Weak antilocalization in quasi-two-dimensional electronic states of epitaxial LuSb thin films

Observation of large nonsaturating magnetoresistance in rare-earth monopnictides has raised enormous interest in understanding the role of its electronic structure. Here, by a combination of molecular-beam epitaxy, low-temperature transport, angle-resolved photoemission spectroscopy, and hybrid density functional theory we have unveiled the band structure of LuSb, where electron-hole compensation is identified as a mechanism responsible for large magnetoresistance in this topologically trivial compound. In contrast to bulk single crystal analogues, quasi-two-dimensional behavior is observed in our thin films for both electron and holelike carriers, indicative of dimensional confinement of the electronic states. Introduction of defects through growth parameter tuning results in the appearance of quantum interference effects at low temperatures, which has allowed us to identify the dominant inelastic scattering processes and elucidate the role of spin-orbit coupling. Our findings open up possibilities of band structure engineering and control of transport properties in rare-earth monopnictides via epitaxial synthesis.

Figure 1

Structural characterization of LuSb/GaSb (001) thin films. (a) HAADF-STEM image along the [110] zone axis. Inset shows the schematic of a proposed atomic arrangement across the GaSb-LuSb interface when viewed along the [110] direction. (b) RHEED images recorded after completion of growths of GaSb and LuSb epitaxial layers both along the [110] and $\left[1\overline{1}0\right]$ azimuths. (c) Out-of-plane $\theta -2\theta$ XRD scans establish that our thin film is single phase. Substrate peaks are marked by asterisks. Inset shows thickness fringes around the (002) LuSb Bragg peak.

Figure 2

Transport and fermiology in LuSb/GaSb (001) thin films. (a) Longitudinal resistivity as a function of temperature indicating three different regimes: (i) substrate dominated (blue background), (ii) LuSb dominated (brown background), (iii) LuSb dominated, where quantum corrections become significant (green background). Blue line is a fit to the data in region (ii), between 8 K and 70 K, to the Bloch-Grüneissen functional form. Inset shows the calculated Fermi surface of LuSb. Current is applied along the [110] crystallographic direction. (b) Longitudinal and Hall resistivity as a function of magnetic field perpendicular to the sample plane. Optical micrograph of a hall bar device is shown in the inset. (c) Fast Fourier transform (FFT) of the quantum oscillation reveals three distinct frequencies corresponding to $\alpha , \beta$, and $\delta$ Fermi surface pockets. (d) Temperature dependence of the amplitudes of two main peaks in the FFT spectra in (c). Blue dotted lines are fits to thermal damping of the oscillations, as described in the main text. (e) Kohler's plot for magnetoresistance curves at different sample temperatures. Red and brown lines are linear fits to the data for low field, high temperature and high field, low temperature regimes, respectively.

Figure 3

ARPES spectra of LuSb/GaSb (001) thin films. (a) Bulk three-dimensional Brillouin zone of LuSb and its surface projection showing high-symmetry points. (b) Two-dimensional Fermi surface map near the bulk $\mathrm{\Gamma }$ point showing both holelike $(\beta ,\delta )$ and electronlike $\left(\alpha \right)$ Fermi surface sheets. (c) Two-dimensional map near the bulk $\mathrm{\Gamma }$ point at a binding energy of 0.495 eV illustrating anisotropy of the $\delta$ pocket. (d) E-k spectral map along $\overline{\mathrm{\Gamma }}-\overline{\mathbf{M}}-\overline{\mathrm{\Gamma }}$ as indicated by brown arrows in panel (b). E-k spectral maps along (e) $\overline{\mathbf{M}}-\overline{\mathrm{\Gamma }}-\overline{\mathbf{M}}$ and (f) $\overline{\mathbf{X}}-\overline{\mathrm{\Gamma }}-\overline{\mathbf{X}}$ indicated by blue and red arrows in (c), respectively. Red dotted lines are calculated band dispersions from DFT.

Figure 4

Weak antilocalization and quasi-two-dimensional behavior in LuSb/GaSb (001) thin films. (a) Dependence of FFT frequencies on relative angles between the surface normal and the magnetic field direction and corresponding fits to the 2D Fermi surface model as described in the main text. The angle is defined in the inset. (b) Temperature dependence of conductance at different out-of-plane magnetic fields. Background colors indicate transport regimes as described in Fig. 2. Fits to quantum corrections to the conductance are shown in dotted black lines. Inset shows the evolution of A, the coefficient of the $ln$(T) term used in the fits, with magnetic field. (c) Evolution of WAL with temperature. Corresponding fits to 2D HLN theory are overlaid as black solid lines. (d) Extracted phase coherence lengths from the fits in (c). Inset shows decrease in the number of channels with increase in temperature as obtained from the same fits in (c). Blue solid line is a fit showing exponential decay in the number of channels with increasing temperature. (e) Inelastic scattering rate as a function of temperature. Blue line is a fit showing ${\mathrm{T}}^n$ dependence ($n=3.47\pm 0.38$) of the inelastic scattering rate.

Figure 5

Angular dependence of weak antilocalization in LuSb/GaSb (001) thin films. (a) Longitudinal resistance as a function of angle between the surface normal and the magnetic field vector. The angle is defined in the inset of Fig. 4. A zoomed-in image between $\pm 0.5$ T, showing positive magnetoresistance due to WAL, is shown in the inset. (b) Same data in (a) plotted as a function of the normal component of the applied magnetic field showing that the WAL scales with the normal component of the magnetic field vector between $\pm 0.05$ T. (c) Parallel field magnetoconductance. Fits to Eq. (2), as described in the text, to the low field magnetoconductance between $\pm 1$ T is shown in blue.