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REVIEW 4 major objections 4 minor 55 references

The experimental determination of exchange mass terms in surface states on both terminations of MnBi4Te7

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper establishes that the topological surface states of MnBi4Te7 are gapped on both exposed terminations: a roughly 23 meV hybridization gap on the Bi2Te3 face and a roughly 30 meV exchange mass on the MnBi2Te4 face.

desk verdict A useful local-probe dataset on both terminations of MnBi4Te7, but the quantitative mass-term extraction on the MBT side is a degenerate fit and the numbers should not outrun the data. read the letter →

arxiv 2505.22058 v1 pith:JPNAWB7C submitted 2025-05-28 cond-mat.mtrl-sci

Dezhi Song , Fuyang Hang , Gang Yao , Jun Zhang , Ye-Ping Jiang , Jin-Feng Jia This is my paper
classification cond-mat.mtrl-sci
keywords magnetictopologicalinsulatorMnBi4Te7surfacestatesexchangemasstermLandaulevelscanningtunnelingspectroscopymolecularbeamepitaxyquantumanomalousHalleffect
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses molecular-beam epitaxy to grow thin films of the magnetic topological insulator MnBi4Te7 with either a Bi2Te3 (BT) or a MnBi2Te4 (MBT) top layer, then probes the surface states with scanning tunneling spectroscopy. On the BT termination it identifies a roughly 23 meV hybridization gap that does not change with magnetic field and attributes it to coupling between the surface Dirac cone and spin-split states in the adjacent MBT layer. On the MBT termination it tracks magnetic-field-dependent Landau levels and, by fitting them to a massive Dirac Hamiltonian with an added parabolic potential, extracts an exchange mass term of about 30 meV, corresponding to a surface gap of about 60 meV. The result matters because a gapped surface state on both exposed faces is the prerequisite for quantum anomalous Hall and axion insulator behavior, and previous photoemission experiments disagreed about whether such a gap exists.

What carries the argument

The central object is the massive Dirac surface-state Hamiltonian $H = \varepsilon_D + \frac{\hbar^2 k^2}{2m^*} + \hbar v_F \mathbf{k}\cdot\boldsymbol{\sigma} + m_z \sigma_z$, whose zero-field dispersion $E = \varepsilon_D + \frac{\hbar^2 k^2}{2m^*} \pm \sqrt{\hbar^2 v_F^2 k^2 + m_z^2}$ opens a gap of $2m_z$. In a perpendicular magnetic field the Landau-level energies are $E_n = \varepsilon_D + \frac{e\hbar B}{m^*}\left(n+\frac12\right) \pm \sqrt{2e\hbar v_F^2 B |n| + \Delta^2}$ for $n=\pm1,\pm2,\dots$ and $E_0 = \varepsilon_D + \frac{e\hbar B}{m^*} + \Delta$, with $\Delta = m_z + \tfrac12 g_s\mu_B B$. The paper's mass extraction uses this level structure, and to reconcile the anomaly that the experimental 0th Landau level does not extrapolate to merge with the other levels at zero field, it adds a parabolic potential $U(r)=\kappa r^2$ and analyzes spectra at local potential extrema. For the BT termination the load-bearing model is instead a coupled QL/SL Hamiltonian with hybridization strength $V_h$ and exchange $m_z$, which shows a hybridization gap only when both terms are present.

What would settle it

A concrete test would be to take field-dependent dI/dV maps at several additional positions, independently measure the potential landscape from conductance maps, and check that the predicted 0th Landau level approaches the band edge at high field with the claimed curvature while the +1 level remains linear. Finding a level crossing, a 0th level that does not bend as predicted, or a momentum-resolved spectrum showing a gapless Dirac cone on the MBT termination would contradict the 60 meV exchange gap.

