Quantum oscillations in the heat capacity of Kondo insulator YbB12

Abstract

We observe the magnetic quantum oscillation in the heat capacity of the Kondo insulator YbB$_{12}$. The frequency of these oscillations $F = 670$ T, aligns with findings from magnetoresistance and torque magnetometry experiments for $μ_0 H > 35$ T in the Kondo insulating phase. Remarkably, the quantum oscillation amplitudes in the heat capacity are substantial, with $Δ\tilde{C}/T \approx$ 0.5 $\rm{mJ}$ $\rm{mol^{-1}K^{-2}}$ at 0.8 K, accounting for 13$\%$ of the known linear heat capacity coefficient $γ$. Double-peak structures of quantum-oscillation amplitudes due to the distribution function of fermions were identified and used to determine the value of the effective mass from the heat capacity, which agrees well with that from torque magnetometry. These observations support charge-neutral fermions contributing to the quantum oscillations in YbB$_{12}$.

Figures (7)

• Figure 1: (a) Heat capacity divided by temperature $C/T$ as a function of the magnetic field at 0.8 K displays a distinctive double-peak structure at a transition at $\mu_0 H \approx 20$ T and quantum oscillations above 35 T. (b) Resistivity $\rho_{xx}$ and the field derivative of torque $d\tau/dH$ as function of the magnetic field at 0.52 K and 0.85 K, respectively. Dashed lines mark the location of the transition at around 20 T and quantum oscillations at about 35 T. (c) $C/T$ as a function of the magnetic field at various temperatures.
• Figure 1: (a) A plot of the integral term $((E-E_F)/(k_B T))^2 df/dE$ versus energy at different temperatures. The distance between the peaks $\Delta B$ increases with temperature as $\Delta E=\Delta B dE/dB=4.8k_B T$. (b) The double peak structure of heat capacity divided by temperature $C/T$ at the Lifshitz transition at 0.43 K. The solid line shows the experimental data, and the dashed line represents the result of the fitting using Eqn. \ref{['HC_integral']}, assuming symmetric $D(E)$ as shown in (c). $B_1$ and $B_2$ mark the peak positions. (c) An illustration of the origin of the double peak structure in heat capacity. The green peak represents a symmetric density of state $D(E)\propto 1/\sqrt{E}$ and the orange curve shows the term $((E-E_F)/(k_B T))^2 df/dE$. The position of the DOS peak shifts with the applied magnetic field, and the convolution of the two terms produces double peaks observed in $C/T$ at the Lifshitz transition. At $B_1$ and $B_2$ the peak of $D(E)$ aligns with the maxima in the integral term. (d) An illustration of the asymmetric integral term $-(E-E_{\rm F})/(k_{\rm B}T) df/dE$ versus energy for thermopower.
• Figure 2: (a) The double peak structure in the heat capacity divided by temperature $C/T$ of the Lifshitz transition Xiang2022 at various temperatures. Dashed lines are fits using a single symmetric cusp-like $D(E)$ in a magnetic field, as shown in Extended Data Fig. \ref{['fig:SFigure1']}. The curves are shifted vertically for clarity. (b) The field positions of the double peaks are plotted as a function of temperature, with error bars indicating the uncertainty in defining the exact peak positions. (c) Temperature dependence of the field separation $\Delta B$ between the double peaks. The green solid line plots $\Delta B {\rm d}E/{\rm d}B=$4.8 $k_{\rm B} T$ expected from the term $-(E-E_F)^2{\rm d}f/{\rm d}E$. (d) Magnetic field dependence of thermopower in YbB$_{12}$ up to 31 T. The asymmetric peak splitting at around 20 T indicates a Lifshitz transition Xiang2022. The sign of the thermopower is consistent with electron-like.
• Figure 2: Top panel shows the oscillatory component of heat capacity $\Delta C/T$ at 0.8 K as a function of the magnetic field after the background subtraction. The peak positions are marked with $B_{1-4}$. The bottom panel plots the Landau level positions for $n=16$ (blue) and $n=17$ (green) with respect to the term $((E-E_F)/(k_B T))^2 df/dE$ at $B=B_{1-4}$, corresponding to the magnetic field value when one of the landau level peaks aligns with one maximum of the double peaks.
• Figure 3: (a) The oscillatory component of the heat capacity divided by temperature $\Delta C/T$ at various temperatures after subtracting the polynomial backgrounds. The curves are shifted vertically for clarity. The points mark the peak positions. (b) Magnetic field positions of the dominant peaks as a function of temperature. The lines are linear fits of the data. The error bars show the uncertainty of defining the peak positions. (c) Field dependence of the effective masses $m^*(39 ~\rm{T})=5.6 m_0$ and $m^*(41.4~\rm{T}) = 6.6 m_0$ from heat capacity compared to the effective masses obtained from the LK fits to the dHvA oscillation amplitudes in torque Xiang2018, where $m_0$ is the free electron mass.