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M-theory frozen singularities are (locally) $D$ - or $E$ -type orbifold singularities with a background fractional $C_3$ -monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their physics. We first give a top-down derivation of how the $D$ - or $E$ -type 7D $\mathcal{N}=1$ gauge theory directly “freezes” to a lower-rank gauge theory due to the $C_3$ background. This relies on a Hanany-Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional $\mathrm{D}p$ probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories of the 7D frozen theories in several duality frames. We apply our results to understanding the evenness condition of strings ending on $\mathrm{O}{7}^{+}$ planes, and calculating the global forms of supergravity gauge groups of M-theory compactified on $T^4/\mathrm{\Gamma }$ with frozen singularities. We also revisit IIA $ADE$ singularities with a $C_1$ -monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees of freedom via confinement. Published by the American Physical Society 2025

Motivated by the recently discovered high-T_c bilayer nickelate superconductor La_3⁢Ni₂⁢O₇, we comprehensively research a bilayer 2×2×2 cluster for different electronic densities n by using the Lanczos method. We also employ the random-phase approximation to quantify the first magnetic instability with increasing Hubbard coupling strength, also varying n. Based on the spin structure factor S(q), we have obtained a rich magnetic phase diagram in the plane defined by n and U/W, at fixed Hund coupling, where U is the Hubbard strength and W the bandwidth. We have observed numerous states, such as A-AFM, Stripes, G-AFM, and C-AFM. At half-filling, n=2 (two electrons per Ni site, corresponding to N=16 electrons), the canonical superexchange interaction leads to a robust G-AFM state (π,π,π) with antiferromagnetic couplings both in-plane and between layers. By increasing or decreasing electronic densities, ferromagnetic tendencies emerge from the “half-empty” and “half-full” mechanisms, leading to many other interesting magnetic tendencies. In addition, the spin-spin correlations become weaker both in the hole or electron doping regions compared with half-filling. At n=1.5 (or N=12), density corresponding to La₃⁢Ni₂⁢O₇, we obtained the “Stripe 2” ground state (antiferromagnetic coupling in one in-plane direction, ferromagnetic coupling in the other, and antiferromagnetic coupling along the z axis) in the 2×2×2 cluster. In addition, we obtained a much stronger AFM coupling along the z axis than the magnetic coupling in the xy plane. The random-phase approximation calculations with varying n give very similar results as Lanczos, even though both techniques are based on quite different procedures. Additionally, a state with q/π=(0.6,0.6,1) close to the E-phase wavevector is found in our RPA calculations by slightly reducing the filling to n=1.25, possibly responsible for the E-phase SDW recently observed in experiments. In conclusion, our predictions can be tested by chemically doping La₃⁢Ni₂⁢O₇.

Motivated by the recently reported signatures of superconductivity in trilayer La₄⁢Ni₃⁢O₁₀ under pressure, here we comprehensively study this system using ab initio and random-phase approximation techniques. Without electronic interactions, the Ni d_3z²–r² orbitals show a bonding-antibonding and nonbonding splitting behavior via the O p_z orbitals inducing a “trimer” lattice in La_4⁢Ni₃⁢O₁₀, analogous to the dimers of La₃⁢Ni₂⁢O₇. The Fermi surface consists of three electron sheets with mixed e_g orbitals, and a hole and an electron pocket made up of the d_{3⁢z²–r²} orbital, suggesting a Ni two-orbital minimum model. In addition, we find that superconducting pairing is induced in the s^±-wave channel due to partial nesting between the M = (π,π) centered pockets and portions of the Fermi surface centered at the Γ = (0,0) point. With changing electronic density n, the s^± instability remains leading and its pairing strength shows a domelike behavior with a maximum around n = 4.2 ( ~6.7% electron doping). The superconducting instability disappears at the same electronic density as that in the new 1313 stacking La₃⁢Ni₂⁢O₇, correlated with the vanishing of the hole pocket that arises from the trilayer sublattice, suggesting that the high-T_c superconductivity of La_3⁢Ni₂⁢O₇ does not originate from a trilayer and monolayer structure. Furthermore, we confirm the experimentally proposed spin state in La₄⁢Ni₃⁢O₁₀ with an in-plane (π, π) order and antiferromagnetic coupling between the top and bottom Ni layers, and spin zero in the middle layer.

