Electron-electron scattering dominated electrical and magnetotransport properties in the quasi-two-dimensional Fermi liquid single-crystal $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$

Recently, the oxide semiconductor $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ nanoplates with an ultrahigh mobility demonstrated superior ultrafast photoelectronic properties of which physical origins are hotly studied theoretically and experimentally. Here we grew the $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystals via the chemical vapor transport method. The $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystal exhibits an ultrahigh Hall mobility $(\sim 2.24\times {10}^5\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}\mathrm{at}2\mathrm{K})$ and a giant magnetoresistance $\left(\mathrm{MR}\sim 0.9\times {10}^4\%\mathrm{at}9\mathrm{T}\mathrm{and}2\mathrm{K}\right)$ that are comparable with those in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ nanoplates. MR data clearly shows Shubnikov–de Haas (SdH) oscillations. Systematic analysis of SdH oscillation verifies that the electrical carrier in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is a conventional Schrödinger fermion and that the Fermi surface of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is quasi-two-dimensional-like. Remarkably, the resistivity of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is quadratically dependent on temperature from 2 to 300 K, inferring the electron-electron scattering in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$. Kohler's rule analysis of temperature-dependent MR verifies only electron-electron scattering dominated by the electrical and magnetotransport properties of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$. Combining first-principle calculations and empirical Landau Fermi liquid theory, we substantiate that the Fermi surface of the electron in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is an elongated ellipsoid, as well as that the electron-electron interaction and screening length of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ are estimated as 7.49 eV and 5.53 Å, respectively. These values are quite large among the conventional doped semiconductors. Our study may shed more light on the physical origin of the ultrafast photoelectric response of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$.

Figure 1

(a) Schematic of the CVT growth equipment used in our experiments. (b) The x-ray diffraction (XRD) of the $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystal sample can be indexed as $\left(002l\right)$ reflection. The inset is the typical photograph of the as-grown $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ single crystals. (c) SEM image and Bi (purple), O (orange) and Se (azure) element mapping images of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystals.

Figure 2

(a) The temperature-dependent resistivity ${\rho }_{xx}\left(2–300\mathrm{K}\right)$ of electron-doped $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ single crystal under the zero and 9 T magnetic field ($B$). The top left inset is the fit with the Landau Fermi liquid model $\rho \left(T\right)={\rho }_o+\alpha ·T^2$. The bottom right inset is the schematic diagram showing the electrodes configuration used in transport measurements. (b) The magnetic field $B$ dependent MR of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystals at various temperatures with $B//c$ axis. The inset is Kohler's plot of the MR data from 2 to 300 K using $\mathrm{MR}=F\left(B/{\rho }_0\right)$. (c) Hall resistivity ${\rho }_{xy}$ as functions of $B//c$ axis for the $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystal with temperatures raised from 2 to 300 K. (d) The temperature dependent charge carrier densities $n$ and carrier mobility μ (semilog plot) of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystals.

Figure 3

(a) The curves of $\mathrm{\Delta }{\sigma }_{xx}$ of SdH oscillation after background subtraction vs $1/B$ for $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystal at different temperatures. (b) The corresponding FFT spectra of Fig. 3. Only a single oscillation frequency $(F=124.5\mathrm{T})$ is observed. (c) The temperature-dependent amplitude of a single SdH oscillation fitted at 8.28 T. The red solid line is the fitted result using the Lifshitz-Kosevich (LK) formula. The inset is the Dingle curve. The band mass of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ is 0.$128{\mathrm{m}}_o$. (d) Linear fitting of minimum conductivity $\mathrm{\Delta }{\sigma }_{xx}$ as a function of the Landau level index $n$ gives a nonzero intercept of −0.019 at 2 K. The nearly zero Berry phase suggests that electrical carriers of $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ are conventional Schrödinger fermions.

Figure 4

(a) The $B$ dependence of MR measured at 2 K for the $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$ crystal by tilting $B$ from the $c$ axis $\left(\perp E\right)$ to the direction parallel to $E$ (in-plane). The inset is the schematic of the experiment. (b) The polar diagram of the angle-dependent MR measured at 2 K under various $B$. (c) The $1/B$ dependent SdH oscillations after subtracting background at 2 K with the $B$ tilting from the $c$ axis $\left(\perp E\right)$ to the direction parallel to $E$ (in-plane). (d) The corresponding FFT spectra of the misaligned angle θ dependent SdH oscillations. The inset is the θ-dependent oscillation frequency $F$ extracted from the FFT analysis of SdH curves. One can see that $F$ is proportional to $1/\cos \theta$.

Figure 5

(a) The Fermi surface of electrons in $\mathrm{B}{\mathrm{i}}_2{\mathrm{O}}_2\mathrm{Se}$. Long axis of ellipse is paralleled to the $c$-axis. The Fermi surface is determined by comparison of the maximum cross section of Fermi surface at $E_F=0.170\mathrm{eV}$ determined by $c$ axis SdH oscillation. (b) The dependence of theoretical oscillation frequency $F$ on misaligned angle θ. θ is the misaligned angle between the $c$-axis and $B$. Black dots are theoretical data and the red line is the fitting of $F\sim 1/\cos \left(\theta \right)$. Obviously, it is in agreement with experimental observation [Fig. 4].