Tunable Kondo effect in a bilayer graphene quantum channel

TL;DR

This study demonstrates a tunable Kondo effect in a gate-defined bilayer graphene QPC, revealing a transition between SU(2) and SU(4) Kondo regimes as the Kondo energy $E_K$ becomes comparable to and exceeds the spin–orbit gap $\Delta_{SO}$. By gating and applying modest magnetic fields, the authors observe a 0.7-like anomaly, a zero-bias Kondo peak that splits under in-plane fields, and universal scaling of $G$ with $T$ consistent with SU(2) and SU(4) Kondo physics, with $T_K$ spanning roughly $0.5$ to $2.4\ \mathrm{K}$. Out-of-plane fields lift valley degeneracy, hinting at a valley-polarized SU(2) Kondo regime, while large in-plane fields reveal detailed spin- and valley-resolved subband structure via a large valley $g$-factor. The work establishes BLG QPCs as a versatile platform for exploring many-body spin–valley physics, including transitions between SU(4) and SU(2) Kondo states and potential valley-polarized Kondo phenomena.

Abstract

The interaction between itinerant electrons and localized spins is key to a wide range of electronic phenomena. Of particular interest is the regime where the interacting electrons exhibit both spin and valley degeneracy, resulting in SU(4) Kondo physics. However, this regime is challenging to realize in typical mesoscopic systems because it requires a strong interaction between electrons, resulting in a Kondo temperature ($T_\mathrm{K}$) significantly larger than the spin and valley splittings. Here, we present conductance measurements of a quantum point contact (QPC) in bilayer graphene (BLG). Beyond the expected quantized conductance plateaus, which reflect spin and valley degeneracy, we observe an additional subband, known as `0.7 anomaly' exhibiting signatures of Kondo physics and a $T_\mathrm{K}$ ranging from approximately 0.5 up to 2.4 K at zero magnetic field, corresponding to Kondo energies between 40 and 200 $μ$eV. Given that the spin-orbit splitting in BLG is between 40 and 80 $μ$eV, we argue that these results are consistent with a transition between four-fold degenerate SU(4) and two-fold degenerate spin-valley locked SU(2) Kondo effects. Furthermore, we break the valley degeneracy of the lowest subband by an out-of-plane magnetic field and show that Kondo signatures remain present, indicating a transition from SU(4) to a valley-polarized SU(2) Kondo effect, and showing the versatility of BLG QPCs for exploring many-body effects.

Figures (13)

• Figure 1: Gate-defined quantum point contact in BLG. (a) Device geometry: The BLG is encapsulated between atomically flat hBN insulating layers and the graphite back gate (bg) is used in combination with two Ti/Au split gates (sg) to form the QPC. The channel gate (ch) is placed on an Al$_2$O$_3$ insulating layer to tune the QPC electrochemical potential. The contacts to the BLG are labeled as source (s) and drain (d). The circuit corresponds to the measurement geometry where $\tilde{V}$ and $V_\mathrm{sd}{}$ are the applied ac and dc voltages, respectively. The ammeter (A) measures the source-drain current. (b) Two-terminal conductance ($G_\mathrm{2T}$) as a function of the bg ($V_\mathrm{bg}$) and sg ($V_\mathrm{sg}$) voltages. The QPC conductance $G$ is obtained from $G_\mathrm{2T}$ by subtracting the contact and ammeter resistances. (c) Channel-gate voltage ($V_\mathrm{ch}$) dependence of $G$ at $V_\mathrm{bg}$$=1.5$ and $3$ V, corresponding to the green and black dots in panel b, respectively.
• Figure 2: Bias spectroscopy of the first subband at $V_\mathrm{bg}$$=3$ V. (a) and (c) Bias dependence of the differential QPC conductance at $B_\mathrm{z}{}=0$ and 0.6 T, respectively. The line color indicates $V_\mathrm{ch}$, as shown by the color bar in a, and the horizontal line at $G=0.7\times 4e^2/h$ indicates the expected position of the bias-induced plateau. (b) and (d) Transconductance ($dG/dV_\mathrm{ch}{}$) obtained from panels a and c, respectively. The brighter regions correspond to the subbands and the darker to the plateaus, as indicated by the color bar. The white digits in b correspond to the subband numbers. The left inset in d shows the lowest subband, which is valley-split by $\Delta E_\mathrm{Z}\approx 1$ meV as shown by the light blue diamond.
• Figure 3: Temperature dependence of the QPC conductance at $V_\mathrm{bg}{}=3$ V, zero $V_\mathrm{sd}$ and zero applied magnetic field. (a) $V_\mathrm{ch}$-dependence of $G$ at different temperatures, indicated by the line colors. (b) and (c) Universal scaling of the (b) SU(2), and (c) SU(4) Kondo function $u_\mathrm{K}$ (see main text) from the fits. In panels b and c, the black line is the expected theoretical value. The dots, colored according to the color bar in b, are obtained from fits to the $G$ vs. $T$ data from panel a. (d) Low-bias zoom to the bias spectroscopy in Fig. \ref{['Figure2']}a showing the progressive widening of the ZBP. The red trace corresponds to $V_\mathrm{ch}{}\approx-7.18$ V, while the other traces are color-coded according to the inset colorbar. (e) SU(2) and SU(4) $T_\mathrm{K}$. At and below the gray patch, which represents the SO gap, SU(2) Kondo is expected. SU(4) is expected above the SO gap. (f) $T$-dependence of the ZBP. The line color indicates $T$, as shown by the color bar.
• Figure 4: In-plane magnetic field effect at $V_\mathrm{bg}{}=3$ V. (a) QPC conductance and (b) transconductance vs. $V_\mathrm{ch}$ and different $B_\mathrm{\parallel}$. The latter has been smoothed using a running average window of 15 points. The lines in both panels are color-coded according to the color bar in a. The squares indicate the $0.7$ subband, the triangles and stars indicate the spin splitting of the $1$ and $2\times 4 e^2/h$ subbands, respectively. (c) Bias dependence of the differential QPC conductance at $B_\mathrm{\parallel}$$=3$ T. The line color indicates $V_\mathrm{ch}$, as shown by the color bar, and the horizontal line at $G=0.7\times 4e^2/h$ serves as a guide to compare with Fig. \ref{['Figure2']}. The triangles indicate the accumulation of traces used to estimate the spin $g$-factor of the $4e^2/h$ subband. The black rectangle highlights the splitting of the zero-bias peak.
• Figure S1: (a) Schematic of the measured device where the graphite back gate (bg) and bilayer graphene (BLG) are black, the hexagonal boron nitride (hBN) flakes are light blue, the Ti/Au split gates (sg), the channel gate (ch), and the source (s) and drain (d) contacts are golden, and the Al$_2$O$_3$ layer under ch is semi-transparent. (b) Atomic force microscopy of the device before channel gate preparation. Its approximate position is indicated by the rectangle. The scale bar is 0.6 $\mu$m.