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Spin and Orbital Spectroscopy in the Absence of Coulomb Blockade in Lead Telluride Nanowire Quantum Dots
by M. Gomanko, E. J. de Jong, Y. Jiang, S. G. Schellingerhout, E. P. A. M. Bakkers, S. M. Frolov
This is not the latest submitted version.
|As Contributors:||Sergey Frolov|
|Arxiv Link:||https://arxiv.org/abs/2111.13242v1 (pdf)|
|Date submitted:||2021-12-10 12:13|
|Submitted by:||Frolov, Sergey|
|Submitted to:||SciPost Physics|
We investigate quantum dots in semiconductor PbTe nanowire devices. Due to the accessibility of ambipolar transport in PbTe, quantum dots can be occupied both with electrons and holes. Owing to a very large dielectric constant in PbTe of order 1000, we do not observe Coulomb blockade which typically obfuscates the orbital and spin spectra. We extract large and highly anisotropic effective Lande g-factors, in the range 20-44. The absence of Coulomb blockade allows direct readout, at zero source-drain bias, of spin-orbit hybridization energies of up to 600 microelectronvolt. These spin properties make PbTe nanowires, the recently synthesized members of group IV-VI materials family, attractive as a materials platform for quantum technology, such as spin and topological qubits.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2022-2-9 (Invited Report)
1. Interesting material (PbTe narrow bandgap semiconductor).
2. MBE-grown nanowires as the objects of magnetotransport measurements.
3. Back-gate voltage dependent transport measurements, quite unique for PbTe.
4. Notion of the absence of Coulomb blockade effects enabling extraction of the spin-orbit hybridization energies.
1. Introductory part does not refer comprehensively to the existing literature concerning IV-VI narrow bandgap semiconductor nanowires.
2. The basic parameters of PbTe NWs used for the measurements - axes orientation, lengths diameters are not specified.
3. The differences between individual devices characterized by magnetotransport measurements are not specified.
The authors report on back-gate voltage dependent magnetotransport of single PbTe nanowires.
They notice the absence of Coulomb blockade effects, due to the high static dielectric constant of PbTe, which allows extracting the spin-orbit hybridization energies.
The paper is scientifically sound and can be published after minor revision; only some doubts concerning the introductory part and some minor details in the main text arise, as specified below.
1. In the introductory part, the authors write;
Previous efforts to grow PbTe nanowires focused on chemical vapor deposition [21, 22]. A related material SnTe is expected to be a topological crystalline insulator, and has been explored in the nanowire form [23, 24].
1a. The authors ignore quite numerous literature reports concerning PbTe nanowires fabricated by chemical methods such as hydrothermal synthesis:
Guoan Tai, Wanlin Guo, and Zhuhua Zhang, Cryst. Growth & Design 8, 2906 (2008);
Qingyu Yan, et al., Chem. Mater. 20, 6298, (2008);
and by MBE:
P. Dziawa, et. al., Cryst. Growth and Design, 10, 109 (2010)
The papers reporting on transport and thermoelectric properties of PbTe NWs also deserve citing:
So Young Jang, et. al., Transport properties of single-crystalline n-type semiconducting PbTe nanowires. Nanotechnology 20, 415204, (2009)
Jong Wook Roh, et. al., Size-dependent thermal conductivity of individual single-crystalline
PbTe nanowires. Appl. Phys. Lett. 96, 103101 (2010).
1b. Further in the introductory part the authors state that:
A related material SnTe is expected to be a topological crystalline insulator, and has been explored in the nanowire form [23, 24].
SnTe is not an “expected” but proved crystalline topological insulator, which is evidenced e.g., here:
Y. Tanaka, et al., Experimental realization of a topological crystalline insulator in SnTe. Nat. Phys. 8, 800 (2012).
Also references 23, and 24 do not grasp the already published reports on SnTe NWs, especially in the context of SnTe NWs grown by MBE:
J. Sadowski, et al., Defect-free SnTe topological crystalline insulator nanowires grown by molecular beam epitaxy on graphene. Nanoscale, 10, 20772, (2018).
