## Abstract

The electric-field-induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor^{1,2,3,4}. In this scheme, ‘on’ is the ballistic flow of charge and spin along dissipationless edges of a two-dimensional quantum spin Hall insulator^{5,6,7,8,9}, and ‘off’ is produced by applying an electric field that converts the exotic insulator to a conventional insulator with no conductive channels. Such a topological transistor is promising for low-energy logic circuits^{4}, which would necessitate electric-field-switched materials with conventional and topological bandgaps much greater than the thermal energy at room temperature, substantially greater than proposed so far^{6,7,8}. Topological Dirac semimetals are promising systems in which to look for topological field-effect switching, as they lie at the boundary between conventional and topological phases^{3,10,11,12,13,14,15,16}. Here we use scanning tunnelling microscopy and spectroscopy and angle-resolved photoelectron spectroscopy to show that mono- and bilayer films of the topological Dirac semimetal^{3,17} Na_{3}Bi are two-dimensional topological insulators with bulk bandgaps greater than 300 millielectronvolts owing to quantum confinement in the absence of electric field. On application of electric field by doping with potassium or by close approach of the scanning tunnelling microscope tip, the Stark effect completely closes the bandgap and re-opens it as a conventional gap of 90 millielectronvolts. The large bandgaps in both the conventional and quantum spin Hall phases, much greater than the thermal energy at room temperature (25 millielectronvolts), suggest that ultrathin Na_{3}Bi is suitable for room-temperature topological transistor operation.

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## Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

M.T.E. was supported by ARC DECRA fellowship DE160101157. M.T.E., J.L.C., C.L. and M.S.F. acknowledge funding support from CE170100039. J.L.C., J.H. and M.S.F. are supported by M.S.F.’s ARC Laureate Fellowship (FL120100038). S.A. acknowledges funding support from ARC Discovery Project DP150103837. M.T.E. and A.T. acknowledge travel funding provided by the International Synchrotron Access Program (ISAP) managed by the Australian Synchrotron, part of ANSTO, and funded by the Australian Government. M.T.E. acknowledges funding from the Monash Centre for Atomically Thin Materials Research and Equipment Scheme. S.A.Y. and W.W. acknowledge funding from Singapore MOE AcRF Tier 2 (grant no. MOE2015-T2-2-144). S.A. acknowledges the National University of Singapore Young Investigator Award (R-607-000-094-133). This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. Part of this research was undertaken on the soft X-ray beamline at the Australian Synchrotron, part of ANSTO. The authors acknowledge computational support from the National Supercomputing Centre, Singapore.

## Author information

### Affiliations

#### School of Physics and Astronomy, Monash University, Clayton, Victoria, Australia

- James L. Collins
- , Chang Liu
- , Jack Hellerstedt
- , Michael S. Fuhrer
- & Mark T. Edmonds

#### Monash Centre for Atomically Thin Materials, Monash University, Clayton, Victoria, Australia

- James L. Collins
- , Chang Liu
- , Jack Hellerstedt
- , Michael S. Fuhrer
- & Mark T. Edmonds

#### ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Monash University, Clayton, Victoria, Australia

- James L. Collins
- , Anton Tadich
- , Chang Liu
- , Michael S. Fuhrer
- & Mark T. Edmonds

#### Australian Synchrotron, Clayton, Victoria, Australia

- Anton Tadich

#### Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore, Singapore

- Weikang Wu
- & Shengyuan A. Yang

#### Department of Physics and Centre for Advanced 2D Materials, National University of Singapore, Singapore, Singapore

- Lidia C. Gomes
- , Joao N. B. Rodrigues
- & Shaffique Adam

#### National Centre for Supercomputing Applications, University of Illinois at Urbana-Champaign, Champaign, IL, USA

- Lidia C. Gomes

#### Institute for Condensed Matter Theory and Department of Physics, University of Illinois at Urbana-Champaign, Champaign, IL, USA

- Joao N. B. Rodrigues

#### Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

- Jack Hellerstedt

#### Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

- Hyejin Ryu
- , Shujie Tang
- & Sung-Kwan Mo

#### Center for Spintronics, Korea Institute of Science and Technology, Seoul, South Korea

- Hyejin Ryu

#### Yale-NUS College, Singapore, Singapore

- Shaffique Adam

#### Centre for Quantum Transport and Thermal Energy Science, School of Physics and Technology, Nanjing Normal University, Nanjing, China

- Shengyuan A. Yang

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### Contributions

M.T.E., J.L.C. and M.S.F. devised the STM experiments. M.T.E. devised the ARPES and XPS experiments. M.T.E. and J.L.C. performed the MBE growth and STM/STS measurements at Monash University. J.H. assisted with the experimental setup at Monash University. M.T.E., J.L.C. and A.T. performed the MBE growth and ARPES measurements at Advanced Light Source with the support from H.R., S.T. and S.-K.M. The MBE growth and XPS measurements at the Australian Synchrotron were performed by M.T.E., J.L.C., A.T., J.H. and C.L. The DFT calculations were performed by L.C.G., J.N.B.R., W.W. and S.A.Y.; S.A. assisted with the theoretical interpretation of the data. M.T.E., J.L.C. and M.S.F. composed the manuscript. All authors read and contributed feedback to the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Mark T. Edmonds.