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Extended reading notes

Core claim

On its own terms, the paper establishes that both exposed surfaces of epitaxial MnBi4Te7 host gapped topological surface states. On the BT termination, the conductance spectra show a U-shaped gap near the Fermi level that is field-independent, and a coupled Dirac-plus-quadratic-band model of the BT/MBT interface shows this hybridization gap appears only when an exchange field is present, with magnitude about 23 meV. On the MBT termination, dI/dV spectra from 0 to 14 T reveal three Landau-level features assigned to the $n=0$, $+1$, and $-1$ levels. Fitting those tracks with the massive Dirac Hamiltonian $H = \varepsilon_D + \frac{\hbar^2 k^2}{2m^*} + \hbar v_F \mathbf{k}\cdot\boldsymbol{\sigma} + m_z \sigma_z$, plus a parabolic potential $U(r)=\kappa r^2$ introduced to explain why the 0th level does not extrapolate to merge with the $+1$ level at zero field, gives $m_z \approx 30$ meV for the nominally undoped film. In a film with heavy BiMn doping in the Mn layer, the 0th level keeps moving with field, which the authors read as an $m_z$ that grows with magnetic field and does not saturate, from about 15 to 28 meV. The paper concludes that surface states on both terminations feel an exchange field dominated by the first MBT septuple layer, and that non-magnetic doping tunes the exchange mass.

Load-bearing premise

The central assumption is that the three spectral peaks that move with magnetic field are the lowest Landau levels of a single massive Dirac surface state, and that an adjustable bowl-shaped potential accounts for their zero-field behavior. If those identifications or the potential model are wrong, the extracted 30 meV exchange mass is not reliable.

Editorial extensions

If this is right

  • If the MBT mass term is real, the Dirac point on that termination sits inside a roughly 60 meV exchange gap, making the surface a genuine magnetic insulator rather than a gapless Dirac metal.
  • The field-independent 23 meV gap on the BT termination, together with the modeling, supports an out-of-plane magnetic moment in the first MBT layer even at zero field, the local condition needed for zero-field quantum anomalous Hall behavior.
  • Because heavy BiMn doping in the Mn layer changes the mass term and makes it field-dependent, non-magnetic doping is a practical knob for tuning the surface gap.
  • The comparable mass magnitudes on the two terminations indicate that the exchange field acting on both surfaces comes primarily from the first MBT septuple layer, constraining layer-resolved models of these films.
  • The demonstration of gapped surface states on both faces in the same epitaxial film provides a local-probe resolution of the earlier photoemission controversy about whether MnBi4Te7 surface states are gapped.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's three measured positions, a stronger cross-check would be to map the local potential landscape independently with conductance maps and verify that a single set of parameters $\kappa$ and $m_z$ reproduces the Landau-level tracks at every position; otherwise the 30 meV value is a fitting artifact.
  • If $m_z$ is indeed tunable by BiMn doping, temperature-dependent tunneling spectroscopy across the magnetic transition should show the MBT gap closing as the out-of-plane moment disappears, which would cleanly separate the exchange contribution from hybridization.
  • The same field-dependent Landau-level analysis could be applied to other members of the MnBi2Te4/(Bi2Te3)$_n$ family, where it might reveal a common rule for how the surface mass term scales with intercalation number $n$ and doping.
  • A momentum-resolved measurement that directly images the MBT surface band at low temperature, if it found a gapless Dirac cone or a gap very different from 60 meV, would force a reinterpretation of the tunneling data.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This manuscript reports an STS/STM study of MBE-grown MnBi4Te7 films with exclusive Bi2Te3 (BT) and MnBi2Te4 (MBT) surface terminations. On the BT termination, the authors observe a 'U'-shaped gap of about 23-28 meV near the Fermi level that is insensitive to an out-of-plane magnetic field; using a four-band model with hybridization between the QL surface state and an exchange-split SL band, they attribute this gap to hybridization plus an exchange field of comparable magnitude. On the MBT termination, field-dependent Landau level spectra (0-14 T) are fitted to a massive Dirac Hamiltonian with an added parabolic potential U(r)=κr², yielding an exchange mass term m_z ≈ 30 meV (gap ≈ 60 meV) for the nominally undoped film, and a field-dependent m_z for a heavily BiMn-doped film (x=0.3), interpreted as non-saturation of the Mn-layer moments. The paper concludes that surface states on both terminations of MnBi4Te7 are gapped and that the mass term can be tuned by non-magnetic doping.