2. The first phrase of the section “Brief methods” reads:
PbTe nanowires are grown using molecular beam epitaxy (MBE) 
Further in the text there is no information neither on the geometrical parameters (lengths diameters) nor on crystalline orientation of NWs, what is the NW axis direction? It can only be deduced that it is  since in one place further in the text the authors mention that the NWs have square cross-sections. Sending the reader to the paper published already - Ref.  is not fair; the reader cannot be forced to dig into the previous papers published by the authors, to understand the current one.
3. On the top of the page 2 the authors introduce Device 1 and 2 without specifying the difference between them.
4. Further on the authors refer to Figs. S9 and S10, without specifying that these figures are placed in the supplementary material.
5. On page 2, right column lines 7-8 for the bottom:
While the conduction band of PbTe is known to have four-fold valley degeneracy [? ]
Do the authors have doubts about the validity of this phrase, or they have forgotten to specify the appropriate reference?
Anonymous Report 1 on 2022-2-3 (Invited Report)
- The authors carry out mesoscopic measurements on PbTe nanowire quantum dots and discuss their potential for quantum devices. PbTe can have strong spin-orbit splitting and has a large g-factor, making it indeed attractive for the application that the authors consider. It is actually surprising that this material has not yet been considered for this research direction.
- The strength and anisotropy of the g-factor are measured for the first time in such structures and argue that PbTe can compete with III-Vs.
- The type of measurements combined with the analysis that is carried out are novel and can lead to progress and more questions in an important research area. This is especially true given the fact that the dielectric constant of PbTe is high, which has both advantages and disadvantages when it comes to quantum device performance as pointed out by the authors.
- A sufficient number of devices have been studied and are reported on.
- Some of the analysis lacks depth. The anisotropy of the g-factor is not discussed in the context of the band structure of PbTe and the anisotropy of its Fermi surface.
- The valley degeneracy of PbTe is ignored but the argument behind why that is done is not sufficient.
The authors report mesoscopic transport measurements done on PbTe nanowire quantum dots. The measurements allow the extraction of the spin-orbit coupling strength and the g-factor of PbTe. The measurements are well presented and the results are important as they demonstrate the potential of PbTe compared to III-V materials for semiconductor-superconductor hybrids. This is especially important for quantum computing devices and the search for Majorana modes. I think the manuscript is suitable for this journal and should be considered for publication based on criterion 3 for acceptance: Open a new pathway in an existing or a new research direction, with clear potential for multipronged follow-up work.
But before it can be accepted, the authors should address the issues listed below, in the requested changes.
1. The Fermi surface of PbTe is inherently anisotropic (non spherical) and valley degenerate. This fact is discussed in several reports on single crystals and films (Melngailis et al. PRB 3 370 1971, Bauer Narrow Gap Semiconductors Physics and Applications: Proceeding of the International Summer School 133 427 (1980) , Hayasaka J. Phys.: Condens. Matter 28 (2016) 31LT01 ). Does that have any impact on the energy levels of the quantum dot and on the g-factor?
2. Related to that, what is the crystallographic direction of the long axis of the nanowire? This is important given the highly anisotropic character of the electronic structure of PbTe.
3. In Fig. 3, could the faint resonances observed at high Vtg be due to lifting of valley degeneracy instead of a separate quantum dot?
4. Can the authors at least mention the limits of an isotropic particle-in-a-box model for PbTe? I am pointing this out both because the Fermi surface of PbTe is anisotropic and because its band structure is highly non-parabolic and approaches a Dirac-like structure at low energies. (see for example Phys. Rev. B 98, 115144 (2018) or NPJ Quantum Material 2 26 (2017)). While I can accept that they limit the discussion in this simple case to a basic model to estimate the size of the quantum dot, a mention of this limitation can at least encourage more elaborate theoretical efforts to compute the electronic structure of these dots.
5. Can the authors mention the temperature at which each measurement is carried out? How robust is their signal to temperatures approaching 4.2K? Grabecki et al report conductance quantization even at 1.8K ref.
6. Some minor things:
- For the dielectric constant of PbTe the authors can reference Preier Applied Physics 20 189 (1980).
- A reference is needed when the authors mention the valley degeneracy of PbTe. The current version has [?] as the reference.
- When mentioning the topological phase in IV-VI materials is mentioned, the authors should give credit to the following experimental work: on Dziawa et al. Nature Materials 11, 1023 (2012), and Tanaka et al Nature Physics 8 800 (2012).