## Extended data figures and tables

### Extended Data Fig. 1 RHEED, LEED and XPS characterization of few-layer Na

_{3}Bi.**a**,**b**, RHEED patterns of Si(111) 7 × 7 reconstruction along the \(\bar{{\rm{\Gamma }}}-\bar{{\rm{M}}}\) direction (**a**) and of few-layer Na_{3}Bi along the \(\bar{{\rm{\Gamma }}}-\bar{{\rm{K}}}\) direction (**b**).**c**, 1 × 1 LEED image of few-layer Na_{3}Bi taken at 32 eV.**d**, XPS of Na 2*p*and Bi 5*d*core level taken at*hv*= 100 eV for few-layer Na_{3}Bi.**e**, Normalized XPS of Si 2*p*core level taken at 350 eV (left panel) and at 850 eV (right panel). Each panel shows the Si 2*p*of the clean Si substrate (black curve) and with few-layer Na_{3}Bi grown on top (red curve). The spectra have been offset in intensity for clarity.### Extended Data Fig. 2

*k*_{z}band dispersion of few-layer Na_{3}Bi from photon-energy-dependent ARPES measurements.These photon-energy-dependent ARPES measurements of ML/BL Na

_{3}Bi demonstrate effectively 2D dispersion. The figure shows a cut through the photon-energy-dependent (*hv*= 45–55 eV) Fermi surface, demonstrating non-dispersion of the gapped Dirac valence band along*k*_{z}, with the intensity of emitted photoelectrons reflected in the colour scale.### Extended Data Fig. 3 Bandgap extraction from scanning tunnelling spectra.

**a**,**b**, d*I*/d*V*spectra taken for ML (red) and BL (black) Na_{3}Bi plotted on a linear (**a**) and a logarithmic (**b**) scale. The logarithmic scale better accounts for the large change in intensity near the band edge.**c**, Normalized d*I*/d*V*spectra at various tip–sample separations, illustrating that the onset in intensity typically occurs at a normalized d*I*/d*V*signal of 0.01 within an error of ±25 meV (when also accounting for tip-induced band bending).**d**, Calculated tip-induced band bending,*ϕ*_{BB}, using equation (3) for different biases.### Extended Data Fig. 4 DFT calculations on the topological nature of Na

_{3}Bi layers.**a**, 2D Brillouin zone for Na_{3}Bi layered structures. Here we also show the projected 1D Brillouin zone used for studying the edge spectrum.**b**–**h**, Results for ML (**b**–**f**) and BL (**g**–**k**) Na_{3}Bi with Na(2) vacancies (with one Na(2) vacancy in a 2 × 2 supercell).**b**,**g**, Electronic band structures, where the energy zero is set to be at the valence band maximum.**c**,**h**, Orbitally resolved band structure without SOC and**d**,**i**, orbitally resolved band structure with SOC. The red dots represent the contribution from the Na*s*and Bi*s*atomic orbitals, and the blue dots represent contribution from the Bi*p*_{x}/*p*_{y}atomic orbitals. Band inversion induced by SOC can be clearly observed at the Γ point for both ML and BL cases, which indicates that both ML and BL Na_{3}Bi are non-trivial 2D topological insulators.**e**,**j**, Projected edge spectrum (edge along the [010] direction), where pairs of \({{\mathbb{Z}}}_{2}\) topological edge states can be observed in the energy gaps (marked by the white arrows) where the colour scale reflects the spectral weight.**f**,**k**, Calculated Wannier function centre evolutions, which indicate a nontrivial \({{\mathbb{Z}}}_{2}\) invariant (\({{\mathbb{Z}}}_{2}=1\)) for the bulk band structure in both ML and BL.### Extended Data Fig. 5 Extracting and fitting the dispersion relation from ARPES MDC and EDC spectra of few-layer Na

_{3}Bi.**a**, ARPES intensity plot (colour scale at right) along the K–Γ–K direction after 30 min of K dosing.**b**, Stack plots of MDCs for the valence band (left panel) and conduction band (right panel) extracted from**a**, where the blue circles represent the Gaussian-fit band locations. Red and yellow lines mark shared constant-energy*k*_{x}vertices used throughout**b**and**c**.**c**, EDCs extracted from**a**.**d**,**e**, Fitting band coordinates that have been extracted by MDC and EDC analysis (red dots) to a hyperbola (**d**) and to a parabola (**e**), showing that Na_{3}Bi-like bands are best described by a hyperbola function.### Extended Data Fig. 6 Displacement field calculations from K dosing in ARPES.

