Flat-Band-Induced Anomalous Anisotropic Charge Transport and Orbital Magnetism in Kagome Metal CoSn

For solids, the dispersionless flat band has long been recognized as an ideal platform for achieving intriguing quantum phases. However, experimental progress in revealing flat-band physics has so far been achieved mainly in artificially engineered systems represented as magic-angle twisted bilayer graphene. Here, we demonstrate the emergence of flat-band-dominated anomalous transport and magnetic behaviors in CoSn, a paramagnetic kagome-lattice compound. By combination of angle-resolved photoemission spectroscopy measurements and first-principles calculations, we reveal the existence of a kagome-lattice-derived flat band right around the Fermi level. Strikingly, the resistivity within the kagome lattice plane is more than one order of magnitude larger than the interplane one, in sharp contrast with conventional (quasi-) two-dimensional layered materials. Moreover, the magnetic susceptibility under the out-of-plane magnetic field is found to be much smaller as compared with the in-plane case, which is revealed to be arising from the introduction of a unique orbital diamagnetism. Systematic analyses reveal that these anomalous and giant anisotropies can be reasonably attributed to the unique properties of flat-band electrons, including large effective mass and self-localization of wave functions. Our results broaden the already fascinating flat-band physics, and demonstrate the feasibility of exploring them in natural solid-state materials in addition to artificial ones.

Figure 1

Electronic band structure of CoSn. (a) Schematic diagram of the wave function self-localization due to the destructive interference on the hexagons in the kagome lattice. (b) Bulk Brillouin zone of CoSn. (c) Perspective and top views of crystal structure of CoSn. The $x$, $y$, and $z$ axes point along the [100], [120], and [001] directions, respectively. (d) Calculated band structure and DOS with spin-orbit coupling. Note that the original Fermi level from the DFT calculation (black dashed line) needs to be shifted down by $\sim 120\mathrm{meV}$ (green dashed line) for better consistency with the ARPES results [see Figs. 1 and 1]. Three flat bands (FB1, 2, 3) and corresponding DOS peaks are marked by black arrows. (e),(g) Highly resolved ARPES results along the $L\text{−}H\text{−}A$ and the $\mathrm{\Gamma }\text{−}M$ directions with photon energies of 45 and 29 eV, respectively. (f),(h) Corresponding DFT band structures (after shifting down the Fermi level) with the inclusion of spin-orbit coupling, where the flat bands (FB1 and FB2) are highlighted in red.

Figure 2

Charge transport anisotropy. (a) Temperature-dependent longitudinal resistivity for the applied current parallel and perpendicular to the $ab$ kagome plane. (b) Typical energy dispersion of electronic band near the Fermi level along $k_x/k_y$ (top panel) and $k_z$ direction (bottom panel), respectively.

Figure 3

Magnetic susceptibility anisotropy. (a) Temperature-dependent magnetic susceptibility ($\chi$) for the applied magnetic field ($H$) parallel and perpendicular to the $ab$ kagome plane (denoted as in plane and out-of-plane, respectively). The intrinsic magnetic susceptibility after subtracting the contribution from magnetic impurities is also shown (green dots). (b) Magnetic susceptibility measured at different angles ($\theta$) between $H$ and $ab$ kagome plane for $T=36$ and 300 K. $\theta$ is better illustrated in the inset.(c) Typical NMR spectrum of ${}^{59}\mathrm{Co}$ under in-plane $H$. Three sets of NMR peaks (as marked by the numbers 1–3) are clearly seen, corresponding to three different sites of Co atoms as displayed in the insert (see more in Sec. 3 of the Supplemental Material [20]). (d) Temperature-dependent ${{}^{59}K}_s$ determined from the Knight shift. (e) $K_s-\chi$ plots.

Figure 4

Orbital diamagnetism in CoSn. (a) Calculated orbital moment of FB1 along the $L\text{−}H$ direction. The red arrows indicate the direction and magnitude of the magnetic moment. (b) Schematic diagram of the magnetic-field-induced diamagnetism in the kagome lattice.