Significance. The qualitative claim that both terminations show gapped surface states is supported by the raw STS data and is a valuable local-probe complement to the conflicting ARPES results in the literature. The paper's strengths include terminated-film MBE growth, field-dependent LL tracking over a wide field range (0-14 T), and the unusually transparent presentation of multi-position datasets in the SI, which allows the reader to see the spread of the fits. If the quantitative determination of m_z were reliable, the paper would establish a key prerequisite (gapped surface states on both exposed surfaces) for QAHE and axion-insulator physics in MnBi4Te7 and would demonstrate a doping route to tune the exchange gap. However, the quantitative claims carry the paper's title and rest on an underdetermined inverse fit with an ad hoc potential term whose quoted parameters imply energies far above every other scale in the model, a neglected Zeeman contribution, and an assumed linear-in-B mass term for the doped film; the spread of fitted Δ values across positions (10-28 meV) is not propagated into any uncertainty.

major comments (4)
  1. [§ 'The derivation of the exchange mass term in surface states on the MBT termination' (LL formulas) and Note II] The MBT-termination fit is underdetermined, so the quoted m_z is not uniquely determined. In the formulas E_0 = ε_D + eℏB/m* + Δ and E_n = ε_D + (eℏB/m*)(n+1/2) ± √(2eℏv_F²B|n|+Δ²), the 0th LL contains the diamagnetic term eℏB/m*. For the x=0.3 film the roughly linear rise of E_0 is attributed entirely to a field-dependent m_z(B), but m* is never quoted or independently constrained, and the same trajectory is reproduced by a constant m_z with a finite m*. The Zeeman term ½g_s μ_B B is discarded as 'small' without a measured g-factor; even for g_s ≈ 10 the Zeeman energy at 10 T is ≈29 meV, comparable to the claimed m_z ≈ 30 meV, so its omission is not justified a priori. The observed -1 LL (x=0.3) and the curvature of the +1 LL could partly lift the degeneracy, but no joint fit, confidence intervals, or uniqueness (χ²) analysis is provided. Please fit positive and negative LLs simultaneously with the Zeeman term included, report m* and v_F with uncertainties, and test the constant-m_z plus finite-m* hypothesis explicitly.
  2. [Note II (parabolic potential U(r)=κr²)] The parabolic potential introduced to reconcile the non-merging of the 0th LL is not validated and appears inconsistent with the energy scales of the problem. Note II states κ = 25 meV/nm² with R0 = 60 nm and energy scale ε* = ℏv_F/R0 ≈ 4.72 meV; these numbers imply κR0² ≈ 90 eV, roughly 10⁴ times ε*, and at the magnetic length of 1 T (≈25 nm) the potential energy is ≈16 eV. A potential of this strength would dominate the LL spectrum at every field in the experiment and cannot represent the small potential fluctuations invoked in the text; if instead r is rescaled by R0 in U(r)=κr², then the units given in Note II are inconsistent and the dimensionless κ is not stated. Because m_z is fitted jointly with κ, and the potential also shifts low-field LLs by a state-dependent amount that grows as the field is reduced, the quoted m_z = 30 meV is contingent on an unvalidated model ingredient. Please present the Hamiltonian in dimensionless form, justify κ quantitatively from the measured spatial potential variations (Fig. S4), and report how m_z and the m_z(B) curve change when κ is varied (e.g., ±50%).
  3. [Note II; Fig. 4; Fig. S5] The headline values are not supported by error analysis, and the central x=0.3 finding is an input assumption rather than an output of the fit. Note II reports Δ = 30, 26, and 28 meV at three positions for x=0 and Δ from 10 to 28 meV across positions for x=0.3, yet the abstract and Fig. 4 quote a single 'about 30 meV' and a single m_z(B) curve. For x=0.3, the text states that the simulation 'takes into account a linear dependence of m_z on the magnetic field', so the later conclusion that the mass term 'does not saturate even at relatively high magnetic fields' is built into the ansatz and is not tested against alternatives (constant m_z with finite m*, or a Zeeman-dominated slope). Please report Δ(B) with uncertainties for every measured position, compare the linear-in-B model with the constant-m_z model using a statistical criterion, and replace the single-parameter quotes in the abstract with the measured ranges.
  4. [§ 'The mass term in surface states of MnBi4Te7 on the BT termination'; Note I] The BT-termination mass term is not obtained by a fit, and the paper quotes inconsistent values for the same gap. Note I specifies m_z = 0.04 and V_h = 0.08 without units or an energy scale; these parameters are chosen so that the model reproduces the observed gap, so the conclusion that the gap implies an exchange field of ~28 meV is a consistency check rather than a determination. The same gap is quoted as ~28 meV in the main text and Fig. 2(c) but as ~23 meV in the abstract and conclusions, with no statement of how the gap width is read off the dI/dV spectra. Please give the model parameters in physical units, define and justify the gap-extraction procedure with an uncertainty, and reconcile the 23 and 28 meV values.
minor comments (4)
  1. [Note II; main-text Hamiltonian] The Fermi velocities are quoted as '5.4×10^5 m/s²' and '4.7×10^5 m/s²' in Note II; the unit should be m/s (the superscript 2 appears to be a typographical error). In the main text the Hamiltonian is written with 'ℏν_F' where the Fermi velocity symbol is elsewhere 'v_F'; please unify the notation.
  2. [Fig. 3 caption] The caption of Fig. 3 labels the two experimental panels as '(a) and (d)', but the text refers to Figs. 3(a) and 3(b) for the x=0 and x=0.3 data; the panel labels in the caption and in the figure should be made consistent.
  3. [Figs. S2, S3, S5 captions] The SI figure cross-references appear scrambled: the caption of Fig. S5 says the fits 'correspond to Fig. S2(a)' and 'Fig. S2(b)', while the data being fitted are the field-dependent LL spectra presumably shown in Fig. S3; please correct the pointers so each dataset (x=0 and x=0.3, and each measured position) can be identified unambiguously.
  4. [Abstract; Introduction] The introduction states that the mass term 'yields a surface state gap of above 50 meV' while the abstract quotes 'about 30 meV' for the MBT termination; please state explicitly in the abstract and conclusions whether 30 meV is the mass m_z (with gap 2m_z) or the gap itself, and use the same convention throughout.