**a**, Electron-band Fermi surface of few-layer Na_{3}Bi after 30 min of K dosing, where the colour scale reflects the intensity of emitted photoelectrons at the Fermi energy.**b**, Red line, radially averaged momentum profile through the Fermi surface, showing the ring structure at*k*_{F}(dashed blue line shows position of*k*_{F}).**c**, Calculated charge density (left-hand*y*axis) using equation (7) and the corresponding electric displacement field (right-hand*y*axis) associated with the net charge transfer from the as-grown film as a function of K-dosing time. Red points are as-measured, and green points are extrapolated based on the*E*_{F}shifting rate with K dosing between 15 min and 50 min.### Extended Data Fig. 7 Electric displacement field-dependence of topological insulator ML/BL Na

_{3}Bi bands near*E*_{F}.**a**, The sum of*Δ*parameters from the best fit of equation (5) to ARPES dispersion versus applied electric displacement field. Both*Δ*_{n,p}are directly calculated from the high-field (purple) measurements, however in low-field (green) measurements,*E*_{F}is not sufficiently shifted for the electron dispersion to be clearly resolved. Here we have used the ratio (*Δ*_{p}+*Δ*_{n})/*Δ*_{p}≈ 1.4 measured from the purple points to extrapolate*Δ*_{n}for undosed film.**b**, The valence edge (blue) and conduction edge (red) calculated from the fitted ARPES dispersion are shown for two high-symmetry directions: circles for K–Γ–K and squares for M–Γ–M.### Extended Data Fig. 8 Electric-field calculations from STM.

**a**,**b**, Tunnelling current as a function of relative tip–sample distance*z*for**a**, Au(111) (bias +500 mV), and**b**, thin film Na_{3}Bi (bias −300 mV). The top axis in**b**represents the total distance,*s*, between tip and sample determined as described in Methods section ‘Calculating tip–sample separation and electric field’. The black lines in**a**and**b**are exponential fits.**c**, Energy-level schematic illustrating the effects of an image potential on the (purple trapezoidal) junction barrier, where*s*is the tip–sample distance, and*ϕ*_{Sample}and*ϕ*_{Tip}are the work function of the sample and tip, respectively. Progression from blue, green, yellow, orange and red curves indicates modification of the apparent barrier height due to the imaging potential at decreasing tip–sample distances*s*.**d**, ln(*I*(*s*)/*I*_{0}) shown as a function of distance for a square barrier model (blue dashed line), for DFT-LDA (black full line), for the image potential model (black dashed-dotted), and for the local orbital basis model (red line). Data are taken from figure 10 of ref.^{41}.### Extended Data Fig. 9 Scanning tunnelling spectra of ML Na

_{3}Bi.Shown are individual d

*I*/d*V*spectra taken on ML Na_{3}Bi at different tip–sample separations (electric field) (shown at right). The spectra have been normalized and offset for clarity.### Extended Data Fig. 10 DFT calculations of Na

_{3}Bi layers with electric field.**a**, Calculated bandgap variation as a function of electric field for ML Na_{3}Bi with an Na(2) vacancy. The gap closes and reopens at about 1.85 V Å^{−1}.**b**, 2D Brillouin zone and the projected 1D boundary Brillouin zone.**c**–**f**, Orbital-resolved band structures and edge spectra for ML Na_{3}Bi at electric fields of 0.0 V Å^{−1}(**c**,**d**) and 2.5 V Å^{−1}(**e**,**f**), which are marked by points A and B in**a**.**c**, Orbital-resolved band structures with SOC in the absence of electric field (the energy zero is set to be at the valence band maximum at the Γ point). The red dots represent the contribution from the Na*s*and Bi*s*atomic orbitals, and the blue dots represent the contribution from the Bi*p*_{x}/*p*_{y}atomic orbitals. A band inversion is observed at the Γ point induced by SOC, indicating that ML Na_{3}Bi is a non-trivial 2D topological insulator.**d**, Projected edge spectrum (edge along the [010] direction) in the absence of electric field, showing topological edge states. Panels**e**and**f**show the corresponding results at an electric field of 2.5 V Å^{−1}. In**e**, the band ordering at Γ is inverted compared to**c**, indicating a topological phase transition to a trivial insulator phase. This is confirmed by the disappearance of topological edge states as shown in**f**.### Extended Data Fig. 11 Crystal structure and symmetries of ML and BL Na

_{3}Bi.**a**,**b**, Tables showing the point group (PG) symmetries for ML and BL Na_{3}Bi, respectively. The second and third rows of each table indicate the effects of electric field (*E*_{z}) and an Na(2) vacancy, respectively. We note that at zero electric field both pristine and Na(2) vacancy ML and BL Na_{3}Bi are 2D QSH insulators, with topological index \(\upsilon \in {{\mathbb{Z}}}_{2}=1\).**c**–**h**, Crystal structure of Na_{3}Bi as a result of an Na(2) vacancy and electric field.**c**,**f**, Pristine ML (**c**) and BL (**f**) Na_{3}Bi;**d**,**g**, ML (**d**) and BL (**g**) Na_{3}Bi each with an Na surface vacancy;**e**,**h**, ML (**e**) and BL (**h**) Na_{3}Bi with Na surface vacancy plus electric field applied perpendicular to the sample.

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