Metal–semiconductor transition in atomically thin Bi₂Sr₂Co₂O₈ nanosheets

The discovery of two-dimensional (2D) atomically thin graphene has generated extensive interests in 2D layered materials for both fundamental investigations and technological applications.^1,2 In general, a large family of layered materials, in which the layers are weakly bonded together by van der Waals interactions to form 3D crystals, can be isolated into single- or few-layered nanosheets through mechanical exfoliation or liquid exfoliation.^3,4 Hence, the layered materials provide a diverse source of 2D material systems. With a reduced dimensionality and/or quantum confinement effect, these 2D nanosheets can often exhibit distinct properties from their 3D bulk counterparts,^1,2,5–7 and therefore provide a rich playground for exploring novel physical phenomena and exciting opportunities for practical application.

In addition to the widely investigated graphene and metal chalcogenides (e.g., MoS₂ and Bi₂Te₃), layered transition metal oxides (TMOs) represent another class of layered materials, in which 3d or 4f electron interactions can lead to new physical phenomena. Cuprates such as Bi₂Sr₂CaCu₂O₈ (Bi2212)⁸ and cobaltites including NaCo₂O₄ (Na124),⁹ Ca₃Co₄O₉ (Ca349),¹⁰ and Bi₂Sr₂Co₂O₈ (BSCO)¹¹ are representative layered TMOs; the former (Bi2212) is a typical high-T_c superconductor whereas the latter (cobaltites) are of particular interest as oxide thermoelectric materials. In these layered cobaltites, the CoO₂ layers constituted by CoO₆ octahedra are identical structural component and considered dominant in electric transport behavior.^9–11 Interestingly, it is found that the hydrated Na124 in which the 2D CoO₂ layers are separated by a thick insulating layer of H₂O molecules becomes a superconductor at T_c < 5 K.¹² Although the origin of superconductivity is still not fully understood, it is believed that the well separation and the breaking of coupling mechanism between the CoO₂ layers may be the key.¹³ Therefore, it is of significant interest to probe the fundamental transport properties of single- or few-layered nanosheets of these layered oxide materials.

BSCO has a similar crystalline structure to the superconductive Bi2212 phase, but contains a layer of CoO₂ instead of CuO₂, which is the same as Na124 (see Fig. 1(a), structure sketch of BSCO). Unlike Na124, there is a rather weak interlayer coupling in BSCO, making it possible to exfoliate BSCO into single or few-layers to allow for directly probing the intrinsic physical properties in such 2D systems containing CoO₂. Here we focus on the electric transport characteristics of BSCO nanosheets with different layer number N. Importantly, our studies show that the materials exhibit a metal–semiconductor transition at N = 3, and demonstrate that the semiconducting BSCO nanosheets could be a natural 2D system consisting of localized states. Figure 1(a) shows the crystalline structure of the BSCO system. Using the Scotch tape-based micromechanical cleavage method,¹⁴ BSCO nanosheets can be readily exfoliated onto Si/SiO₂ substrates from a bulk BSCO single crystal grown by the floating zone method.¹⁵ The thickness and the layer number N can be determined by using optical microscope contrast and atomic force microscopy (AFM) images (see Figs. 1(b)–1(d)). The step height from the substrate to flake “1L” is measured to be 3 nm, which agrees well with the lattice spacing of 2.98 nm for BSCO layers.¹⁵ Similarly, we can identify region “2L,” “3L,” and “5L” as bilayer, trilayer, and quinquelayer, respectively.

To probe the electronic transport behavior of these BSCO nanosheets, three-terminal nanosheet devices were fabricated on silicon substrates with a 300-nm-thick SiO₂ layer. The silicon substrate acts as the back-gate, the SiO₂ layer as the gate dielectric, and thermally evaporated silver electrodes as the source and drain contacts (Fig. 2(a)). An optical image of a representative BSCO monolayer device is shown in Fig. 2(b). The room-temperature transport characteristics of BSCO devices consisting of different layers are presented in Figs. 2(c) and 2(d), in which the current is normalized by the dimension. The drain-source current (I_ds) versus the drain-source voltage (V_ds) (I_ds-V_ds) curves are linear in a wide range of voltages (Fig. 2(c)), indicating that our silver contacts are ohmic.