Circularity Check

1 steps flagged · score 6.0 of 10

The field-dependent mass term in the x=0.3 film is an input ansatz (linear m_z(B)) presented as the derived result; the static mass fits are standard inverse determinations.

  1. fitted input called prediction [Main text, 'The derivation of the exchange mass term in surface states on the MBT termination' (Figs. 4(b,d)); Supplementary Note II.]
    "For the x = 0.3 film, the 0th LL at higher fields does not approach a constant value ... Note that the 0th LL indicates the band edge of the upper branch of surface states as well as the exchange mass mz. Thus, the varying 0th LL in this case indicates the varying mz in response to the magnetic field. Figure 4(b) shows the simulation that takes into account a linear dependence of mz on the magnetic field."

    The linear-in-B m_z is inserted into the model Hamiltonian as the fitting ansatz intended to reproduce the rising 0th Landau level, and the subsequent figure of the 'derived field-dependent exchange mass m_z' plots this same ansatz. The conclusion that heavy BiMn doping makes the mass term field-dependent and unsaturating is therefore the input assumption restated, not a quantity whose B-dependence was determined independently. The extracted m_z(B) is also degenerate with the unquoted diamagnetic term eℏB/m* and with the parabolic-potential strength κ, so the attribution of the 0th-LL slope specifically to m_z(B) is forced by the chosen model rather than by the data alone.

