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Gateinduced decoupling of surface and bulk state properties in selectivelydeposited Bi2Te3 nanoribbons
by Daniel Rosenbach, Kristof Moors, Abdur. R. Jalil, Jonas Kölzer, Erik Zimmermann, Jürgen Schubert, Soraya Karimzadah, Gregor Mussler, Peter Schüffelgen, Detlev Grützmacher, Hans Lüth, Thomas Schäper
Submission summary
As Contributors:  Daniel Rosenbach 
Preprint link:  scipost_202108_00005v1 
Date submitted:  20210803 11:54 
Submitted by:  Rosenbach, Daniel 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Experimental 
Abstract
Threedimensional topological insulators (TIs) host helical Dirac surface states at the interface with a trivial insulator. In quasionedimensional TI nanoribbon structures the wave function of surface charges extends phasecoherently along the perimeter of the nanoribbon, resulting in a quantization of transverse surface modes. Furthermore, as the inherent spinmomentum locking results in a Berry phase offset of pi of selfinterfering charge carriers an energy gap within the surface state dispersion appears and all states become spindegenerate. We investigate and compare the magnetic field dependent surface state dispersion in selectively deposited Bi2Te3 TI micro and nanoribbon structures by analysing the gate voltage dependent magnetoconductance at cryogenic temperatures. Hall measurements on microribbon field effect devices show a high bulk charge carrier concentration and electrostatic simulations show an inhomogeneous gate potential profile on the perimeter of the TI ribbon. In nanoribbon devices we identify a magnetic field dependency of the surface state dispersion as it changes the occupation of transverse subbands close to the Fermi energy. We quantify the energetic spacing in between these subbands by measuring the conductance as a function of the applied gate potential and use an electrostatic model that treats the inhomogeneous gate profile and the initial charge carrier densities on the top and bottom surface. In the gate voltage dependent transconductance we find oscillations that change their relative phase by pi at halfinteger values of the magnetic flux quantum applied coaxial to the nanoribbon providing evidence for a magnetic flux dependent topological phase transition in narrow, selectively deposited TI nanoribbon devices.
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Reports on this Submission
Anonymous Report 2 on 20211020 (Invited Report)
Report
The authors report on the electrical investigation of gated Bi2Te3 ribbons. Whereas I do not have an issue with the quality of presented measurements, the main issue is to determine in which respect the presented data and conclusions surpass the stateoftheart in the field. From the presented manuscript it is not clear which groundbreaking experimental discovery it details or that it opens a new pathway in an existing or a new research direction. The manuscript may be considered for SciPost Physics Core if the authors can meet its acceptance expectations, which, unfortunately, at present the manuscript does not.
Anonymous Report 1 on 2021105 (Invited Report)
Report
The authors studied transport in micro and nanoribbons of the Bi2Te3 topological insulator, grown by MBE following a technique developed previously in the group, the selective growth area growth approach. They focus on transconductance measurements using top gates, down to low temperature (T about 2K). They characterize their samples by measuring a microribbon in the first part of the paper and investigate the quantum transport properties and the formation of 1D subbands in a 200nm wide nanoribbon in the second part of the paper. The paper combines both experimental results and numerical simulations.
Considering the difficulty to fabricate such devices and to realize this kind of experiments, the results are of very good quality and can be considered as stateoftheart results.
Nevertheless, this work raises major criticism concerning its novelty and the main results shown in the paper were already reported or discussed in the literature in the last years, some of these reports being cited in the present work (see for instance PRB 97, 035157; Nat. Nanotechnol. 11, 345; PRL 110, 186806). I couldn’t identify any significant step ahead beyond what has been published so far in the present version of the manuscript. In order to meet the novelty requirements, a clear (new) message should be formulated, supported by a (new?) set of data.
Apart from this, I have some important and less important comments:
1) About the existence of 1D subbands in the nanoribbon: the mobility and the density are known so that it is possible to extract the mean free path l_0 and to compare it with the perimeter of the nanoribbon. Thanks to the relation µ=el_0/(hbar k_F), I could roughly estimate l_0 to be about 20 nm for the microribbon. This value, compared to the perimeter of the nanoribbon, precludes the formation of any quantized 1D subbands as presented in the paper. In other term, the strong scattering induces a strong coupling between each subbands and the transverse wave vectors cannot be considered as good quantum number anymore. The description of the band structure in terms of 1D subbands fails down quickly as soon as l_0 becomes smaller than the perimeter (see for instance PRB 97, 075401).
2) About the topological (or trivial) nature of the phase shift: there is a confusion about the topological nature of the phase shift in the gate voltage dependence of the AB oscillations. It should be clearly stated that such a phase shift has a trivial origin and can be attributed to confinement effects only as shown in PRB 97, 075401. Similar measurement in (topologically trivial) carbon nanotubes should also lead to such phase shifts.
3) The nature of the 2DEG at the origin of the AB oscillations: the author claim that “Our analysis shows evidence of quantized transversemomentum states on the perimeter of the TI nanoribbon and the electrostatic model treatment allows to distinguish these features from bulk effects or conventional two dimensional space charge layers without spinmomentum locking.” If the influence of the bulk is shortly (maybe not enough for the nanoribbon) discussed, an extended discussion about the nature 2DEG is lacking in the manuscript, where a simple mention of the spin degeneracy g_s of the 2DEG is made. A more detailed discussion should highlight this important result. Moreover, the fitting scenario corresponding to g_s=2 and a capacitance twice as large as the one considered here should be discussed and excluded to support the conclusion of the paper. As measured in the microribbon, such a larger capacitance would roughly correspond to the capacitance of the top surface and would support the scenario of a conventional 2DEG.
4) Quantum interferences: there is again here some confusion. According to the value of the phase coherence length, we should be between D=1 and D=2. At two dimensions, one expects tau_phi propto T1 leading to L_phi propto T1/2 providing that we are in the diffusive regime (L_phi propto tau_phi1/2) that precludes the formation of 1D subbands. If we are at D=1, we should have tau_phi propto T2/3 leading to L_phi propto T1/3 in the diffusive regime and L_phi propto T2/3 in the ballistic regime. A clear discussion of the different cases is lacking in the paper.
5) Universal Conductance fluctuations: in the analysis of the gate voltage dependence of the AB oscillations, there is no mention of the influence of universal conductance fluctuations of the surface states and of the bulk states. In the diffusive regime, such quantum interference should nevertheless lead to fluctuations that are, in amplitude, comparable to AB oscillations.
Less important points:
 A clear definition of C(s) is lacking in the paper.
 According to their simulations, the authors show that in the case of the wide ribbon, the total capacitance is not the average capacitance integrated along the perimeter but rather the top capacitance for the nanoribbon so that the model of the effective capacitance fails to reproduce the measured conductance. It is stated that the main reason for that is the screening by bulk charge carriers. For the nanoribbon nevertheless, the model of the effective capacitance works well. This is surprising since the bulk carrier density should not vary significantly between a micro and a nanoribbon. Does the aspect ratio (100nm dielectric for a 200nm wide ribbon vs 15nm thick dielectric and 1µm wide ribbon) causes such a large difference between the micro and the nanoribbon? This point should be discussed in the manuscript.
 The bulk doping is about 7,6 – 4,5 10^21 cm3. This are some very large values for such a thin structure. We could naively expect that in such thin nanostructures, the bulk would be close to the depletion regime. What is the screening length?
 What about the reproducibility? The fabrication and growth technique used by the authors should allow the fabrication of measurement of different devices. Do the authors have some measurements on other devices?