For bulk BSCO, the in-plane charge transport property is metallic and the dominant carriers are holes, but it exhibits semiconducting-like behavior below ∼100 K.¹⁵ Like many strongly correlated systems, BSCO is considered a “bad metal” at high temperature, exhibiting metallic properties with a rather high conductivity and large thermopower.¹¹ With temperature decreasing below ∼100 K, the localized spins induced by the interlayer magnetic correlation result in a semiconducting-like transport behavior, so the metallic conduction does not persist at low temperatures.^15,16 From the measured I_ds-V_ds and the I_ds versus back-gate voltage (V_bg) (I_ds-V_bg) curves (Figs. 2(c) and 2(d)), we noticed that the N = 4 nanosheets remain metallic at room temperature, similar to the case of bulk material, and their resistivities are on the same order (10 mΩ cm). However, the conductance of decreases rapidly when reducing the number of layers below 4. This observation is similar to Bi2212 atomic crystals in which the layers become electrically insulating.¹ Especially, the N = 1, 2, and 3 BSCO nanosheets exhibit a clear field-effect behavior (Fig. 2(d)), in which a negative gate voltage increases the conductance while a positive gate voltage suppresses the conductance, typical for p-type semiconductors. As our devices display ohmic I_ds-V_ds behavior, the possibility that the field-effect behavior is induced by the Schottky barriers at the electrode contacts can be excluded. For monolayers in particular, the current modulation can reach up to 10² between gate voltages of ±84 V, suggesting the formation of a substantial transport gap (Fig. 2(e) and 2(f)).

The temperature dependences of sheet conductance G of these nanosheets confirm the semiconducting behavior in the N = 1, 2, and 3 samples (see Fig. 3 and the supplementary material).¹⁷ Conductance G decreases monotonically with decreasing temperature for the N = 1, 2, and 3, whereas G exhibits an inflection around 140 K for the N = 4 (Figs. 3(a)–3(d)). In fact, for all N ≥ 4, the nanosheets have almost identical G-T behavior with bulk BSCO and remain metallic around room temperature, but display localized behavior at low temperature. For N = 1, 2, or 3, the nanosheets become semiconducting throughout the temperature range of 2-300 K. Next we discuss the origin of this N-dependent metal-semiconductor transition.

Overall, the normalized current, or sheet conductance, decreases moderately (less than 1 order of magnitude) with decreasing number of layers. However, it can be seen that the current of monolayer BSCO exhibits a sudden drop of over two orders of magnitude compared to multilayers (see the inset of Fig. 2(c)). Additionally, the shape of the I_ds-V_bg curve at room temperature changes from linear in two or more layers to nonlinear in monolayers (Fig. 2(d)). These observations manifest the strong characteristics of semiconducting behavior and carrier localization in monolayers. The monotonous decrease in field-effect mobility (μ) with reducing temperature along with the small μ values (see the supplementary material)¹⁷ also suggests a strong localization effect. Moreover, I_ds-V_ds curve exhibits a nonlinearity at lower temperatures with a clear drain-source gap (Δ_bias) ∼ 5.6 meV (Fig. 3(e)). Such nonlinear I_ds-V_ds characteristics further confirm the emergence of a transport gap. Such a gap exists in not only in monolayers, but also the semiconducting bilayer and trilayer nanosheets. Similar nonlinear characteristics are also observed in bilayer and trilayer devices at low temperatures, but with a much smaller drain-source gap (Δ_bias ∼ 1.3 meV for N = 2, and ∼0.5 meV for N = 3) (Figs. 3(f) and 3(g)). In contrast, the quadrilayer does not show any nonlinear conductance suppression down to T = 2 K (Fig. 3(h)). A two-dimensional plot of the differential conductance vs. drain-source voltage and temperature (Figs. 3(i)–3(l)) clearly shows that all the semiconducting nanosheets (N = 1, 2, 3) exhibit a strong conductance suppression in the bias direction as the temperature decreases, while no such suppression is seen in the quadrilayer device. These two-dimensional plots show that both the nonlinear region and the initial temperature for the emergence of nonlinearity increase with the reducing number of layer. Although the above described electrical transport characteristics are based on measurements with a gate voltage of −84 V, qualitatively similar results are obtained from measurements at zero gate voltage as well (see the supplementary material).¹⁷ 

