The modulation of the magnetic and electronic properties of $1T\text{−}\mathrm{Cr}{\mathrm{S}}_2$ monolayer through hydrogenation is systematically investigated from first principles. The hydrogenated $\mathrm{Cr}{\mathrm{S}}_2$ monolayer exhibits both dynamical and thermal stabilities at room temperature. The magnetic ground state of $\mathrm{Cr}{\mathrm{S}}_2$ monolayer transforms from a ${120}^{\circ }$ noncollinear antiferromagnetic state to a ferromagnetic state upon hydrogenation, accompanied by the transition from metal to semiconductor. These transitions can be attributed to the induced tensile strain and charge redistribution resulting from the adsorption of hydrogen. When hydrogen is adsorbed on both sides of $\mathrm{Cr}{\mathrm{S}}_2$, the estimated ferromagnetic transition temperature of $\mathrm{Cr}{\mathrm{S}}_2\text{−}2H$ monolayer is 310 K, and it can be further enhanced to 430 K under a compressive strain of –4%. Moreover, by performing 0.05 hole or 0.05 electron doping in $\mathrm{Cr}{\mathrm{S}}_2\text{−}2H$ monolayer, 100% spin polarization at the Fermi energy in either the spin-down or spin-up channel can be effectively achieved, indicating that a double-gate-controlled field-effect spin filter based on $\mathrm{Cr}{\mathrm{S}}_2\text{−}2H$ monolayer can be designed for potential application in spintronic devices.

We propose a fresh class of ${M\mathrm{B}}_3{\mathrm{C}}_3$ $(M=\mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}, \mathrm{Sc}, \text{and} \mathrm{Y})$ compounds, in which B and C atoms form $s{p}^2$-hybridized honeycomb layers with $M$ atoms serving as electron donors in the interlayers. Calculations indicate that these ambient-pressure layered structures are more stable than their reported $s{p}^3$-bonded counterparts, namely, the cubic clathrates of ${M\mathrm{B}}_3{\mathrm{C}}_3$ $(M=\mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}, \mathrm{Sc}, \text{and} \mathrm{Y})$. By solving the Migdal-Eliashberg equations, we find that the layered ${M\mathrm{B}}_3{\mathrm{C}}_3$ compounds are ambient-pressure anisotropic superconductors with critical temperatures $T_c\mathrm{s}$ of 13–58 K. Interestingly, superconducting carriers originate exclusively from the itinerant $\sigma$ electrons, with soft doubly degenerate $E$ phonon modes playing a pivotal role in the superconductivity. In particular, both ${\mathrm{ScB}}_3{\mathrm{C}}_3$ and ${\mathrm{YB}}_3{\mathrm{C}}_3$ show double-gap superconductivity, attributed to the presence of three distinct Fermi surface sheets with separate orbital features, among which only the $\sigma$-type sheets couple with phonons. Furthermore, investigation of isostructural ${\mathrm{TiB}}_3{\mathrm{C}}_3$ uncovers that, although $d$ electrons dominate the electronic states near the Fermi level, superconducting carriers are still provided by the $\sigma$ bands, whereas the $d$ orbitals make a negligible contribution to electron pairing.

The high-pressure phase diagram of the Ca-Li system remains controversial, particularly regarding the stability of ${\mathrm{CaLi}}_2$ and its possible decomposition pathways under compression. Intermetallic electrides under high pressure have emerged as a promising platform for accomplishing unconventional charge transfer and superconducting behaviors due to their unique interplay between interstitial anionic electrons (IAEs) and metal cations. Motivated by these challenges and opportunities, we perform an extensive first-principles structure search and identify P4/mnc ${\mathrm{Ca}}_4\mathrm{Li}$ as the only thermodynamically stable compound under pressure. This compound adopts a tetragonal host-guest framework with a two-dimensional windmill-shaped IAE network. X-ray diffraction simulations indicate that ${\mathrm{Ca}}_4\mathrm{Li}$ could be a viable candidate for the experimentally observed Ca-Li phase. Notably, it is a rare bimetal-donor electride at low pressure, but upon compression it undergoes a successive enhancement of Ca $s\to d$ transition/Li $2s\to \mathrm{Ca}3d$ charge transfer and a progressive reduction of IAEs, transforming Ca from an electron donor to an acceptor. This unique charge redistribution enhances the coupling between Ca $3d$ electrons and low-frequency phonons associated with the Ca framework, leading to a continuous increase in superconducting critical temperature, reaching 17.8 K at 150 GPa. Our work expands the understanding of charge transfer and superconductivity in intermetallic electrides, enabling design of novel electride superconductors with tunable properties.

