# Gate-induced decoupling of surface and bulk state properties in selectively-deposited Bi$_2$Te$_3$ nanoribbons

### Submission summary

 As Contributors: Daniel Rosenbach Arxiv Link: https://arxiv.org/abs/2104.03373v3 (pdf) Date accepted: 2022-03-14 Date submitted: 2022-02-09 10:21 Submitted by: Rosenbach, Daniel Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Experiment Approach: Experimental

### Abstract

Three-dimensional topological insulators (TIs) host helical Dirac surface states at the interface with a trivial insulator. In quasi-one-dimensional TI nanoribbon structures the wave function of surface charges extends phase-coherently along the perimeter of the nanoribbon, resulting in a quantization of transverse surface modes. Furthermore, as the inherent spin-momentum locking results in a Berry phase offset of $\pi$ of self-interfering charge carriers an energy gap within the surface state dispersion appears and all states become spin-degenerate. We investigate and compare the magnetic field dependent surface state dispersion in selectively deposited Bi$_2$Te$_3$ TI micro- and nanoribbon structures by analysing the gate voltage dependent magnetoconductance at cryogenic temperatures. While in wide microribbon devices the field effect mainly changes the amount of bulk charges close to the top surface we identify coherent transverse surface states along the perimeter of the nanoribbon devices responding to a change in top gate potential. We quantify the energetic spacing in between these quantized transverse subbands by using an electrostatic model that treats an initial difference in charge carrier densities on the top and bottom surface as well as remaining bulk charges. In the gate voltage dependent transconductance we find oscillations that change their relative phase by $\pi$ at half-integer values of the magnetic flux quantum applied coaxial to the nanoribbon, which is a signature for a magnetic flux dependent topological phase transition in narrow, selectively deposited TI nanoribbon devices.

Published as SciPost Phys. Core 5, 017 (2022)

Based on the comments of two anonymous referees as well as the editor in charge we are happy to re-submit our manuscript with the title 'Gate-induced decoupling of surface and bulk state properties in selectively-deposited Bi$_2$Te$_3$ nanoribbons' to the SciPost Physics Core journal.

Together with the help of the referees we have identified an inconsistency in our data analysis, with respect to the dimensionality and the underlying mode of transport on the surface of our three dimensional topological insulator nanoribbons. While the h/e -period of Aharonov-Bohm oscillations identified from the magnetoconductance point to ballistic surface state transport, we used a classical two-dimensional diffusive model for the temperature dependency of the oscillation amplitude of the same Aharonov-Bohm oscillations. After another literature research we therefore adapted the model we use to fit our $\delta G(T)$ data.

### List of changes

**List of changes**
Section 3.2, 2nd paragraph: We added the argument that in case of ballistic surface transport an h/e periodicity of Aharonov-Bohm oscillations is expected. We also added that for interference within time-reversed paths in the diffusive limit an $h/(2e)$ period is anticipated. In this context we added reference [44].

Section 3.2, 3rd paragraph: We pointed out that, while transport on the surface is ballistic, the bulk conductivity along the nanoribbon is diffusive. This argument is of importance to understand the following discussion of the temperature dependency of the Aharonov-Bohm oscillation amplitude in the next paragraph.

Section 3.2, 4th paragraph and Fig. 4 b): We changed the model used to describe the temperature dependency of the Aharonov-Bohm oscillation amplitude and the phase-coherence length resulting from the new model applied to the data.

Conclusions section, 2nd paragraph: We updated the value for the phase-coherence length identified.

### Submission & Refereeing History

Resubmission 2104.03373v3 on 9 February 2022
Resubmission 2104.03373v2 on 8 November 2021
Submission scipost_202108_00005v1 on 3 August 2021

## Reports on this Submission

### Report

The authors have improved the manuscript and they answer the questions raised in the previous reports. I recommend therefore this work for a publication in SciPost Physics Core.

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### Report

The manuscript fulfils the acceptance criteria for SciPost Physics Core.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -