Quantum transport of two-species Dirac fermions in dual-gated three-dimensional topological insulators

Abstract

Topological insulators are a novel class of quantum matter with a gapped insulating bulk, yet gapless spin-helical Dirac fermion conducting surface states. Here, we report local and non-local electrical and magneto transport measurements in dual-gated BiSbTeSe₂ thin film topological insulator devices, with conduction dominated by the spatially separated top and bottom surfaces, each hosting a single species of Dirac fermions with independent gate control over the carrier type and density. We observe many intriguing quantum transport phenomena in such a fully tunable two-species topological Dirac gas, including a zero-magnetic-field minimum conductivity close to twice the conductance quantum at the double Dirac point, a series of ambipolar two-component half-integer Dirac quantum Hall states and an electron-hole total filling factor zero state (with a zero-Hall plateau), exhibiting dissipationless (chiral) and dissipative (non-chiral) edge conduction, respectively. Such a system paves the way to explore rich physics, ranging from topological magnetoelectric effects to exciton condensation.

Novel physics of topological aspects are obscured due to lack of effective way to manipulate topological particles. Here, Xu et al. demonstrate independent control of Dirac fermions on top and bottom surfaces of BiSbTeSe₂ flakes by dual-gating, which suggests a way to manipulate exotic particles.

A three-dimensional (3D) topological insulator (TI) is characterized by an insulating bulk band gap and gapless conducting topological surface states (TSS) of spin-helical massless two-dimensional (2D) Dirac fermions¹,². Such surface states are topologically non-trivial and protected by time-reversal symmetry, thus immune to back scattering. The potential novel physics offered by this system, such as topological magnetoelectric (TME) effects³,⁴, Majorana fermions⁵ and effective magnetic monopoles⁶, has drawn intense interest. One of the most iconic transport signatures for 2D Dirac electronic systems is the half-integer quantum Hall effect (QHE) in a perpendicular magnetic field (B), as first observed in graphene⁷,⁸ and later also studied in HgTe⁹,¹⁰. The Landau levels (LLs) of 2D Dirac fermions have energies E_N=sgn(N)v_F(2eBħ|N|)^1/2, where sgn is the sign function, N is the LL index (positive for electrons and negative for holes), v_F is the Fermi velocity, e is the elemental charge and ħ is the Plank's constant h divided by 2π. The zeroth LL at E₀=0 is equally shared between electrons and holes, giving rise to the half-integer shift in the quantized Hall conductivity σ_xy=g(N+1/2)e²/h, where g is the number of degenerate species of Dirac fermions (for example, g=4 for graphene, and g=1 for TSS with a single Dirac cone). This 1/2 can also be related to the Berry-phase due to the spin or pseudospin locking to the momentum of Dirac fermions⁷,⁸,⁹,¹⁰.

In most commonly studied TI materials such as Bi₂Se₃, Bi₂Te₃ and other Bi/Sb-based chalcogenides, it is often challenging to observe characteristic TSS transport (particularly QHE) due to bulk conduction caused by unintentional impurity doping. Only very recently has well-developed QHE arising from TSS been observed in exfoliated flakes from BiSbTeSe₂ (BSTS) single crystals¹¹ and molecular beam epitaxy grown (Bi_1−xSb_x)₂Te₃ or Bi₂Se₃ thin films¹²,¹³. In this work, we fabricate dual-gated¹⁴,¹⁵,¹⁶ TI devices from exfoliated BSTS thin flakes with undetectable bulk carrier density and conduction at low temperature¹¹. Such a dual-gating structure is also promising for exploring exciton condensation proposed for TIs¹⁷ and topological quantum phase transitions induced by displacement electric field¹⁸.

In our dual-gated BSTS devices, the independent, ambipolar gating of parallel-conducting top and bottom surfaces realize two independently controlled species of 2D Dirac fermions, allowing us to investigate such interesting transport phenomena as the minimum conductivity of TSS at Dirac point (DP), and two-species (two-component) Dirac fermion QHE of electron+electron, electron+hole and hole+hole types, involving various combinations of top and bottom surface half-integer filling factors ν_t and ν_b, respectively. When (ν_t, ν_b)=(−1/2, 1/2) or (1/2, −1/2), there's an intriguing ν=0 state characterized by zero-Hall plateau and a large longitudinal resistance peak¹¹,¹², attributed to the formation of dissipative and non-chiral edge states. We also perform non-local transport measurements and compare them with the normal local measurements in our dual-gated 3D TI devices in the quantum Hall (QH) regime to probe the nature of edge-state transport for both standard QH states and the novel ν=0 dissipative QH-like state. We further demonstrate that the dissipative edge states at ν=0 have temperature-independent conductance, revealing that the transport in such a quasi-one-dimensional (1D) dissipative metallic edge channel could evade standard localization.

