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1. Anisotropic positive linear and sub-linear magnetoresistivity in the cubic type-II Dirac metal Pd3In7

   https://doi.org/10.1038/s41535-023-00601-7  

   Flessa Savvidou, Aikaterini; Ptok, Andrzej; Sharma, G.; Casas, Brian; Clark, Judith K.; Li, Victoria M.; Shatruk, Michael; Tewari, Sumanta; Balicas, Luis (November 2023, npj Quantum Materials)

   Abstract We report a transport study on Pd₃In₇which displays multiple Dirac type-II nodes in its electronic dispersion. Pd₃In₇is characterized by low residual resistivities and high mobilities, which are consistent with Dirac-like quasiparticles. For an applied magnetic field (μ₀H) having a non-zero component along the electrical current, we find a large, positive, and linear inμ₀Hlongitudinal magnetoresistivity (LMR). The sign of the LMR and its linear dependence deviate from the behavior reported for the chiral-anomaly-driven LMR in Weyl semimetals. Interestingly, such anomalous LMR is consistent with predictions for the role of the anomaly in type-II Weyl semimetals. In contrast, the transverse or conventional magnetoresistivity (CMR for electric fieldsE⊥μ₀H) is large and positive, increasing by 10³−10⁴% as a function ofμ₀Hwhile following an anomalous, angle-dependent power law$${\rho }_{{{{\rm{xx}}}}}\propto {({\mu }_{0}H)}^{n}$$ ${\rho }_{\mathrm{xx}}\propto {\left({\mu }_{0}H\right)}^n$withn(θ) ≤ 1. The order of magnitude of the CMR, and its anomalous power-law, is explained in terms of uncompensated electron and hole-like Fermi surfaces characterized by anisotropic carrier scattering likely due to the lack of Lorentz invariance. 

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2. Spin-resolved topology and partial axion angles in three-dimensional insulators

   https://doi.org/10.1038/s41467-024-44762-w  

   Lin, Kuan-Sen; Palumbo, Giandomenico; Guo, Zhaopeng; Hwang, Yoonseok; Blackburn, Jeremy; Shoemaker, Daniel P.; Mahmood, Fahad; Wang, Zhijun; Fiete, Gregory A.; Wieder, Benjamin J.; et al (January 2024, Nature Communications)

   Abstract Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($${{{{{{{\mathcal{T}}}}}}}}$$ $T$-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and$${{{{{{{\mathcal{T}}}}}}}}$$ $T$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate thatβ-MoTe₂realizes a spin-Weyl state and thatα-BiBr hosts both 3D QSHI and T-DAXI regimes. 

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3. Spectroscopic investigation of $$^{54}$$Cr via $$\alpha $$-transfer reaction

   https://doi.org/10.1140/epja/s10050-025-01619-0  

   Das, Biswajit; Kundu, A.; Palit, R.; Dey, P.; Malik, Vishal; Garg, U.; Negi, D.; Laskar, S_R; Santra, Rajkumar; Jadhav, S_K; et al (June 2025, The European Physical Journal A)

   Abstract Low-lying states in$$^{54}$$ $_{}^{54}$Cr have been investigated via the$$\alpha $$ $\alpha$-transfer reaction$$^{50}$$ $_{}^{50}$Ti($$^{7}$$ $_{}^7$Li,t) at a bombarding energy of 20 MeV. The exclusive$$\alpha $$ $\alpha$-transfer channel is separated from other reaction channels through the appropriate energy gate on the complementary particle, triton. Levels of$$^{54}$$ $_{}^{54}$Cr populated exclusively by the$$\alpha $$ $\alpha$-transfer process could be identified up to$$\approx $$ $\approx$5 MeV excitation energy and angular momentum up to$$(8)^{+}$$ ${\left(8\right)}^{+}$, by identifying the corresponding known$$\gamma $$ $\gamma$-rays. These include multiple low-lying non-yrast 2$$^+$$ $_{}^{+}$and 4$$^+$$ $_{}^{+}$states, which would otherwise be unfavorable via fusion evaporation reactions. The feeding-subtracted$$\gamma $$ $\gamma$-ray yields have been extracted to estimate the population of various excited states through the transfer process. The measured integrated transfer cross sections for all the observed yrast and non-yrast states are compared with Coupled Channels calculations usingfrescoto extract the$$\alpha $$ $\alpha$+$$^{50}$$ $_{}^{50}$Ti core spectroscopic factors. For the yrast states, a higher$$\alpha $$ $\alpha$+core overlap is seen for the$$2^+$$ $2^{+}$and$$4^+$$ $4^{+}$states, while it is seen to be less favorable for the$$6^+$$ $6^{+}$and$$(8)^+$$ ${\left(8\right)}^{+}$states when$$\alpha $$ $\alpha$-transfer is considered to occur predominantly as a direct one-step process to the$$^{50}$$ $_{}^{50}$Ti core ground state. The yrast$$2^+$$ $2^{+}$, and$$4^+$$ $4^{+}$states are predominantly populated by single-step transfer, while for the states with spin$$\ge $$ $\ge$5, the possibility of core excitation followed by$$\alpha $$ $\alpha$-transfer shows a larger$$\alpha $$ $\alpha$-core overlap. For the non-yrast$$0^+$$ $0^{+}$,$$2^+$$ $2^{+}$, and$$4^+$$ $4^{+}$states, single-step transfer shows moderate to small$$\alpha $$ $\alpha$-core overlap. No higher spin non-yrast states are observed. 