full rationale

The paper's central determination on the MBT termination is an inverse fit: the massive Dirac Hamiltonian with m_z is used to calculate Landau-level energies, and m_z is adjusted to match the measured 0th and +1st LL positions. That procedure is a legitimate experimental determination of a model parameter, not by itself circular. However, for the x=0.3 film the field dependence of the mass term is put into the Hamiltonian as an explicit linear-in-B ansatz, then presented in Fig. 4(d) as the derived result and highlighted in the conclusions as the finding that the mass term does not saturate. That step reduces to its own input by construction. The BT-termination gap argument is not circular: it uses prior ARPES values (28 meV) and a k·p model to interpret the observed gap-like feature, and the modeling is transparent about the hybridization mechanism. The supplementary self-citations for the Landau-level-in-potential formalism are not load-bearing because the same formulas are supported by an independent external reference (Rodriguez-Nieva and Levitov). Overall, the static 30 meV mass and the ~23 meV hybridization gap have independent empirical content, but the field-dependent m_z claim in the doped film is a fitted ansatz renamed as a discovery, giving partial circularity.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The quantitative claims rest on a model Hamiltonian with multiple fitted or hand-chosen parameters (m_z, κ, v_F, m*) and on several modelling assumptions (parabolic potential, linear-in-B m_z, negligible Zeeman term). The BT-termination inference also relies on an illustrative four-band model. These are the load-bearing premises beyond the raw spectra.

free parameters (6)
  • m_z (MBT, x=0) = 30 meV (26 and 28 meV at other positions)
    Exchange mass term fitted to field-dependent Landau level spectra using the massive Dirac model plus parabolic potential (Note II).
  • m_z (MBT, x=0.3) = 15-28 meV, 12-28 meV, 10-28 meV (position-dependent)
    Exchange mass term fitted with a linear-in-B dependence to reproduce the non-constant 0th LL; the field dependence is assumed and then reported as a result.
  • κ (potential curvature) = 25 meV/nm²
    Curvature of the ad hoc parabolic potential U(r)=κr² used to explain the zero-field LL extrapolation anomaly; chosen to give 'best fitting'.
  • v_F for x=0.3 film = 4.7×10^5 m/s
    Fermi velocity adjusted for the doped film 'due to doping'; the x=0 value (5.4×10^5 m/s) is taken from literature.
  • m* (electron effective mass) = not specified
    The quadratic kinetic term coefficient in the Hamiltonian; its value is not given, but it enters the LL energies via (eℏB/m*)(n+1/2).
  • m_z and V_h in BT-termination four-band model = m_z=0.04, V_h=0.08 (dimensionless)
    Hand-chosen illustrative parameters demonstrating that a hybridization gap forms only when both the exchange field and hybridization are present; not fitted to the measured 23 meV gap.
assumptions (6)
  • domain assumption The topological surface states on the MBT termination are described by the massive Dirac Hamiltonian H = ε_D + (ℏ²k²)/(2m*) + ℏ v_F k·σ + m_z σ_z.
    Main text after Fig. 3(b). Standard model for TI surface states with exchange mass; the quadratic term is added to describe nonlinear Fermi velocity.
  • standard math Peierls substitution yields the Landau level energies E_n = ε_D + (eℏB/m*)(n+1/2) ± sqrt(2eℏ v_F² B |n| + Δ²), E_0 = ε_D + eℏB/m* + Δ.
    Main text LL formula; standard quantum mechanics with the assumption that the square term is treated in the same way.
  • domain assumption The BT-termination surface-state gap originates from hybridization between the QL surface Dirac state and the spin-split band of the adjacent MBT layer, and a gap appears only when an exchange field m_z is present.
    Main text 'The mass term in surface states...BT termination'; Note I uses a four-band model with hand-chosen m_z=0.04, V_h=0.08; this links the observed 23-28 meV gap to an inferred exchange field.
  • ad hoc to paper An additional parabolic potential U(r)=κr² describes potential fluctuations in the sample and explains why the 0th LL does not merge with other LLs at zero field.
    Main text: 'This controversy can be reconciled by adding a potential term...'; κ=25 meV/nm² chosen to fit; the potential is introduced post hoc to fix the extrapolation anomaly.
  • ad hoc to paper For the x=0.3 film, m_z depends linearly on the magnetic field.
    Note II gives Δ values varying linearly with B (e.g., 15-28 meV); the linear dependence is assumed in the simulation and then presented as the finding that m_z varies with field.
  • ad hoc to paper The Zeeman term (1/2) g_s μ_B B is negligible compared with m_z.
    Main text: 'Neglecting the small Zeeman term gives Δ = m_z.' No g_s value or estimate is provided, and for surface states g_s can be large enough to shift the gap by several meV at 14 T.

