Tuning topological phase and Dirac point position via Pb and Sb substitution in Mn$_{1-x}$Pb$_{x}$(Bi$_{1-y}$Sb$_{y}$)$_{2}$Te$_{4}$

Technical Summary: Tuning Topological Phase and Dirac Point Position via Pb and Sb Substitution in Mn1−xPbx(Bi1−ySby)2Te4

Problem Statement
MnBi2Te4 is a prominent magnetic topological system combining antiferromagnetic order with non-trivial electronic topology, offering potential for the quantum anomalous Hall effect (QAHE) and axion insulator states. However, realizing these phenomena in bulk crystals faces two primary obstacles: (1) intrinsic MnBi antisite defects cause heavy n-type doping, pushing the Fermi level ($E_F$) into the conduction band, and (2) the topological surface state (TSS) band gap exhibits significant sample-to-sample variability. While chemical substitution has been explored to address these issues, previous studies treated substitutions independently. Substituting Bi with Sb induces p-type doping and opens a reproducible TSS gap but does not alter the bulk band gap closure mechanism. Conversely, substituting Mn with Pb can close the bulk band gap and induce a topological phase transition but fails to position $E_F$ within the gap. The critical unresolved question is whether simultaneous substitution of Mn with Pb and Bi with Sb can independently control the topological phase and the Fermi level position to achieve a state where $E_F$ lies within a robust TSS gap.

Methodology
The authors synthesized a series of approximately 40 single crystals of Mn1−xPbx(Bi1−ySby)2Te4 with Pb concentrations ($x$) ranging from 10% to 60% and Sb concentrations ($y$) from 5% to 60%. Crystal growth was performed using a modified Bridgman method with a Bi2Te3-based flux.
To characterize the electronic structure, the study employed Angle-Resolved Photoemission Spectroscopy (ARPES) at two photon energies:

• $h\nu = 21.2$ eV (He I$\alpha$ source) to probe the bulk band structure.
• $h\nu = 6.3$ eV (laser source) to enhance the visibility of surface states.
  Circular Dichroism ARPES (CD-ARPES) was utilized to distinguish TSS from bulk states based on spin-momentum locking signatures.
  Magnetic properties were assessed using SQUID magnetometry to measure magnetic susceptibility $\chi(T)$ and magnetization $M(H)$, determining Néel temperatures ($T_N$) and spin-flop transition fields.
  Machine learning (Random Forest algorithm) was applied to the experimental dataset to quantify the functional dependence of the bulk band gap ($E_g$) and Dirac point position ($E_D$) on the chemical composition.

Key Results

1. Bulk Band Gap and Topological Phase Transition: The value of the bulk band gap ($E_g$) is determined almost exclusively by the Pb concentration ($x$), with a relative feature importance of $\approx 0.75$ in the machine learning model. As $x$ increases, $E_g$ decreases linearly, closing completely at Pb concentrations of 40–50%. This closure signifies a topological phase transition from a topological insulator (TI) to a trivial phase (semimetal/trivial insulator). This transition occurs regardless of the Sb concentration.
2. Dirac Point Position: The position of the Dirac point ($E_D$) relative to the Fermi level is not governed by the absolute Sb concentration but by the ratio of Pb to Sb ($x/y$). Machine learning analysis identified the Pb/Sb ratio as the dominant factor (importance $\approx 0.7–0.85$).
   • At low Pb/Sb ratios (Sb dominance), the system is p-type, and $E_D$ shifts to lower binding energies.
   • At high Pb/Sb ratios (Pb dominance), the system transitions to n-type.
   • The transition from p-type to n-type conductivity occurs at a Pb/Sb ratio of $\approx 0.5$, corresponding to a compensated semiconductor where $E_F$ is near the Dirac point.
3. Surface States (TSS): CD-ARPES measurements confirm that TSS are preserved in samples with Pb content below 40%. In samples with Pb $\ge$ 40–50%, the characteristic CD signal of TSS disappears, and the spectral features broaden, confirming the loss of the topological phase. The presence of Sb modulates the Dirac point position but does not prevent the Pb-induced phase transition.
4. Magnetic Properties: Magnetic measurements reveal that the antiferromagnetic order is preserved across the entire composition range ($x=10–60\%$, $y=5–60\%$).
   • The Néel temperature ($T_N$) and spin-flop transition fields are primarily determined by the dilution of the Mn sublattice by non-magnetic Pb.
   • For samples with $\sim$20% Pb, $T_N$ is 19–20 K, and the spin-flop field is 1.6–2 T.
   • For samples with $\sim$50% Pb, $T_N$ drops to 8–9.5 K, and the spin-flop field decreases to 1.16 T.
   • Crucially, variations in Sb concentration (e.g., 32% vs. 58% at fixed Pb) have negligible effects on magnetic ordering, indicating that the exchange mechanism (likely Mn–Te–Mn superexchange) is insensitive to the electronic environment changes at the Bi/Sb sites.

Significance and Claims
The paper demonstrates that simultaneous substitution of Mn with Pb and Bi with Sb in MnBi2Te4 allows for the independent control of the topological phase and the Fermi level position.

• Pb concentration acts as the primary knob for tuning the bulk band gap and determining the topological phase (TI vs. trivial).
• The Pb/Sb ratio serves as the control parameter for positioning the Dirac point relative to the Fermi level without altering the topological phase (provided Pb < 40%).
• Sb concentration effectively tunes the carrier type and Fermi level position while preserving the antiferromagnetic order and the topological nature of the surface states (in the TI regime).

The authors conclude that this dual-substitution strategy offers a pathway to engineer materials where the Fermi level can be tuned into the TSS band gap while maintaining a robust topological phase and antiferromagnetic order, addressing the critical challenges required for observing the QAHE in this material family. The study does not claim to have achieved QAHE but establishes the necessary conditions for its potential realization.