Results

Transport properties at zero and low magnetic field

Qualitatively, similar data are measured in multiple samples, while results from a typical sample A (channel length L=9.4 μm, width W=4.0 μm, with ∼100 nm-thick BSTS and 40 nm-thick h-BN as top-gate dielectric, see schematic in Fig. 1a) are presented below unless otherwise noted. The h-BN as a substrate or gate dielectric is known to preserve good electronic properties for graphene, resulting from the atomic flatness and relatively low density of impurities in h-BN¹⁹. The carrier densities of the top and bottom surface of the BSTS flake are tuned by top-gate voltage V_tg and back-gate voltage V_bg, respectively.

Figure 1. Device configuration and dual-gated field effect at zero and low magnetic field.

(a) Device schematic. Inset is an optical microscope image of a typical dual-gated BSTS device before depositing the top-gate metal; Scale bar, 10 μm. (b,c) show 2D maps of ρ_xx at B=0 T and ρ_xy at B=1 T as functions of V_tg and V_bg on sample A. The blue (red) dashed lines in b are guides to the eye for the top (bottom) surface DP. The 2D map is generated by data measured from V_tg-sweeps at a series of V_bg values, with one example at V_bg=3 V shown in the inset of c. (d) Zero-magnetic-field minimum conductivity σ_min (bottom axis) measured in six dual-gated samples at low temperature (<2 K) plotted as a function of the sample thickness (data in circles) and 2D aspect ratio (L/W, data in squares). The vertical dashed line indicates 3.8e²/h.

Figure 1b,c shows the double-gated electric field effect measured at T=0.3 K. The longitudinal resistivity ρ_xx (=R_xx × W/L, with R_xx being longitudinal resistance) at magnetic field B=0 T (Fig. 1b) and Hall resistivity ρ_xy (=R_xy, Hall resistance) at B=1 T (Fig. 1c) are plotted in colour scale as functions of both top and bottom gate voltages (V_tg and V_bg). The extracted field effect and Hall mobilities are typically several thousands of cm² V⁻¹ s⁻¹. A minimum carrier density n^* ∼9 × 10¹⁰ cm⁻² per surface can be extracted from the maximum Hall coefficient (absolute value) ∼3.5 kΩ T⁻¹ (when both surfaces are slightly n-type or p-type) measured in Fig. 1c. A set of exemplary V_tg-sweeps with V_bg=3 V is shown in Fig. 1c inset. By adjusting V_tg (or V_bg), the device can be gated through a R_xx peak, identified as the charge-neutrality DP of the top (or bottom) surface, marked by the blue (or red) dashed lines in Fig. 1b. Gating through the DP, the carriers in the corresponding surface change from hole-like to electron-like (that is, ambipolar), as evidenced by Hall measurements (Fig. 1c). The slight deviation of the two lines from being perfectly vertical and horizontal arises from the weak capacitive coupling between the top (bottom) surface and the back (top) gate¹⁶. The crossing of these two lines corresponds to the double DP (both surfaces tuned to DP), where ρ_xx (σ_xx=1/ρ_xx) reaches a global maximum (minimum). Within the gate voltage range used, the carriers predominantly come from the TSS and we observe relatively good particle-hole symmetry in the transport properties (for example, the symmetrical appearance of ρ_xx on both sides of DP in each surface in Fig. 1b and the similar absolute values of the positive and negative maximum Hall coefficient in Fig. 1c).