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Pith. "Pith review of The experimental determination of exchange mass terms in surface states on both terminations of MnBi4Te7." pith.science (2026). https://pith.science/paper/JPNAWB7C

@misc{pith2026250522058,
  author       = {Pith},
  title        = {Pith review of: The experimental determination of exchange mass terms in surface states on both terminations of MnBi4Te7},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JPNAWB7C}},
  note         = {Machine review of arXiv:2505.22058}
}
read the original abstract

The intrinsic antiferromagnetic topological insulators in the Mn-Bi-Te family, composed of superlattice-like MnBi2Te4/(Bi2Te3)n (n = 0, 1, 2, 3...) layered structure, present intriguing states of matter such as quantum anomalous Hall effect and the axion insulator. However, the surface state gap, which is the prerequisite for the observation of these states, remains elusive. Here by molecular beam epitaxy, we obtain two types of MnBi4Te7 films with the exclusive Bi2Te3 (BT) or MnBi2Te4 (MBT) terminations. By scanning tunneling spectroscopy, the mass terms in the surface states are identified on both surface terminations. Experimental results reveal the existence of a hybridization gap of approximately 23 meV in surface states on the BT termination. This gap comes from the hybridization between the surface states and the spin-split states in the adjacent MBT layer. On the MBT termination, an exchange mass term of about 30 meV in surface states is identified by taking magnetic-field-dependent Landau level spectra as well as theoretical simulations. In addition, the mass term varies with the field in the film with a heavy BiMn doping level in the Mn layers. These findings demonstrate the existence of mass terms in surface states on both types of terminations in our epitaxial MnBi4Te7 films investigated by local probes.

Figures

Figures reproduced from arXiv: 2505.22058 by the authors.

Figure 1
Figure 1. The structure and the STM topography of epitaxial MnBi4Te7 films. (a) Schematic of the lattice structure of MnBi4Te7. (b) Large-scale STM image (3 V, 10 pA) of the MBT/BT film grown on STO (111). (c) The height profile of the film along the line in (b). (d) and (e) Typical STM images (1 V, 50 pA) on the MBT and BT terminations, respectively [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. The surface states on the BT termination (BT/MBT/BT/MBT/BT). (a) and (b) Characteristic STS on the BT termination in the larger and smaller energy scales, respectively. (c) STS in the magnetic fields from 0 to 14 T. (d) Simulation of the hybridization gap in the surface states [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Field-dependent Landau level spectra on the MBT termination for differently doped MnBi4Te7 films (MBT/BT/MBT/BT/MBT/BT). (a) and (d) Experimentally field-dependent Landau level spectra for the x = 0 and x = 0.3 films, respectively. (c) Simulation of the surface state structures on the MBTtermination with different exchange mass mz, where the dashed one has a smaller mz. (d) The corresponding Landau level spectra (ca… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Determination of the exchange term on the MBT termination. (a) and (b) Experimental LLs along with the calculated ones for the x = 0 and x = 0.3 films, respectively where the yellow triangles and red dots are the +1th and 0th LLs, respectively. (c) Schematic of a poten…

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Works this paper leans on

55 extracted references · 51 canonical work pages

  1. [1]

    Chang et al., Science 340, 167 (2013)

    C.-Z. Chang et al., Science 340, 167 (2013)

    2013

  2. [2]

    Neglecting the small Zeeman term gives Δ = 𝑚𝑧

    ± √2𝑒ℏ𝑣𝐹 2𝐵|𝑛| + Δ2 (𝑛 = ±1 ±2 … ) and 𝐸0 = 𝜀𝐷 + 𝑒ℏ𝐵 𝑚∗ + Δ , where Δ = 𝑚𝑧 + 1 2 𝑔𝑠𝜇𝐵𝐵 is the mass term. Neglecting the small Zeeman term gives Δ = 𝑚𝑧. This yields the field-dependent LLs in Fig. 3(d), describing quite well the suppressed LLs with negative indexes. Note that the -1th LL on the x = 0.3 sample is more apparent than that on the x = 0 sample....

    work page

  3. [3]

    R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Science 329, 61 (2010)

    2010

  4. [4]