To better understand the transport mechanism of these semiconducting BSCO nanosheets, we further examined the temperature dependence of the conduction behavior. For the entire measured temperature range, a linear dependence can be found for BSCO bilayer and trilayer when the conductance G is plotted on a logarithmic scale against T^−1/3 (see Figs. 4(a) and 4(b)), characteristic of the Mott 2D variable range hopping (VRH) conduction.¹⁸ Such a scaling behavior is reasonable for 2D semiconductor nanosheets as the electrons are confined in a very thin layer. However, for BSCO monolayers, the lnG vs T^−1/3 plot exhibits an inflection point around 75 K. Below this temperature the resistance increases sharply (see the supplementary material),¹⁷ with the relationship of lnG vs T^−1/3 obviously departing from linearity (Fig. 4(c)). Instead, a 1/2 exponent is observed: lnG vs T^−1/2 obeys linearity from ∼75 K down to the lowest temperature (Fig. 4(d)). Such a transition in conduction characteristics suggests the changes in localized behavior and a different conduction mechanism. Below we address the underlying physics and discuss the intrinsic transport mechanism of the BSCO nanosheets, especially for the monolayer. Analysis of transport data obtained at −84 V gate voltage yields a similar conclusion but with a smaller ES-VRH to Mott-VRH crossover temperature (T_cross ≈ 55 K) (see the supplementary material).¹⁷ 

In the BSCO system, Co³⁺ and Co⁴⁺ have low-spin t_2g⁶ and t_2g⁵ configurations respectively, and the holes are mainly located in the a_1g orbital among the three t_2g orbitals.¹⁹ Since the kinetic energy of the t_2g electrons are considerably smaller than that of the e_g electrons, the transport properties are dominated by the electron-lattice interaction.^19,20 In particular, the electron hopping process between neighboring Co ions is mediated by the O_2p states, so the hopping process depends strongly on surface/edge distortion and disorder. When a bulk BSCO crystal is exfoliated, the electronic properties of the resulting atomically thin flakes are strongly affected by surface disorder and defects. Similar to the effect of edge or surface disorder/defects on graphene,^21,22 the surface disorder and defects may induce localization of the wave function, leading to a transport gap with strongly localized states.²³ In another word, the surface disorder could give rise to a rapid variation in the local density of states (DOS) over the entire layer to block the conductive paths and induce VRH transport as is observed. Therefore, carriers become confined temporally when transporting from one dot to another because of the reduction in the number of conducting channels (see Fig. 5(a), sketch). This also accounts for the observed reduction of conductance with decreasing thickness. Moreover, within this scenario, the Coulomb charging effect is also expected to play a role in charge transport and can suppress the phase coherence between successive tunneling events.²⁴ Hence the disorder potential and the Coulomb charging effect jointly give rise to a transport gap in our BSCO nanosheets. Next we estimate the energy scales along with characteristic parameters of VRH transport in these nanosheets.

