Gate-tunable weak antilocalization in a few-layer InSe

Indium selenide (InSe) has attracted tremendous research interest due to its high mobility and potential applications in next-generation electronics. However, the underlying transport mechanism of carriers in thin InSe at low temperatures remains unknown. Here we report the gate voltage and temperature-dependent magnetotransport properties of $\gamma$-InSe transistor devices with Hall mobility up to $2455\mathrm{c}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at the temperature of 1.7 K. We observe a gate-tunable weak antilocalization behavior at lower magnetic field $B$, which shows a transition to weak localization at higher $B$ region. We find that the magnetotransport data agree well with the Hikami-Larkin-Nagaoka theory. The conductivity and temperature dependence of phase-coherence length reveal that the electron-electron ($e\text{−}e$) interactions are dominated dephasing mechanism for electronic transport in $\gamma$-InSe at low temperatures. The maximum phase-coherence length is found to be 320 nm at 1.7 K, larger than that of monolayer $\mathrm{Mo}{\mathrm{S}}_2$ and few-layer black phosphorus. These results enrich the fundamental understanding of electronic transport properties of InSe.

Figure 1

$\gamma$-InSe/hBN devices. (a) Schematic of $\gamma$-InSe crystal structure. Left panel shows a honeycomb lattice in basal plane and right panel displays a bulk unit cell. (b) Raman spectra of the InSe device. (c) Optical image of a typical fabricated $\gamma$-InSe/hBN field-effect transistor device. The scale bar is $10\mu \mathrm{m}$.

Figure 2

(a) The conductivity ${\sigma }_{2\mathrm{p}}$ vs $V_{\mathrm{bg}}$ of three InSe/hBN devices (red lines) and four $\mathrm{InSe}/\mathrm{Si}{\mathrm{O}}_2$ devices (blue lines). (b) The histogram of mobility of three InSe/hBN devices (red pillars) and four $\mathrm{InSe}/\mathrm{Si}{\mathrm{O}}_2$ devices (blue pillars).

Figure 3

Transfer curves at various temperatures. (a) Two-terminal conductivity ${\sigma }_{2\mathrm{p}}$ varies with back-gate voltage $V_{\mathrm{bg}}$. (b) Four-terminal conductivity ${\sigma }_{\mathrm{xx}}$ as a function of $V_{\mathrm{bg}}$.

Figure 4

(a) $R_{\mathrm{xy}}$ as a function of $B$ at fixed gate voltage $V_{\mathrm{bg}}=50\mathrm{V}$ and different temperatures between 1.6 and 70 K. (b) Temperature-dependent Hall and field-effect mobility.

Figure 5

Analysis of the gate-voltage-dependent magnetotransport of $\gamma$-InSe at $T=1.7\mathrm{K}$. (a) $\mathrm{\Delta }{\sigma }_{\mathrm{xx}}$ as a function of magnetic field $B$ at different gate voltages. The black solid lines are the fittings of the MC data with HLN model. (b) Gate-voltage-dependent characteristic field $B_{\phi ,}{B}_{\mathrm{SO}}$ extracted from the fittings in (a). (c) The corresponding phase-coherence length $l_{\phi }$ and spin-orbit scattering length $l_{\mathrm{SO}}$ versus gate voltage.

Figure 6

Temperature-dependent phase-coherence length of $\gamma$-InSe. Fitting of the MC data with HLN model (the black solid lines) for $V_{\mathrm{bg}}=40\mathrm{V}$ (a) and 45 V (b). (c) Characteristic field $B_{\phi }$ estimated from the fitting with HLN model. The black solid lines are guides for the eye. The Inset shows curves of ${\tau }_{\phi }\mathrm{vs}{T}^{-1}$ for $V_{\mathrm{bg}}=40$ and 45 V. (d) Phase-coherence length $l_{\phi }$ varies with temperatures, showing a power-law rule of $T^{-\gamma }$ (the black solid lines) with the $\gamma =0.431\pm 0.01$, $\gamma =0.483\pm 0.01$ for $V_{\mathrm{bg}}=40$ and 45 V, respectively.