    Y . L. Chen et al., Science 329, 659 (2010)

    work page 2010

  5. [5]

    Tokura, K

    Y . Tokura, K. Yasuda, and A. Tsukazaki, Nat. Rev. Phys. 1, 126 (2019)

    work page 2019

  6. [6]

    E. D. L. Rienks et al., Nature 576, 423 (2019)

    work page 2019

  7. [7]

    M. M. Otrokov et al., Nature 576, 416 (2019)

    2019

  8. [8]

    R. Xu, L. Xu, Z. Liu, L. Yang, and Y . Chen, Natl. Sci. Rev. 11, nwad313 (2024)

    work page 2024

Show all 55 references
  1. [9]

    C. Hu, T. Qian, and N. Ni, Natl. Sci. Rev. 11, nwad282 (2024)

    2024

  2. [10]

    J. Ge, Y . Liu, J. Li, H. Li, T. Luo, Y . Wu, Y . Xu, and J. Wang, Natl. Sci. Rev. 7, 1280 (2020)

    2020

  3. [11]

    Y . Deng, Y . Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y . Zhang, Science 367, 895 (2020)

    2020

  4. [12]

    Liu et al., Nat

    C. Liu et al., Nat. Mater. 19, 522 (2020)

    2020

  5. [13]

    N. H. Jo, L. -L. Wang, R. -J. Slager, J. Yan, Y . Wu, K. Lee, B. Schrunk, A. Vishwanath, and A. Kaminski, Phys. Rev. B 102, 045130 (2020)

    2020

  6. [14]

    J. Wu, F. Liu, C. Liu, Y . Wang, C. Li, Y . Lu, S. Matsuishi, and H. Hosono, Adv. Mater. 32, 2001815 (2020)

    2020

  7. [15]

    R. C. Vidal et al., Phys. Rev. B 100, 121104 (2019)

    2019

  8. [16]

    Swatek, Y

    P. Swatek, Y . Wu, L.-L. Wang, K. Lee, B. Schrunk, J. Yan, and A. Kaminski, Phys. Rev. B 101, 161109 (2020)

    2020

  9. [17]

    Nevola, H

    D. Nevola, H. X. Li, J. Q. Yan, R. G. Moore, H. N. Lee, H. Miao, and P. D. Johnson, Phys. Rev. Lett. 125, 117205 (2020)

    2020

  10. [18]

    Y. J. Chen et al., Phys. Rev. X 9, 041040 (2019)

    2019

  11. [19]

    M. Liu, C. Lei, H. Kim, Y . Li, L. Frammolino, J. Yan, A. H. Macdonald, and C.- K. Shih, PNAS 119, e2207681119 (2022)

    2022

  12. [20]

    Huang, M.-H

    Z. Huang, M.-H. Du, J. Yan, and W. Wu, Phys. Rev. Mater. 4, 121202 (2020)

    2020

  13. [21]

    Qiao et al., Appl

    Y . Qiao et al., Appl. Phys. Lett. 124 (2024)

    2024

  14. [22]

    V olckaert et al., Adv

    K. V olckaert et al., Adv. Mater. 35, 2301907 (2023)

    2023

  15. [23]

    Yan et al., Nano Lett

    C. Yan et al., Nano Lett. 22, 9815 (2022)

    2022

  16. [24]

    Tan and B

    H. Tan and B. Yan, Phys. Rev. B 105, 165130 (2022)

    2022

  17. [25]

    R. C. Vidal et al., Phys. Rev. Lett. 126, 176403 (2021)

    2021

  18. [26]

    Lu et al., Phys

    R. Lu et al., Phys. Rev. X 11, 011039 (2021)

    2021

  19. [27]

    Fukasawa et al., Phys

    T. Fukasawa et al., Phys. Rev. B 103, 205405 (2021)

    2021

  20. [28]

    Chen et al., Phys

    B. Chen et al., Phys. Rev. B 104, 075134 (2021)

    2021

  21. [29]

    Xu et al., Sci

    L. Xu et al., Sci. Bull. 65, 2086 (2020)

    2020

  22. [31]

