Dimensionality tuning of heavy-fermion states in ultrathin CeSi2 films

Abstract

Dimensionality tuning is an important method to modify the electronic states of quantum materials. However, the mechanism of such tuning in heavy fermion systems and its connection with transport properties remain largely unexplored. Here by combining molecular beam epitaxy (MBE), in-situ angle-resolved photoemission spectroscopy (ARPES) and transport measurements, we study the electronic states of the heavy-fermion compound CeSi2 as a function of film thickness. In three dimensional thick films, our measurements reveal a dispersive Kondo peak at the Fermi level (EF) and satellite peaks originating from crystal electric field (CEF) excitations, characteristic of heavy fermion systems. For two-dimensional ultrathin films, the CEF satellites are largely suppressed while the ground-state Kondo peak at EF remains strong, although it develops at lower temperatures. Simultaneously, the maximum temperature Tmax of the magnetic resistivity, \r{ho}m(T), changes from ~100 K in thick films to ~35 K in ultrathin films. This can be attributed to the dimensionality driven reduction of CEF excitations during the Kondo process, in good agreement with spectroscopic results. Our work provides direct insight to understand the quantum confinement effects on strongly correlated 4f-electron systems and opens up new opportunities to explore emergent phenomena in two-dimensional heavy-fermion materials.

Figures (5)

• Figure 1: Growth and characterization of epitaxial CeSi$_{2}$ films on Si(100). (a) Three-dimensional view of one u.c. CeSi$_{2}$, which consists of four Ce-Si-Si trilayers stacked along [001] with alternating in-plane positions. (b) The three-dimensional bulk BZ (black) and the two-dimensional surface BZ (red). The surface BZ corresponds to the reciprocal lattice of the top layer and is often used for presenting the ARPES data. (c) RHEED patterns of a 2x1 reconstructed Si(100) substrate and an as-grown CeSi$_{2}$ film. (d) XRD scans for the bare Si(100) substrate (black curve) and two representative thick CeSi$_{2}$ films (red curves) taken along $z$. The substrate peaks are labelled with black asterisks and the film peaks are labelled in red. Note that the X-ray photons contain a tiny contribution from Cu $K$$_{\beta}$ lines, in addition to the dominant Cu $K$$_{\alpha}$ line. (e) A STEM image of a CeSi$_{2}$ film near the interface, taken with the HAADF mode. (f) A high-resolution view of atomic structures in the dashed light blue box of (e), taken with the iDPC mode. The observed Ce and Si atoms show good agreement with the expected atomic structures in CeSi$_{2}$ and Si, as indicated on the left. Here the in-plane direction is along the [120] direction of CeSi$_{2}$ and the [130] direction of Si. This indicates that the in-plane [100] direction of CeSi$_{2}$ aligns with the Si [110] direction, consistent with RHEED results. (g) Resistivity of a thick CeSi$_{2}$ film as a function of temperature. Inset is a zoom-in view at very low temperature, indicating the absence of magnetic order.
• Figure 2: Fermi surface and valence bands of thick CeSi$_{2}$ films and comparison with DFT calculations. (a) Constant-energy $k_x$-$k_y$ maps at $E$ = $E_F$ (0 eV), -0.5 eV and -0.8 eV. The surface BZ is indicated by light green box. The bulk bands ($\alpha$, $\beta$, $\gamma$ and $\gamma$') and surface states (SSs) are also labelled. (b) Constant-energy $k_x$-$k_y$ contours from DFT calculations of bulk CeSi$_{2}$ for comparison with (a). Contour colors indicate different Fermi velocities. (c) Large-range energy-momentum dispersion along $\bar{\Gamma}-\bar{X}-\bar{\Gamma}$. (d) DFT slab calculations, for comparison with (c). (e) Energy-momentum dispersion along $\bar{M}-\bar{X}-\bar{M}$ (left), in comparison with slab calculation (right). (f) Zoom-in view of band disperison (top panels) near $E_F$ along $\bar{X}-\bar{\Gamma}-\bar{X}$ and $\bar{M}-\bar{X}-\bar{M}$, in comparison with slab calculations (bottom panels). All experimental data were taken with 21.2 eV photons. Curve colors in (d-f) indicate surface (blue) or bulk (red) contributions. The calculated bulk bands in (b,d-f) include contributions from all $k_z$'s.
• Figure 3: The thickness-dependent electronic structure of CeSi$_{2}$ films along $\bar{X}-\bar{\Gamma}-\bar{X}$ at 6 K. (a) Thickness evolution of the valence bands taken with 21.2 eV photons. The valence bands from the Si(100) substrate are also shown for comparison. (b) Zoom-in view near $E_F$ from (a), from 1 u.c. to 4 u.c.. White arrows indicate the reversed U-shaped bands from hybridization between $4f$ and valence bands. (c) Top panel: a schematic plot of the quasiparticle dispersion as a result of hybridization between $4f$ (red curve) and valence (blue curve) bands in a periodic Anderson model. The pink and red diffuse lines indicate the CEF satellites above and below $E_F$. Bottom panel: a schematic diagram illustrating the origin of the CEF satellites. (d) Thickness evolution of the quasiparticle bands near $E_F$ taken with 40.8 eV photons, highlighting the $4f$ contributions. (e) The EDCs near $\bar{\Gamma}$ as a function of thickness, taken with 40.8 eV photons. The EDCs are integrated from -0.25 Å$^{-1}$ to 0.25 Å$^{-1}$. The ground-state Kondo peak and CEF satellites are labelled by red and black/blue arrows, respectively. The EDCs are shifted vertically for different thicknesses.
• Figure 4: Temperature evolution of the resistivity and $4f$ states. (a) The temperature-dependent resistivity for CeSi$_{2}$ films with different thicknesses. The absolute values of resistivity were multiplied by a prefactor shown for each curve, so that the data can be displayed properly in one plot. (b) The extracted magnetic part of resistivity $\rho_m$, from the data in (a). $\rho_m$ is obtained by subtracting the resistivity of LaSi$_{2}$ films from that of CeSi$_{2}$ films with identical thickness. Arrows indicate the positions of the maximum $T_{max}$. (c) The temperature-dependent EDCs near $\bar{\Gamma}$ for 16 u.c. (top) and 2 u.c. (bottom) films, taken with 40.8 eV photons. The EDCs are integrated from -0.25 Å$^{-1}$ to 0.25 Å$^{-1}$. (d) The EDCs from (c) divided by the RC-FDD function, for different films at 6 K, 50 K and 100 K, respectively. Only the energy region of $E <$ 6$k_B$$T$ is shown here. All data are offset vertically for display clarity.
• Figure 5: Schematic diagrams illustrating the dimensionality tuning of the temperature-dependent Kondo process in CeSi$_{2}$. From three to two dimensions, the many-body Kondo effect at intermediate temperatures becomes diminished due to reduced participations of excited CEF states (see middle panels), resulting in a decrease of $T_{max}$ in $\rho_m$($T$). Nevertheless, the heavy-fermion state at low temperatures, derived from the $|\pm5/2>$ ground-state doublet, remains robust in the two-dimensional limit.