We have studied six dual-gated BSTS devices with different thicknesses (t) and aspect ratios (L/W). These devices are measured at low temperatures (T<2 K) and the results are repeatable after multiple thermal cycles. When both surfaces are tuned to DP, the minimum 2D conductivity σ_min at B=0 T exhibits relatively constant value (3.8±0.1)e²/h for all the devices measured (with the uncertainty representing 90% confidence interval), whose thicknesses range from ∼50 to ∼200 nm and L/W range from 1.3 to 3.5 (Fig. 1d). Our observation indicates that the conductivity at the DP for each major surface (top or bottom) is ∼2e²/h (one unit of conductance quantum), within the range of values (2∼5 e²/h) reported by Kim et al.¹⁴ on thin flakes of Bi₂Se₃ (∼10 nm). The better consistency over multiple samples in our dual-gated BSTS devices may be attributed to the more insulating bulk (whose conduction is immeasurably small at low temperature) and uniformity of the exfoliated BSTS flakes, which are sandwiched between SiO₂ and h-BN to achieve better device stability. The minimum conductivity at DP has also been discussed in graphene with considerable interest²⁰,²¹,²²,²³,²⁴,²⁵.

The experiments in graphene revealed that the minimum conductivity is strongly affected by carrier-density inhomogeneities (puddles) induced by disorder on or near graphene²⁴,²⁵, such as the absorbates or charged impurities in the substrates. In 3D TIs, one source of impurities likely relevant to the observed quasi-universal minimum conductivity in our dual-gated BSTS devices could be bulk defects (located near surface)²⁶,²⁷, such as those revealed in scanning tunnelling microscopy studies²⁸.

Two-component QHE

For the rest of the paper, we focus on the transport phenomena in the QH regime under a high magnetic field B perpendicular to the top and bottom surfaces. Figure 2a,c shows in colour scales the longitudinal conductivity σ_xx (=ρ_xx/(ρ_xx²+ρ_xy²)) and Hall conductivity σ_xy (=ρ_xy/(ρ_xx²+ρ_xy²)) for Sample A as functions of V_tg and V_bg at B=18 T and T=0.3 K. The colour plots in Fig. 2a,c divide the (V_tg, V_bg) plane into a series of approximate parallelograms, centred around well-developed or developing QH states with vanishing or minimal σ_xx (Fig. 2b) and quantized σ_xy in integer units of e²/h (Fig. 2d). These QH parallelograms are bounded by approximately (but slightly tilted) vertical and horizontal lines, which represent the top and bottom surface LLs, respectively. By increasing (decreasing) either V_tg or V_bg to fill (exhaust) one LL on the top or bottom surface, σ_xy increases (decreases) by e²/h, taking consecutive quantized values of νe²/h, where integer ν=ν_t+ν_b=N_t+N_b+1. The N_t(b) is the corresponding top (bottom) surface LL integer index that can be adjusted by top (back) gate to be of either Dirac electrons or holes. In Fig. 2d, different fixed V_bg values (from −17 to 40 V) set ν_b around consecutive half integers −3/2, −1/2, 1/2, 3/2 and 5/2 (such that the bottom surface contributes σ_xy^b=ν_be²/h to the total σ_xy), explaining the vertical shift of e²/h at QH plateaux of consecutive V_tg-sweeps.

Figure 2. QHE modulated by top and bottom gates.

(a) σ_xx and (c) σ_xy, shown as 2D colour maps, as functions of V_tg and V_bg at B=18 T and T=0.3 K in the sample ‘A', with representative cuts at 5 different values of V_bg shown in b and d. The (ν_t, ν_b) labels (top, bottom) surface filling factors for corresponding quantum Hall states. The σ_xx curves in b are shifted vertically (in consecutive step of e²/h) for clarity (the corresponding zero σ_xx levels are indicated by the same-coloured horizontal dashed lines).

It is also notable that in Fig. 2, there are a few states with zero-quantized Hall conductivity (σ_xy=0, manifesting as white regions in Fig. 2c, separating the electron-dominated regions in red and the hole-dominated regions in blue) and non-zero σ_xx minimum, marked by equal and opposite half-integer values of ν_t and ν_b thus total ν=0, for example (ν_t, ν_b)=(−1/2, 1/2), (1/2, −1/2) and (3/2, −3/2). These states with total ν=0, exhibiting zero-Hall plateaux (see also Fig. 2d), have non-zero σ_xx minimum (Fig. 2a,b) but very large R_xx maximum (see next, Fig. 3).

Figure 3. Local and non-local resistance in dual-gated TI in high magnetic field.

(a) Local resistance R_xx and (b) non-local resistance R_nl measured in sample A as functions of V_tg and V_bg at B=18 T and T=0.3 K, with insets showing the measurement setup schematics. (c) A few representative cuts of a and b at different values of V_bg. Filing factors for the local R_xx peaks are labeled in each sub-panel.