Motivated by the recently proposed alternating single-layer trilayer stacking structure for the nickelate La₃⁢Ni₂⁢O₇, we comprehensively study this system using ab initio and random-phase approximation techniques. Here, our analysis unveils similarities between this novel La_3⁢Ni₂⁢O₇ structure and other Ruddlesden-Popper nickelate superconductors, such as a similar charge-transfer gap value and orbital-selective behavior of the eg orbitals. Pressure primarily increases the bandwidths of the Ni e_g bands, suggesting an enhancement of the itinerant properties of those e_g states. By changing the cell volume ratio V/V₀ from 0.9 to 1.10, we found that the bilayer structure in La₃⁢Ni₂⁢O₇ always has lower energy than the single-layer trilayer stacking La₃⁢Ni₂⁢O₇. In addition, we observe a “self-doping” effect (compared to the average 1.5 electrons per eg orbital per site of the entire structure) from the trilayer to the single-layer sublattices and this effect will be enhanced by overall electron doping. Moreover, we find a leading d_x²-y²-wave pairing state that is restricted to the single layer. Because the effective coupling between the single layers is very weak, due to the nonsuperconducting trilayer in-between, this suggests that the superconducting transition temperature T_c in this structure should be much lower than in the bilayer structure.

The nodal-line semiconductor Mn₃Si₂Te₆ is generating enormous excitment due to the recent discovery of a field-driven insulator-to-metal transition and associated colossal magnetoresistance as well as evidence for a new type of quantum state involving chiral orbital currents. Strikingly, these qualities persist even in the absence of traditional Jahn-Teller distortions and double-exchange mechanisms, raising questions about exactly how and why magnetoresistance occurs along with conjecture as to the likely signatures of loop currents. Here, we measured the infrared response of Mn₃Si₂Te₆ across the magnetic ordering and field-induced insulator-to-metal transitions in order to explore colossal magnetoresistance in the absence of Jahn-Teller and double-exchange interactions. Rather than a traditional metal with screened phonons, the field-driven insulator-to-metal transition leads to a weakly metallic state with localized carriers. Our spectral data are fit by a percolation model, providing evidence for electronic inhomogeneity and phase separation. Modeling also reveals a frequency-dependent threshold field for carriers contributing to colossal magnetoresistance which we discuss in terms of polaron formation, chiral orbital currents, and short-range spin fluctuations. These findings enhance the understanding of insulator-to-metal transitions in new settings and open the door to the design of unconventional colossal magnetoresistant materials.

Quasi-one-dimensional correlated electronic multiorbital systems with either ladder or chain geometries continue attracting considerable interest due to their complex electronic phases arising from the interplay of the hopping matrix, the crystal-field splitting, the electronic correlations (Hubbard repulsion U and Hund coupling J_H), and strong quantum fluctuations. Recently, the intriguing cobalt zigzag chain system BaCoTe₂⁢ O₇, with electronic density n=7, was prepared experimentally. Here, we systematically study the electronic and magnetic properties of this quasi-one-dimensional compound from the theoretical perspective. Based on first-principles density functional theory calculations, strongly anisotropic one-dimensional electronic Co 3⁢d bands were found near the Fermi level. By evaluating the relevant hopping amplitudes, we provide the magnitude and origin of the nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping matrices in BaCoTe₂⁢ O₇. With this information, we constructed a three-orbital electronic Hubbard model for this zigzag chain system, and studied two cases: with only a NN hopping matrix, and with NN plus NNN hopping matrices. Introducing the Hubbard and Hund couplings and studying the model via the density matrix renormalization group method, we constructed the ground-state phase diagram. A robust staggered ↑ - ↓ - ↑ - ↓ antiferromagnetic (AFM) region was found when only the NN hopping matrix in the chain direction was employed. However, for the realistic case where the NNN hopping matrix is also included, the dominant state becomes instead a block AFM ↑ - ↑ - ↓ - ↓ order, in agreement with experiments. The system displays Mott insulator characteristics with three half-filled orbitals, when the block AFM order is stable. In conclusion, our results for BaCoTe₂ ⁢O₇ provide guidance to experimentalists and theorists working on this zigzag one-dimensional chain and related materials.

Motivated by the recently discovered high-T_c superconductor La₃Ni₂O₇, we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y^2- mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y^2- mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector (π, 0) was stable at the intermediate region. Pairing is induced in the s_±-wave channel due to partial nesting between the M = (π, π) centered pockets and portions of the Fermi surface centered at the X = (π, 0) and Y = (0, π) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La₃Ni₂O₇ is qualitatively different from infinite-layer nickelates and cuprate superconductors.