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4. Towards a Schinzel–Wójcik theorem for number fields

   https://doi.org/10.1007/s40879-025-00819-8  

   Pollack, Paul (April 2025, European Journal of Mathematics)

   Abstract Schinzel and Wójcik have shown that for every$$\alpha ,\beta \in \mathbb {Q}^{\times }\hspace{0.55542pt}{\setminus }\hspace{1.111pt}\{\pm 1\}$$ $\alpha ,\beta \in Q^{\times }\backslash \{\pm 1\}$, there are infinitely many primespwhere$$v_p(\alpha )=v_p(\beta )=0$$ $v_p\left(\alpha \right)=v_p\left(\beta \right)=0$and where$$\alpha $$ $\alpha$and$$\beta $$ $\beta$generate the same multiplicative group modp. We prove a weaker result in the same direction for algebraic numbers$$\alpha , \beta $$ $\alpha ,\beta$. Let$$\alpha , \beta \in \overline{\mathbb {Q}} ^{\times }$$ $\alpha ,\beta \in {\overline{Q}}^{\times }$, and suppose$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\alpha )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\alpha \right)|\ne 1$and$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\beta )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\beta \right)|\ne 1$. Then for some positive integer$$C = C(\alpha ,\beta )$$ $C=C(\alpha ,\beta )$, there are infinitely many prime idealsPof Equation missing<#comment/>where$$v_P(\alpha )=v_P(\beta )=0$$ $v_P\left(\alpha \right)=v_P\left(\beta \right)=0$and where the group$$\langle \beta \bmod {P}\rangle $$ $⟨\beta modP⟩$is a subgroup of$$\langle \alpha \bmod {P}\rangle $$ $⟨\alpha modP⟩$with$$[\langle \alpha \bmod {P}\rangle \,{:}\, \langle \beta \bmod {P}\rangle ]$$ $[⟨\alpha modP⟩:⟨\beta modP⟩]$dividingC. A key component of the proof is a theorem of Corvaja and Zannier bounding the greatest common divisor of shiftedS-units. 

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5. The $$L^p$$-Fisher–Rao metric and Amari–C̆encov $$\alpha $$-Connections

   https://doi.org/10.1007/s00526-024-02660-5  

   Bauer, Martin; Le Brigant, Alice; Lu, Yuxiu; Maor, Cy (February 2024, Calculus of Variations and Partial Differential Equations)

   Abstract We introduce a family of Finsler metrics, called the$$L^p$$ $L^p$-Fisher–Rao metrics$$F_p$$ $F_p$, for$$p\in (1,\infty )$$ $p\in (1,\infty )$, which generalizes the classical Fisher–Rao metric$$F_2$$ $F_2$, both on the space of densities$${\text {Dens}}_+(M)$$ ${\text{Dens}}_{+}\left(M\right)$and probability densities$${\text {Prob}}(M)$$ $\text{Prob}\left(M\right)$. We then study their relations to the Amari–C̆encov$$\alpha $$ $\alpha$-connections$$\nabla ^{(\alpha )}$$ ${\nabla }^{\left(\alpha \right)}$from information geometry: on$${\text {Dens}}_+(M)$$ ${\text{Dens}}_{+}\left(M\right)$, the geodesic equations of$$F_p$$ $F_p$and$$\nabla ^{(\alpha )}$$ ${\nabla }^{\left(\alpha \right)}$coincide, for$$p = 2/(1-\alpha )$$ $p=2/(1-\alpha )$. Both are pullbacks of canonical constructions on$$L^p(M)$$ $L^p\left(M\right)$, in which geodesics are simply straight lines. In particular, this gives a new variational interpretation of$$\alpha $$ $\alpha$-geodesics as being energy minimizing curves. On$${\text {Prob}}(M)$$ $\text{Prob}\left(M\right)$, the$$F_p$$ $F_p$and$$\nabla ^{(\alpha )}$$ ${\nabla }^{\left(\alpha \right)}$geodesics can still be thought as pullbacks of natural operations on the unit sphere in$$L^p(M)$$ $L^p\left(M\right)$, but in this case they no longer coincide unless$$p=2$$ $p=2$. Using this transformation, we solve the geodesic equation of the$$\alpha $$ $\alpha$-connection by showing that the geodesic are pullbacks of projections of straight lines onto the unit sphere, and they always cease to exists after finite time when they leave the positive part of the sphere. This unveils the geometric structure of solutions to the generalized Proudman–Johnson equations, and generalizes them to higher dimensions. In addition, we calculate the associate tensors of$$F_p$$ $F_p$, and study their relation to$$\nabla ^{(\alpha )}$$ ${\nabla }^{\left(\alpha \right)}$. 

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