Non-local transport at ν=0 states

To further characterize the observed QH and ν=0 states, we have performed non-local transport measurements of R_nl (=V_nl/I, I is the current and V_nl is the non-local voltage, see the schematic measurement setup in the inset of Fig. 3b) as functions of V_tg and V_bg at B=18 T and T=0.3 K and compared the results with the standard (local) measurements of the longitudinal resistance R_xx (Fig. 3a). It is intriguing that unlike other QH states typified by a zero or minimum in R_xx, the states with ν=ν_t+ν_b=0 (labelled by (ν_t, ν_b) in Fig. 3a with ν_t=−ν_b =±1/2 or ±3/2) are accompanied by a R_xx maximum. The best-developed ν=0 states are those at (ν_t, ν_b)=(−1/2, 1/2) or (1/2, −1/2), where R_xx reaches ∼220 kΩ (ρ_xx ∼100 kΩ), exceeding the resistance quantum (h/e²=∼25.8 kΩ) by an order of magnitude. The non-local R_nl also becomes very large (∼100 kΩ) and the similar order of magnitude as R_xx at these two ν=0 states, while negligibly small at other (ν_t, ν_b) QH states (see Fig. 3b and also the representative cuts in Fig. 3c).

The simultaneously large local and non-local resistance at ν=0 states in the QH regime has been reported in other 2D electron-hole systems²⁹,³⁰ and understood in a picture of dissipative edge channels. We emphasize that the pronounced R_nl signal cannot be explained from R_xx by a classical Ohmic non-local resistance from the stray current connecting the remote leads. Such a contribution (=∼ρ_xxe^−πL/W) would decay exponentially with L/W (=2.4 in our case), and be three orders of magnitude smaller than the local R_xx (which is the case at B=0 T, Supplementary Fig. 1). As another comparison, the middle panel of Fig. 3c shows the cuts in Fig. 3a,b at V_bg=3 V, crossing the double-DP (also zeroth LL) of both top and bottom surfaces at (ν_t, ν_b)=(0, 0), where we observe a relatively large peak in R_xx but significantly smaller R_nl. Such a result is consistent with the ‘extended' state transport (at the center of zeroth LL) as the current flows through the bulk of the 2D surface.

From the colour plots in Figs 2 and 3, the parallelogram centred around (ν_t, ν_b)=(−1/2, 1/2) state is enclosed by boundaries representing N_t=0 and −1, N_b=0 and 1 LLs. Similarly, the (ν_t, ν_b)=(1/2, −1/2) state is bound by N_t=0 and 1, N_b=0 and −1 LLs. We conclude that such a ν=0 state can exist when the potential difference V between top and bottom surfaces (equivalently the energy separation between top and bottom surface DPs) is in the range of 0<|V|<2E₀₋₁ (≅2 × 50 meV at B=18 T, where E₀₋₁ is the 0−1 LL separation of TSS Dirac fermions¹¹). The large energy scale of E₀₋₁ can help make the ν=0 and ν=±1 QH states observable at significantly elevated temperatures as demonstrated below.

Temperature dependence of the ν=0 and ±1 states

We have studied the temperature (T) dependence of the QHE and ν=0 states from 0.3 K to 50 K at B=18 T (Fig. 4). At each temperature, the bottom surface density is tuned by V_bg to set ν_b near 1/2 (dashed lines) or −1/2 (solid lines), and the peaks in local R_xx and non-local R_nl corresponds to the (ν_t, ν_b)=(−1/2, 1/2) or (1/2, −1/2), respectively (Fig. 4a,b, detailed raw data are shown in Supplementary Fig. 2). The R_xx peaks (>∼150 kΩ) are seen to be more robust up to the highest temperature (T=50 K) measured, while R_nl peaks decrease rapidly (approximately linearly in T, shown in Fig. 4c) with increasing T and is nearly suppressed above 50 K. We also show the T-dependence of σ_xx and σ_xy at (ν_t, ν_b)=(−1/2, 1/2), (1/2, −1/2), (1/2, 1/2) and (−1/2, −1/2) in Fig. 4e,f. The σ_xy maintains good quantization at νe²/h (ν=0, ±1) up to T=50 K, while σ_xx increases with T (the gate-dependent σ_xx and σ_xy traces at different temperatures are shown in Supplementary Fig. 3). The σ_xx for ν=±1 states is found to show thermally activated behaviour at high temperatures¹¹, where the finite σ_xx is attributed to the thermally excited 2D surface or 3D bulk carriers. Such carriers can shunt the edge-state transport and suppress the non-local R_nl response at high T (ref. ²⁹). We also note that the σ_xx versus T curves for ν=0 and ν=±1 states follow the similar trend and have approximately constant separation. We find the averaged separation Δσ_xx=1/2 × (σ_xx(−1/2, 1/2)+σ_xx(1/2, −1/2)−σ_xx(1/2, 1/2)−σ_xx(−1/2, −1/2)) to be largely T-independent with a value of (0.27±0.01)e²/h, which we attribute to the conductivity of the quasi-1D dissipative edge channel.

