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1. Low leakage current in heteroepitaxial ${\mathrm{Al}}_{0.7}{\mathrm{Sc}}_{0.3}\mathrm{N}$ ferroelectric films on $\mathrm{Ga}\mathrm{N}$

   https://doi.org/10.1103/PhysRevApplied.23.014036  

   Yazawa, Keisuke; Evans, Charles; Dickey, Elizabeth C; Tellekamp, M Brooks; Brennecka, Geoff L; Zakutayev, Andriy (January 2025, Physical Review Applied)

   Wurtzite $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$ ferroelectrics are attractive for microelectronics applications due to their chemical and structural compatibility with wurtzite semiconductors, such as $\mathrm{Ga}\mathrm{N}$ and $(\mathrm{Al},\mathrm{Ga})\mathrm{N}$ . However, the leakage current in epitaxial stacks reported to date should be reduced for reliable device operation. Here, we demonstrate low leakage current in epitaxial ${\mathrm{Al}}_{0.7}{\mathrm{Sc}}_{0.3}\mathrm{N}$ films on $\mathrm{Ga}\mathrm{N}$ with well-saturated ferroelectric hysteresis loops that are orders of magnitude lower (i.e., 0.07 A ${\mathrm{cm}}^{-2}$ ) than previously reported films (1–19 A ${\mathrm{cm}}^{-2}$ ) having similar or better structural characteristics. We also show that, for these high-quality epitaxial $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$ films, structural quality (edge and screw dislocations), as measured by diffraction techniques, is not the dominant contributor to leakage. Instead, the small leakage in our films is limited by thermionic emission across the interfaces, which is distinct from the large leakage due to trap-mediated bulk transport in the previously reported $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$ films. To support this conclusion, we show that ${\mathrm{Al}}_{0.7}{\mathrm{Sc}}_{0.3}\mathrm{N}$ on lattice-matched ${\mathrm{In}}_{0.18}{\mathrm{Ga}}_{0.82}\mathrm{N}$ buffers with improved structural characteristics but higher interface roughness exhibit increased leakage characteristics. This demonstration of low leakage current in heteroepitaxial $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$ films and understanding of the importance of interface barrier and surface roughness can guide further efforts toward improving the reliability of wurtzite ferroelectric devices. Published by the American Physical Society2025 

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2. Generalizations of the quadratic bound optimization principle

   https://doi.org/10.1073/pnas.2525320123  

   Li, Xun-Jian; Tian, Guo-Liang; Zhou, Hua; Lange, Kenneth (January 2026, Proceedings of the National Academy of Sciences)

   The quadratic bound (QB) principle proposed by Böhning and Lindsay in 1988 is an important special case of the majorization–minimization or minorization-maximization optimization principle. The quadratic upper-bound (QUB) principle is pertinent to minimization; the analogous quadratic lower-bound principle is pertinent to maximization. Unfortunately, in minimizing a loss $f\left(\mathit{\theta }\right)$ , the QUB principle is limited by the difficulty of finding a constant positive definite matrix $\mathit{B}$ such that $\mathit{B}-d^{2}f\left(\mathit{\theta }\right)$ is positive semidefinite for all $\mathit{\theta }$ . This paper proposes a generalization of the QB principle that avoids this limitation. In particular, we construct QUB algorithms by replacing the matrix $\mathit{B}$ by a continuous matrix-valued function $B_n\left(\mathit{\theta }\right)$ that dominates the Hessian $d^{2}f\left(\mathit{\theta }\right)$ and depends on the both the current iterate ${\mathit{\theta }}_n$ and the next potential iterate $\mathit{\theta }$ . In practice, we require $B_n\left(\mathit{\theta }\right)$ to be diagonal with its diagonal entries separated in $\mathit{\theta }$ . In other words, the $i$ th diagonal entry of $B_n\left(\mathit{\theta }\right)$ depends on $\mathit{\theta }$ only through its $i$ th entry ${\theta }_i$ . Theoretical analysis confirms that this class of generalized QB algorithms enjoys global convergence in favorable circumstances. For the scalar case, the tangency condition that the second derivative equals the bound function at the current point promotes superlinear convergence. Several numerical experiments implemented in Julia illustrate the power of the generalized QB principle. 

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3. Don’t Follow Reinforcement Learning Blindly: Lower Sample Complexity of Learning Optimal Inventory Control Policies with Fixed Ordering Cost

   https://doi.org/10.1177/10591478251378851  

   Fan, Xiaoyu; Chen, Boxiao; Olsen, Tava; Qin, Hanzhang; Zhou, Zhengyuan (April 2026, Production and Operations Management)