    Tian et al., Phys

    S. Tian et al., Phys. Rev. B 102, 035144 (2020)

    2020

  23. [33]

    I. I. Klimovskikh et al., npj Quantum Mater. 5, 54 (2020)

    2020

  24. [34]

    Hu et al., Phys

    Y . Hu et al., Phys. Rev. B 101, 161113 (2020)

    2020

  25. [35]

    Hu et al., Nat

    C. Hu et al., Nat. Commun. 11, 97 (2020)

    2020

  26. [36]

    Hu et al., Sci

    C. Hu et al., Sci. Adv. 6, eaba4275 (2020). 9

    2020

  27. [37]

    Hirahara et al., Nat

    T. Hirahara et al., Nat. Commun. 11, 4821 (2020)

    2020

  28. [38]

    Wu et al., Sci

    J. Wu et al., Sci. Adv. 5, eaax9989 (2019)

    2019

  29. [39]

    R. C. Vidal et al., Phys. Rev. X 9, 041065 (2019)

    2019

  30. [40]

    S. K. Chong, C. Lei, S. H. Lee, J. Jaroszynski, Z. Mao, A. H. MacDonald, and K. L. Wang, Nat. Commun. 14, 4805 (2023)

    2023

  31. [41]

    Jiang et al., Phys

    Y . Jiang et al., Phys. Rev. B 92, 195418 (2015)

    2015

  32. [42]

    Jiang et al., Phys

    Y . Jiang et al., Phys. Rev. Lett. 108, 016401 (2012)

    2012

  33. [43]

    M.-H. Du, J. Yan, V . R. Cooper, and M. Eisenbach, Adv. Funct. Mater. 31, 2006516 (2021)

    2021

  34. [44]

    Li et al., Adv

    Q. Li et al., Adv. Mater. 36, 2312004 (2024)

    2024

  35. [45]

    Zhu et al., J

    K. Zhu et al., J. Phys.: Condens. Matter 32, 475002 (2020)

    2020

  36. [46]

    Garnica et al., npj Quantum Mater

    M. Garnica et al., npj Quantum Mater. 7, 7 (2022)

    2022

  37. [47]

    Cheng et al., Phys

    P. Cheng et al., Phys. Rev. Lett. 105, 076801 (2010)

    2010

  38. [48]

    See supplementary materials for additional supplementary text and data, including the simulation of the Landau level in the potential field, the simulation of the hybridization gap, variable magnetic field data for the other two points of the SL termination, characterization o...

  39. [49]

    Zhang, Y .-P

    J. Zhang, Y .-P. Jiang, X. -C. Ma, and Q. -K. Xue, Phys. Rev. Lett. 128, 126402 (2022)

    2022

  40. [51]

    Y . Lai, L. Ke, J. Yan, R. D. McDonald, and R. J. McQueeney, Phys. Rev. B 103, 184429 (2021). 10 Figure Captions Fig. 1. The structure and the STM topography of epitaxial MnBi4Te7 films. (a) Schematic of the lattice structure of MnBi4Te7. (b) Large-scale STM image (3 V , 10 pA...

    2021

  41. [52]

    Hu et al., Sci

    C. Hu et al., Sci. Adv. 6, eaba4275 (2020)

    2020

  42. [53]

    Wu et al., Phys

    X. Wu et al., Phys. Rev. X 10, 031013 (2020)

    2020

  43. [54]

    Ma et al., Phys

    X.-M. Ma et al., Phys. Rev. B 102, 245136 (2020)

    2020

  44. [55]

    Huang, M

    H. Huang, M. Chen, D. Song, J. Zhang, and Y .-p. Jiang, Phys. Rev. B 109, 115414 (2024)

    2024

  45. [56]

    Zhang, Y .-P

    J. Zhang, Y .-P. Jiang, X .-C. Ma, and Q. -K. Xue, Phys. Rev. Lett. 128, 126402 (2022)

    2022

  46. [57]

    J. F. Rodriguez-Nieva and L. S. Levitov, Phys. Rev. B 94, 235406 (2016)

    2016

  47. [58]

    Yan et al., Chin

    G. Yan et al., Chin. Phys. Lett. 36, 076801 (2019)

    2019

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.