The recent discovery of superconductivity in bilayer La₃Ni₂O₇ (327-LNO) under pressure stimulated much interest in layered nickelates. However, superconductivity was not found in another bilayer nickelate system, La₃Ni₂O₆ (326-LNO), even under pressure. To understand the similarities and differences between 326-LNO and 327-LNO, using density functional theory and the random phase approximation (RPA), we systematically investigate 326-LNO under pressure. The large crystal-field splitting between the e_g orbitals caused by the missing apical oxygen moves the d_3z²-r² orbital farther away from the Fermi level, implying that the d_3z²-r² orbital plays a less important role in 326-LNO than in 327-LNO. This also results in a smaller bandwidth for the d_x²-y² orbital and a reduced energy gap for the bonding-antibonding splitting of the d_3z²-r² orbital in 326-LNO, as compared to 327-LNO. Moreover, the in-plane hybridization between the d_x²-y² and d_3z²-r² orbitals is found to be small in 326-LNO, while it is much stronger in 327-LNO. Furthermore, the low-spin ferromagnetic state is found to be the likely ground state in 326-LNO under high pressure. The weak interlayer coupling suggests that s_±-wave pairing is unlikely in 326-LNO. The robust in-plane ferromagnetic coupling also suggests that d-wave superconductivity, which is usually caused by antiferromagnetic fluctuations of the d_x²-y² orbital, is also unlikely in 326-LNO. These conclusions are supported by our many-body RPA calculations of the pairing behavior. Additionally, contrasting with the cuprates, for the bilayer cuprate HgBa₂CaCu₂O₆, we find a strong self-doping effect of the d_x²-y² orbital under pressure, with the charge of Cu being reduced by approximately 0.13 electrons from 0 GPa to 25 GPa. In contrast, we do not observe such a change in the electronic density in 326-LNO under pressure, establishing another important difference between the nickelates and the cuprates.

Motivated by the recently reported high-temperature superconductivity in the bilayer La₃Ni₂O₇ (LNO) under pressure, we comprehensively study this system using ab initio techniques. The Ni 3d orbitals have a large bandwidth at ambient pressure, increasing by ~22% at 29.5 GPa. Without electronic interactions, the Ni d_3z²-r² orbitals form a bonding-antibonding molecular orbital state via the O p_z inducing a “dimer” lattice in the LNO bilayers. The Fermi surface consists of two-electron sheets with mixed e_g orbitals and a hole pocket defined by the d_3z²-r² orbital, suggesting a Ni two-orbital minimum model. Different from the infinite-layer nickelate, we obtained a large interorbital hopping between d_3z²-r² and d_x²-y² states in LNO, caused by the ligand “bridge” of in-plane O p_x or p_y orbitals connecting those two orbitals, inducing d-p σ-bonding characteristics. The competition between the intraorbital and interorbital hoppings leads to an interesting dominant spin stripe (π,0) order because of bond ferromagnetic tendencies via the recently discussed “half-empty” mechanism.

The recent discovery of pressure-induced superconductivity in the bilayer La₃ Ni₂ O₇ (LNO) has opened a new platform for the study of unconventional superconductors. In this publication, we investigate theoretically the whole family of bilayer 327-type nickelates R₃ Ni₂ O₇ (R = rare-earth elements) under pressure. From La to Lu, the lattice constants and volume decrease, leading to enhanced in-plane and out-of-plane hoppings, resulting in an effectively reduced electronic correlation U / W. Furthermore, the Ni's t_2g states shift away from the e_g states, while the crystal-field splitting between d_3z²-r² and d_x²-y² is almost unchanged. In addition, six candidates were found to become stable in the Fmmm phase, with increasing values of critical pressure as the atomic number increases. Similar to the case of LNO, the s_± -wave pairing tendency dominates in all candidates, due to the nesting between the M = (π , π) and the X = (π , 0) and Y = (0 , π) points in the Brillouin zone. Then, T_c is expected to decrease as the radius of rare-earth (RE) ions decreases. In conclusion, our results suggest that LNO is already the “optimal” candidate, with Ce a close competitor, among the whole of the RE bilayer nickelates, and to increase T_c we suggest growing on special substrates with larger in-plane lattice spacings.