T/E_C$ ($E_{C1}=E_{C2}=E_C$) with $|r_1|=\sqrt{0.001},\left|r_2\right|=\sqrt{0.1}$ (a) for the FL-FL regime (top). (b) For the FL-NFL regime (middle). (c) For the NFL-NFL regime (bottom). (Right) Plots of the minimum of thermopower $eS$ as a function of temperature $T/E_C$ for different left/right asymmetries $|r_1/r_2|=0.01$ (black curve), $|r_1/r_2|=0.3$ (red curve), and $|r_1/r_2|=0.6$ (blue curve) with $|r_2|=\sqrt{0.1}$ for the regimes of the left panels correspondingly.

Figure 3

Sketch of “Bell test” thermoelectric experiment: central red circle denotes “hot” QD weakly coupled by left and right tunnel barriers (blue dashed lines) to the “cold” QD-QPC devices. All other notations are identical to those used in Fig. 1.

Figure 4

Schematic representation of a hybrid metal-semiconductor device engineering a strong coupling of two quantum dots. A peanut-shape 2DEG area is formed by opening a conducting channel between dots (central quantum point contact at $x=0$) by the split gate (light green boxes). All other notations are the same as in Fig. 1. The hybrid device can be fine tuned to different multichannel ($1\to 4$ channel) Kondo regimes of a single quantum impurity (fully transparent central QPC) and different regimes of multichannel ($1\to 2$ channel) double quantum impurity setups (see detailed discussion in Sec. 5). Fine tuning the split gates at positions A-B (at $x=-L$) and/or C-D (at $x=L$) to a weak (tunnel) regime and heating one of the peripheral contacts allows to measure a thermoelectric transport on a weak link between one-to-three channel Kondo regimes.