Tuning Insulator-Semimetal Transitions in 3D Topological Insulator thin Films by Intersurface Hybridization and In-Plane Magnetic Fields

A pair of Dirac points (analogous to a vortex-antivortex pair) associated with opposite topological numbers (with $\pm \pi$ Berry phases) can be merged together through parameter tuning and annihilated to gap the Dirac spectrum, offering a canonical example of a topological phase transition. Here, we report transport studies on thin films of ${\mathrm{BiSbTeSe}}_2$, which is a 3D topological insulator that hosts spin-helical gapless (semimetallic) Dirac fermion surface states for sufficiently thick samples, with an observed resistivity close to $h/4e^2$ at the charge neutral point. When the sample thickness is reduced to below $\sim 10\mathrm{nm}$ thick, we observe a transition from metallic to insulating behavior, consistent with the expectation that the Dirac cones from the top and bottom surfaces hybridize (analogous to a “merging” in the real space) to give a trivial gapped insulator. Furthermore, we observe that an in-plane magnetic field can drive the system again towards a metallic behavior, with a prominent negative magnetoresistance (up to $\sim -95\%$) and a temperature-insensitive resistivity close to $h/2e^2$ at the charge neutral point. The observation is consistent with a predicted effect of an in-plane magnetic field to reduce the hybridization gap (which, if small enough, may be smeared by disorder and give rise to a metallic behavior). A sufficiently strong magnetic field is predicted to restore and split again the Dirac points in the momentum space, inducing a distinct 2D topological semimetal phase with two single-fold Dirac cones of opposite spin-momentum windings.

Figure 1

(a) Schematic of a dual-gated TI device based on BSTS. (b), (c) Optical images of device N3 before (b) and after (c) top-gate metal deposition. (d)–(g) Measured conductivities (in color scale, with contours) as functions of $V_{tg}$ and $V_{bg}$ in four representative devices with decreasing thickness ($t$). In (d), (e) the black (white) dashed lines trace the top (bottom) surface DPs. Data are measured at temperature $T=0.35\mathrm{K}$ in (d)–(f), and at $T=1.6\mathrm{K}$ in (g). (h) Temperature dependence of ${\rho }_{\max }$ (log scale) for five representative devices. (i) The ${\sigma }_{\min }$ ($=1/{\rho }_{\max }$, left axis) at low $T$ ($<2\mathrm{K}$) and the extracted gap ${\mathrm{\Delta }}_0^{*}$ (right axis) as functions of sample thickness $t$. The dashed-dotted vertical line marks the critical thickness $t_c=\sim 10\mathrm{nm}$ that separates the semimetal ($t>t_c$, corresponding to the 3D TI phase in the inset with gapless Dirac SS) and insulator ($t\le t_c$, corresponding to the trivial insulator phase in the inset with gapped SS) behaviors. The inset plot shows ${\mathrm{\Delta }}_0^{*}$ in log scale vs $t$ and an exponential fitting.

Figure 2

(a), (c), (e) Resistivity of three representative devices (N2, N3, and N5) measured as a function of $V_{tg}$ at various in-plane $B$ fields at $T=0.3\mathrm{K}$. The corresponding $V_{bg}\mathrm{s}$ are fixed at chosen values such that the $V_{tg}$ sweeps go through ${\rho }_{\max }$. (b), (d), (f) The ${\rho }_{\max }$ (and the corresponding MR, right axis) measured (at fixed $V_{bg}$ and $V_{tg}$ labeled in the figure) as a function of in-plane $B$ field for the three devices (N2, N3, and N5, respectively).

Figure 3

(a) The ${\rho }_{\max }$ of device N5 ($t\sim 10\mathrm{nm}$) vs $T$ at different in-plane $B$ from 11.4 up to 45 T. Inset shows corresponding thermal activation [${\rho }_{\max }(T)\propto e^{{\mathrm{\Delta }}_B^{*}/2k_{B}T}$] fittings, while the extracted ${\mathrm{\Delta }}_B^{*}$ is plotted (filled circles) as a function of $B$ in (b) along with data measured from another (second) cool down. (b) The linear fits for both cool downs indicate a gap closing at $B_c$ between 35 to 40 T, consistent with the inset showing the convergence (at $B_c=36T$) of all the linear fittings of $\mathrm{Ln}[(2e^2/h){\rho }_{\max }]$ vs $B$ at different temperatures.

Figure 4

(a) Predicted evolution of the surface band structure from a trivial insulator towards a 2D TSM, upon increasing in-plane $B$ field in a thin TI sample with hybridized SS. (b) Schematic of the orbital motion (normal to $B$ and $x$ direction) of spin-helical SS electrons for a 3D TI film. In (a) and (b), the red and blue arrows denote the associated spin direction. (c) The gap size extracted from thermal activation can be underestimated (resulting in a smaller measured value ${\mathrm{\Delta }}_B^{*}={\mathrm{\Delta }}_B-\delta$) compared to the real gap ${\mathrm{\Delta }}_B$ due to the smearing effect of disorder induced potential fluctuations ($\delta$) at different positions.