RECORD
Quantum Hall effect and semiconductor to semimetal transition in biased black phosphorus
Mesoscale and Nanoscale Physics · Submitted 20 Dec 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We obtain a $\sigma_{xy}\propto 2n$ quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a $\sigma_{xy}\propto 4(n+1/2)$ quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not equidistant anymore, but follow the $\varepsilon_n\propto \sqrt{nB}$ characteristic of Dirac crystals as graphene. By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. We obtain a $\sigma_{xy}\propto 2n$ quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a $\sigma_{xy}\propto 4(n+1/2)$ quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. | contribution 0.97 | 0.91 | 0.04 | asserted 0.89 |
| s1 | In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. | result 0.66 | 0.50 | 0.04 | asserted 1.00 |
| s2 | The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. | result 0.96 | 0.65 | 0.22 | asserted 1.00 |
| s3 | This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. | result 0.63 | 0.62 | 0.11 | asserted 1.00 |
| s4 | As a consequence, the Landau levels are not equidistant anymore, but follow the $\varepsilon_n\propto \sqrt{nB}$ characteristic of Dirac crystals as graphene. | result 0.84 | 0.76 | 0.14 | asserted 1.00 |
| s5 | By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. | method 1.00 | 0.95 | 0.03 | asserted 0.99 |
| s6 | We obtain a $\sigma_{xy}\propto 2n$ quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a $\sigma_{xy}\propto 4(n+1/2)$ quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology. | result 1.00 | 0.95 | 0.72 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not equidistant anymore, but follow the $\varepsilon_n\propto \sqrt{nB}$ characteristic of Dirac crystals as graphene. By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. We obtain a $\sigma_{xy}\propto 2n$ quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a $\sigma_{xy}\propto 4(n+1/2)$ quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology.
Human review
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it · 1 sentence without a confident label
Uses its method or tool 1 paper
-
Our method, presented in Ref [ref] and applied to quantum transport calculations of different solid state systems [ref] consists in expanding the Green's functions in the integrand of eq.([ref]) in terms of Chebyshev polynomials using the kernel polynomial method [ref] .
Kubo-Bastin approach for the spin Hall conductivity of decorated graphene · Chebyshev expansion of the Kubo-Bastin formula · 0.92
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.