   We study the sample complexity of offline learning for a class of structured Markov decision processes (MDPs) describing the inventory control system with fixed ordering cost/setup cost, a fundamental problem in supply chains. We find that a naive plug-in sampling-based approach applied to the inventory MDPs leads to strictly lower sample complexity bounds compared to the optimal bounds recently obtained for the general MDPs. More specifically, in the infinite-horizon discounted cost setting, we obtain an $\tilde{O}(min\{\frac{(\overline{S}-\underset{\_}{s}{)}^2}{(1-\gamma {)}^2{ϵ}^2},\frac{1}{(1-\gamma {)}^4{ϵ}^2}\})$ sample complexity bound, where ${(\overline{S}-\underset{\_}{s})}^2$ corresponds to the number of state-action pairs in a generic MDP with state space $\mathcal{S}$ and action space $\mathcal{A}$ . As such, $\tilde{O}\left(\frac{(\overline{S}-\underset{\_}{s}{)}^2}{(1-\gamma {)}^2{ϵ}^2}\right)$ improves on the optimal generic reinforcement learning (RL) bound $\tilde{\mathrm{\Theta }}\left(\frac{(\overline{S}-\underset{\_}{s}{)}^2}{(1-\gamma {)}^3{ϵ}^2}\right)$ (when directly applying $\tilde{\mathrm{\Theta }}\left(\frac{|\mathcal{S}||\mathcal{A}|}{(1-\gamma {)}^3{ϵ}^2}\right)$ here) by a factor of $(1-\gamma {)}^{-1}$ , and $\tilde{O}\left(\frac{1}{(1-\gamma {)}^4{ϵ}^2}\right)$ is able to completely remove the dependence on state and action cardinality. In the infinite-horizon average cost setting, we obtain an $\tilde{O}\left(\frac{(\overline{S}-\underset{\_}{s}{)}^2}{{ϵ}^2}\right)$ bound, improving on the generic optimal RL bound $\tilde{\mathrm{\Theta }}\left(\frac{(\overline{S}-\underset{\_}{s}{)}^2{t}_{mix}}{{ϵ}^2}\right)$ (when directly applying $\tilde{\mathrm{\Theta }}\left(\frac{|\mathcal{S}||\mathcal{A}|t_{mix}}{{ϵ}^2}\right)$ here) by a factor of $t_{mix}$ , and hence removing the mixing time dependence. By carefully leveraging the structural properties of the inventory dynamics in various settings, we are able to improve on those “best-possible” bounds developed in the RL literature. Our results demonstrate the drawbacks one could face by blindly following RL algorithms and the necessity of designing sample efficient algorithms that properly incorporate the special structures of the inventory systems. 

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4. The Eisenstein ideal at prime-square level has constant rank

   https://doi.org/10.1073/pnas.2500729122  

   Lang, Jaclyn; Wake, Preston (July 2025, Proceedings of the National Academy of Sciences)

   LetNandpbe prime numbers with $p\ge 5$ such that $p\mid \mid (N+1)$ . In a previous paper, we showed that there is a cuspformfof weight 2 and level ${\mathrm{\Gamma }}_0\left(N^2\right)$ whoseℓ-th Fourier coefficient is congruent to $\ell +1$ modulo a prime abovepfor all primesℓ. In this paper, we prove that this formfis unique up to Galois conjugacy, and the extension of ${\mathbb{Z}}_p$ generated by the coefficients offis exactly ${\mathbb{Z}}_p[{\zeta }_p+{\zeta }_p^{-1}]$ . We also prove similar results when a higher power ofpdivides $N+1$ . 

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5. Stabilizing Ti ₃ C ₂ T _x MXene flakes in air by removing confined water

   https://doi.org/10.1073/pnas.2400084121  

   Fang, Hui; Thakur, Anupma; Zahmatkeshsaredorahi, Amirhossein; Fang, Zhenyao; Rad, Vahid; Shamsabadi, Ahmad A; Pereyra, Claudia; Soroush, Masoud; Rappe, Andrew M; Xu, Xiaoji G; et al (July 2024, Proceedings of the National Academy of Sciences)

   MXenes have demonstrated potential for various applications owing to their tunable surface chemistry and metallic conductivity. However, high temperatures can accelerate MXene film oxidation in air. Understanding the mechanisms of MXene oxidation at elevated temperatures, which is still limited, is critical in improving their thermal stability for high-temperature applications. Here, we demonstrate that Ti ${}_3$ C ${}_2$ T ${}_x$ MXene monoflakes have exceptional thermal stability at temperatures up to 600 ${}^{°}$ C in air, while multiflakes readily oxidize in air at 300 ${}^{°}$ C. Density functional theory calculations indicate that confined water between Ti ${}_3$ C ${}_2$ T ${}_x$ flakes has higher removal energy than surface water and can thus persist to higher temperatures, leading to oxidation. We demonstrate that the amount of confined water correlates with the degree of oxidation in stacked flakes. Confined water can be fully removed by vacuum annealing Ti ${}_3$ C ${}_2$ T ${}_x$ films at 600 ${}^{°}$ C, resulting in substantial stability improvement in multiflake films (can withstand 600 ${}^{°}$ C in air). These findings provide fundamental insights into the kinetics of confined water and its role in Ti ${}_3$ C ${}_2$ T ${}_x$ oxidation. This work enables the use of stable monoflake MXenes in high-temperature applications and provides guidelines for proper vacuum annealing of multiflake films to enhance their stability. 

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