In a disordered semiconductor, the most frequent electron hopping among localized sites is through VRH instead of nearest neighbor hopping.^18,25 For VRH, conductance G ∝ exp (−2r/ξ − ΔE/k_BT), where ξ is the localization length, and ΔE denotes the energy difference between the initial and final sites (average disordered potential) and is related to hopping distance (r), DOS (g₀) and dimension (D) of material (ΔE ∼ 1/g₀r^D). Maximizing the hopping probability leads to the Mott-VRH law²⁵:

in which T_M is the Mott-VRH characteristic temperature, given by T_M = β_D/k_Bg₀ξ^D; β₂ = 13.8 for a 2D system and β₃ = 21.2 for a 3D system. However, Efros and Shklovskii argued that if the localization scale is small, the Coulomb potential Δ may open up a soft gap at low temperatures and the conductance follows an exponential 1/2 law.²⁶ In this model, conductance G obeys the ES-VRH law expressed by

in which the ES-VRH characteristic temperature T_ES = α_De²/κk_Bξ; α₂ = 6.5 and α₃ = 2.8 are numerical constants, and κ is the dielectric constant. Therefore, if k_BT < Δ, the ES-VRH should be predominant, whereas when k_BT > Δ, the Coulomb effect becomes negligible, and the conduction crosses over from ES-VRH to Mott-VRH as T increases. Namely, there is a crossover temperature T_cross: below T_cross, conductance obeys ES's law, while above T_cross, it obeys the Mott's law.

For our BSCO monolayers, G in the high temperature and low temperature regions can be well fitted by Mott-VRH and ES-VRH, respectively, with T_cross ∼75 K (see Figs. 4(c) and 4(d)). The T_M = 1.11 × 10⁵ K and T_ES = 1.82 × 10³ K can be extracted from the linear fittings. The VRH characteristic temperatures reflect the degree of disorder. Higher T_M and T_ES mean larger disorder. In the BSCO system, T_M is 6.7 × 10², 4.3 × 10³, and 1.1 × 10⁵ K for the N = 3, 2, and 1 samples, respectively, indicating an increase in disorder with decreasing layer number. The T_M values in the N = 3 and 2 samples are comparable to those in other Mott-VRH systems; however, the T_M value (as well as the T_ES value) of BSCO monolayers is considerably large, suggesting that the BSCO monolayers are rather disordered.^27,28 According to the DOS g₀ of bulk BSCO (∼10²⁰ cm⁻³ eV⁻¹, estimated from the carrier density and specific heat¹⁹), g₀ of our 2D BSCO nanosheets is estimated to be ∼10¹³ cm⁻² eV⁻¹. With these parameters, the Coulomb gap Δ, disorder potential ΔE (corresponding to the variation of Fermi level E_F by applying V_bg²⁹), and localization length ξ are estimated, as summarized in Table I.

For monolayers, the Coulomb gap is ∼6 meV, whereas the disorder potential is on the order of ∼100 meV. This means that there are two energy scales contributing to the transport gap, one is the Coulomb charging energy of the localized dots and the other is the relatively large disorder potential. The Coulomb gap Δ of ∼6 meV corresponds to a temperature of ∼70 K, which is quite consistent with the observed ES-VRH to Mott-VRH transition temperature (T_cross ∼75 K). In contrast, for the bilayer and trilayer nanosheets, the estimated Coulomb gap is around 1 meV or smaller, so Mott-VRH is the dominant mechanism and no ES-VRH is observed in the entire measured temperature range. With increasing layer number, the T_M, disorder potential and Coulomb gap are all reduced whereas the localization length ξ becomes larger, which means the system becomes less disordered and less localized. The localization length ξ of BSCO monolayers (∼2-3 nm) is much smaller than those of bilayer and trilayer nanosheets (∼10 and ∼24 nm, respectively), confirming that the monolayers consists of strongly localized state dots. Lastly, the application of a −84 V gate reduces the VRH characteristic temperatures or disorder potential and increases the localization length, suggesting that the disorder is partially suppressed under a negative gate voltage. As the electron hopping is fully confined in the plane, distinct from the artificial granular electronic materials,³⁰ few-layered BSCO represents a natural 2D system consisting of localized states (see the sketch in Fig. 5(a)).