Figure 4. Temperature dependence and illustrative schematics of the QHE and v=0 state in TI.

(a) R_xx and (b) R_nl measured in sample ‘A' as functions of V_tg for different temperatures at B=18 T, where V_bg is chosen to set ν_b at 1/2 (dashed lines) and −1/2 (solid lines), respectively. (c) The R_nl value at (ν_t, ν_b)=(−1/2, 1/2) and (1/2, −1/2) shows approximately linear dependence on temperature. (d) σ_xx versus V_tg (with the same two values of V_bg chosen in a and b) at T=0.3 K as an example, with each highlighted circle corresponding to a state in e plotted with corresponding coloured symbols. (e) σ_xx and (f) σ_xy of ν=+1, −1 and 0 states as functions of temperature. In e, we also plot Δσ_xx (difference between averaged ν=0 states' σ_xx and averaged ν=±1 states' σ_xx), which barely changes with T. (g,h) Schematics of surface band structure (energy spectrum) in high magnetic field, showing LLs from top and bottom surfaces (blue and red) in the middle of the sample transitioning into side surface sub-bands at sample edge, and (i,j) edge states in a slab-shaped sample for ν=1 and ν=0 states. The dashed line indicates a representative Fermi level E_f and circles in g label chiral edge modes.

Discussions

In our measurement setup, the contacts connect to the top, bottom and side surfaces, all of which are probed simultaneously. The side surface only experiences an in-plane field and can be viewed as a quasi-1D domain boundary that separates the top and bottom surfaces with B pointing outward and inward, respectively, thus can support QH edge states³¹. When the top and bottom surfaces are doped to the same carrier type (either n or p), the corresponding QH edge states (on the side surface) would have the same chirality and give the observed total σ_xy=νe²/h=(ν_t+ν_b)e²/h, restricted to integer multiples of e²/h. When the two surfaces have opposite carrier types but one of the them dominates, well-defined QH states with ν=ν_t+ν_b may still be observed, such as the (−1/2, 3/2) state with σ_xy=(−1/2+3/2)e²/h=e²/h and vanishing ρ_xx. Previous studies in InAs/(AlSb)/GaSb heterostructure-based electron-hole systems³²,³³ also revealed QH effect with R_xy=h/(νe²)=h/(ν_e−ν_h)e² (ν_e and ν_h are electron and hole-filling factors, both are positive integers) and vanishing R_xx when the AlSb barrier (separating electron and hole gases) is sufficiently thin to enable electron-hole hybridization. Despite the phenomenological similarities, our QH system is distinctive in the sense that the spatially separated electrons and holes residing on the top and bottom surfaces have half-integer filling factors, and the hybridization only happens at the side surface.

We show the schematic energy spectrum when the two surfaces are degenerate with V=0 (refs ^{34, 35, 36}) in Fig. 4g, which depicts the Fermi energy E_f inside the 0−1 LL gap and corresponds to the (1/2, 1/2) QH state. For a relatively thick sample such as ours (∼100 nm>magnetic length l_B=(ħ/eB)^1/2≅6 nm at B=18 T); however, it has been suggested that even in the presence of well-quantized LLs, a standard TI Hall measurement would exhibit deviations from perfectly quantized values due to conduction through the side surfaces³¹,³⁴,³⁵,³⁶. On the other hand, it has also been suggested that when net chiral modes exist (Fig. 4g,i show one such net chiral mode), the QH effect may be restored by the local equilibrium between non-chiral edge modes³⁷, possibly explaining the good quantization in σ_xy and vanishing ρ_xx (also R_nl) observed in our experiments.

