Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi$_2$Se$_3$ (1003.3883v2)

Abstract: We report a transport study of exfoliated few monolayer crystals of topological insulator Bi$_2$Se$_3$ in an electric field effect (EFE) geometry. By doping the bulk crystals with Ca, we are able to fabricate devices with sufficiently low bulk carrier density to change the sign of the Hall density with the gate voltage $V_g$. We find that the temperature $T$ and magnetic field dependent transport properties in the vicinity of this $V_g$ can be explained by a bulk channel with activation gap of approximately 50 meV and a relatively high mobility metallic channel that dominates at low $T$. The conductance (approximately 2 $\times$ 7$e^2/h$), weak anti-localization, and metallic resistance-temperature profile of the latter lead us to identify it with the protected surface state. The relative smallness of the observed gap implies limitations for EFE topological insulator devices at room temperature.

• The paper demonstrates that voltage tuning in Ca-doped Bi2Se3 isolates high-mobility surface conduction by shifting the chemical potential within a ~50 meV bulk gap.
• It employs advanced e-beam lithography and precise Hall measurements to distinguish bulk and surface transport contributions.
• The study highlights surface state dominance below 100K, paving the way for low-temperature spintronic device applications.

Insights into Electronic Transport in Voltage-Tuned Bi$_2$Se$_3$ Topological Insulators

The paper focuses on the transport properties of the topological insulator (TI) Bi$_2$Se$_3$ under the influence of electric field effect (EFE) techniques. By introducing calcium (Ca) doping into the Bi$_2$Se$_3$ crystals, the research team effectively reduced bulk carrier density, providing an opportunity to explore surface state (SS) conduction more thoroughly. Through sophisticated experimental setups, the authors successfully tune the chemical potential $\mu$ within the bulk band gap via gate voltage adjustments, enabling the investigation of both bulk and surface conduction in these systems.

Key Experimental Findings

• Sample Preparation and Characteristics: The Ca-doped Bi$_2$Se$_3$ crystals were mechanically exfoliated onto Si substrates with SiO$_2$ layers and measured across different thicknesses. Electrical contacts employed e-beam lithography, ensuring precise Hall geometry setups. The authors highlight the correlations between optical images and atomic force microscopy measurements to estimate film thickness.
• Transport Properties: The transport measurements revealed distinct behavior governed by both bulk and surface contributions. The Hall density sign was adjustable via gate voltage, signifying effective tuning of carrier types between electron-like and hole-like regimes. The experiments demonstrated that a parallel conduction model comprising a metallic surface state and a bulk gapped channel effectively describes the observed characteristics.
• Gap Characterization and Surface-State Domination: The paper found a bulk activation gap of approximately 50 meV, limiting the EFE-induced surface-dominated transport at room temperature. Below approximately 100 K, the surface channels become prominent, characterized by high mobility and weak anti-localization.
• Conductance Analysis: Hall measurements established the emergence of surface-dominated conduction below certain temperatures. Conductance fluctuations, magnetic response, and scaling behavior provided insights into coherence length and disorder effects.

Theoretical and Practical Implications

From a theoretical perspective, the paper confirms and extends our understanding of how surface states in TIs like Bi$_2$Se$_3$ can be isolated and studied through advanced sample preparation and electric field control. The observed linear dispersion and spin-polarized nature of these surface states are fundamental to understanding their potential for novel quantum phases and particles characteristic of high-energy physics, further elucidated by fitting measures such as equation $$\Delta G_{\textrm{xx}}(H) = A \frac{e^2}{h}\left[\ln\frac{H_0}{H} - \psi\left(\frac{1}{2} + \frac{H_0}{H}\right)\right]$$.

In terms of practical implications, the research validates the application potential of Bi$_2$Se$_3$ TIs in spintronic devices and other technology domains leveraging the robustness of surface states against non-magnetic scatterers. The paper suggests room-temperature limitations but opens avenues for low-temperature device constructions and further explorations in material synthesis aiming to circumvent inherent material obstacles such as remnant electron density from Se vacancies.

Prospects for Future Research

The findings suggest a pathway toward leveraging voltage-tuning methods in TIs for exploring various applications involving magnetic and superconducting states. Future research could explore alternative doping strategies, interface engineering, or strain applications to extend the viable temperature range for surface state operation. Additionally, integration with other novel materials or heterostructures can advance the integration of TIs in complex device architectures.

In summary, this paper adds meticulous experimental results and theoretical validation to the growing body of work on TIs, driving forward the field's knowledge base and offering promising directions for both fundamental and applied research in advanced quantum materials.