Finally, we note the metal–semiconductor transition happened at N = 3. For BSCO with layer number N > 1, the interlayer quantum wave functions will begin to overlap (Fig. 5(b)), leading to what is known as exchange coupling; meanwhile, the disorder potential decreases. As the strength of exchange coupling increases, it will begin to overcome the disorder potential as well as the Coulomb charging energy, and thus the transport gap decreases. With further increase in the number of layers, the disorder becomes less important and the transport gap vanishes eventually, so the system undergoes a semiconductor-to-metal transition (see the sketch in Fig. 5(b)). Additionally, disorder effect caused by underlying SiO₂/Si substrate has been widely reported in 2D materials. This disorder can be increasingly screened in thicker sheets, and could partly contribute to the layer number dependent transport behavior as well. Nonetheless, it is important to note that the substrate effect is likely to play a much less significant role in the BSCO system (see the discussion in the supplementary material).¹⁷ From the transport measurements, we estimate that the average hopping distance r is ∼10 nm, which is almost the thickness of the trilayer nanosheets. This may be the reason why a metal–semiconductor transition occurs at N = 4 to 3. The Raman results also support this hypothesis (see the supplementary material).¹⁷ The out-of-plane vibration mode A_1g sharply weakens at N = 3, suggesting a discontinuous interlayer exchange coupling. Additionally the calculated strength of electron–phonon coupling suddenly increases from N = 4 to 3, indicating a noticeable enhancement of carrier localization (see the supplementary material).¹⁷ This metal–semiconductor transition may also reflect the variations in Fermi level E_F or mobility edges of the system. For the nanosheets with N > 3, the E_F is located in the extended states; as the degree of disorder increases with decreasing N, the E_F gradually enters the localized states through the mobility edges to develop a metal–semiconductor transition. The E_F in the critical N = 3 nanosheets corresponds to the position of the mobility edge. In summary, we find that BSCO nanosheets show a gradually enhanced insulating state with reduced dimensionality due to the increasing role of surface disorder. As a result, the monolayer, bilayer, and trilayer nanosheets become semiconductors, in contrast to the metallic nature of their bulk counterpart. In these nanosheets, the disorder potential and Coulomb charging effect give rise to a transport gap, which is responsible for the observed semiconductor behavior. We have demonstrated that, different from the artificial granular electronic materials, the semiconducting BSCO nanosheets function as a natural 2D system consisting of localized states. Our systematic studies provide important insight into a new class of 2D materials from exfoliated transition metal oxides and motivate additional studies to probe their thermal conduction, magnetic transport, and thermoelectric properties of this and other similar, unexplored layered material systems. This study opens new opportunities to tune hopping modes, modulate transport mechanisms, and adjust carrier mobility/density by controlling layer thickness. It could enable exciting opportunities for fundamental research as well as use for new types of electronic switches.

BSCO nanosheets were mechanical exfoliated from BSCO single crystal onto silicon wafers with a 300-nm-thick SiO₂ dielectric layer. The samples were then rinsed with acetone and isopropanol to remove residue, and blown dry using nitrogen. Electron-beam lithography was used to define the source and drain electrodes of devices, and silver thin films were evaporated with a thermal evaporator as contact electrodes. For the sample morphology characterization, tapping-mode AFM imaging was carried out with a Veeco 5000 system, and SEM imaging was performed on a JEOL 6700F system operating at 5 kV. For the device characterization, the DC electrical transport measurements were conducted with a Lakeshore probe station (Model TTP4), physical property measurement system (PPMS, Quantum Design) with a computer-controlled analogue-to-digital converter (National Instruments model 6030E).

We acknowledge the Nanoelectronics Research Facility (NRF) at UCLA for technical support. We thank N. Weiss for reading the manuscript. X.D. acknowledges partial support by NSF CAREER award 0956171.