For the (ν_t, ν_b)= (−1/2, 1/2) or (1/2, −1/2) state, the carrier density on the top and bottom surfaces are opposite. Since E_f is within the LL gap on both the surfaces, the finite residual σ_xx and large R_nl we observed are indicative of dissipative edge transport. We show a schematic energy spectrum³⁸ of this ν=0 state with V slightly smaller than E₀₋₁ in Fig. 4h, where the Fermi level E_f resides between the N_t=−1 and 0 LL of top surface (marked in blue), thus ν_t=−1/2, and also between the N_b=0 and 1 LL of bottom surface, thus ν_b=1/2. Overall, such energy spectrum represents a (ν_t, ν_b)=(−1/2, 1/2) and ν=0 state. The E_f crosses an even number (only two shown in this illustrative example in Fig. 4h) of counter-propagating edge modes (arising from sub-bands of the quasi-1D side surface). The disorder can cause scattering and local equilibrium between the counter-propagating modes, giving rise to non-chiral dissipative transport (depicted by a series of conducting loops that can hop between adjacent ones in Fig. 4j) on the side surface with a large and finite resistance. While the energy spectrum (Fig. 4h) is expected to have a gap (Δ) near the edge (due to the hybridization between top (marked with blue) and bottom (red) surface zeroth LLs and approximately the finite-size confinement-induced gap ≅hv_F/t≅10 meV opened at DP of the side surface³⁸), we did not observe a truly insulating state with vanishing σ_xx and diverging R_xx (Figs 2a and 4a). This is likely due to the disorder potential (spatial fluctuation of DP²⁸) comparable or larger than Δ and thus smearing out this gap (effectively E_f always crosses the non-chiral edge modes). It would be an interesting question for future studies to clarify whether the weak T-dependence (at T<∼50 K) of the observed conductance (Fig. 4e), similar to the behaviour reported in InAs/GaSb based electron-hole systems³⁹, may indicate an absence of localization⁴⁰,⁴¹,⁴²,⁴³ in such quasi-1D resistive edge channels.

Several recent theories have pointed out that the ν=1/2−1/2=0 state in the TI QH system may bring unique opportunities to realize various novel physics. It has been suggested that both the ν=0 state in TI QHE and an analogous quantum anomalous Hall (QAH) state with zero-Hall-conductance plateau in a magnetic-doped TI around the coercive field can be used as platforms to observe the TME effect⁴⁴,⁴⁵, where an electric (magnetic) field induces a co-linear magnetic (electric) polarization with a quantized magnetoelectric polarizability of ±e²/2 h. A zero-Hall-plateau state has been recently observed in the QAH case in ultrathin (few-nm-thick) films of Cr_x(Bi,Sb)_2-xTe₃ at low temperature (<1 K) (refs ^{46, 47}). In comparison, our samples have much larger thickness (>∼50 nm, suggested to be preferable for better developed TME effect⁴⁵,⁴⁸), and our ν=0 state survives at much higher temperatures (∼50 K). It has also been proposed that excitonic condensation and superfluidity can occur in thin 3D TIs at the ν=0 state in QH regime⁴⁹ (in addition to the at-zero B field¹⁷) induced by spontaneous coherence between strongly-interacting top and bottom surfaces. In future studies, much thinner samples are likely needed to investigate the possibility of such exciton superfluidity.

Methods

Sample preparation

3D TI single crystals BiSbTeSe₂ (BSTS) were grown by the vertical Bridgman technique¹¹. BSTS flakes (typical thickness ∼50–200 nm) are exfoliated (Scotch tape method) onto highly doped Si (p+) substrates (with 300 nm-thick SiO₂ coating), and lithographically fabricated into Hall bar-shaped devices with Cr/Au contacts. A thin flake of hexagonal boron nitride (h-BN, typical thickness ∼10–40 nm) is transferred¹⁹ on the BSTS flake to serve as a top-gate dielectric and a top-gate metal (Cr/Au) is deposited afterwards. The thickness of BSTS and h-BN flakes are measured by atomic force microscopy.

Transport measurement

Transport measurements are performed with the standard lock-in technique using a low-frequency (<20 Hz) excitation current of 20 nA in a helium-4 variable temperature system (with base temperature down to 1.6 K) or a helium-3 system equipped with magnetic fields (B) up to 18 T (down to 0.3 K).

Additional information

How to cite this article: Xu, Y. et al. Quantum transport of two-species Dirac fermions in dual-gated three-dimensional topological insulators. Nat. Commun. 7:11434 doi: 10.1038/ncomms11434 (2016).

Supplementary Material

Supplementary Information

Supplementary Figures 1-3