We study the orbital angular momentum (OAM) $L_z$ of two-dimensional chiral ${(p_x+i{p}_y)}^{\nu }$-wave superfluids (SFs) in the presence of an axisymmetric multiply quantized vortex with vorticity $k$ on a disk at zero temperature, in the framework of Bogoliubov–de Gennes (BdG) theory. Focusing on spectral asymmetry (or spectral flow), we find that $L_z=(k+\nu )N/2$ for any integer $\nu$ and $k$ in the Bose-Einstein condensation (BEC) regime, where $N$ is the total number of fermions. While in the weak-pairing Bardeen-Cooper-Schrieffer (BCS) regime, only for chiral ($p+ip$)-wave SF with $k=\pm 1, L_z=(k+\nu )N/2$ still holds. For chiral SFs with $\nu \ge 2$ or $\left|k\right|\ge 2$ in the BCS regime, the OAM $L_z$ is remarkably reduced from its “full” value in the BEC regime. However, the deviations differ in these two cases. For chiral SFs with $\nu \ge 2, L_z$ is sharply suppressed in this ideal setting with a specular wall, while the suppression caused by the $\left|k\right|\ge 2$ vortex is moderate, which is core-size dependent. Furthermore, for ($p+ip$)-wave SF with $k=-1$, the total OAM $L_z$ is zero, but the distribution $L_z\left(r\right)$ is nontrivial compared with that of vortex-free $s$-wave SF, in which the total OAM is zero as well. For chiral SFs with $\nu \ge 2$ and $\left|k\right|\ge 2$, the effects of circulation due to vortex and chiral pairing can coexist, and hence depress the OAM simultaneously. These observations can be explained by spectral asymmetry and unpaired fermions in the ground state of the BdG Hamiltonian. We also investigate the spatial distribution of particle density, OAM, by solving the BdG equation.

Ori-kirigami structures provide a versatile platform for designing deployable structures and multistable systems. Waterbomb origami, as a classic crease pattern, has been widely applied in mechanical metamaterials and deployable structures due to its novel mechanical properties, such as multistability and flat foldability. This paper develops a multiwaterbomb unit based on the waterbomb crease pattern, constructing two flat-foldable modules, a rectangular module, and a hexagonal module. Furthermore, four distinct multiwaterbomb units with different numbers of creases are generalized. The unique kinematic and mechanical properties of these units are investigated, and their potential applications as metamaterials featuring negative stiffness, hysteresis effects are explored. By axially stacking modules and introducing slits, two types of ori-kirigami tubes are constructed. Spatial arrangement of these tubes enables the creation of periodic mechanical metamaterials. Then, the incorporation of hyperelastic materials within slits of adjacent modules enables multistable configurations, with theoretical validation conducted via the Yeoh constitutive model. Finally, based on the rectangular module, a deployable modular beam with uniform thickness is developed. Unlike traditional ori-kirigami-inspired deployable mechanisms in which modifying one parameter often affects others, this beam allows independent tuning of cross-sectional dimensions without influencing other parameters, demonstrating superior engineering adaptability and spatial efficiency.

First-principles calculations combined with the stochastic self-consistent harmonic approximation reveal significant effects of the quantum ionic fluctuations and lattice anharmonicity on the structural stability and superconducting properties of $\mathrm{Nb}{\mathrm{H}}_3$ under high pressure. Previous theoretical predictions, which ignored ionic fluctuations and relied on the harmonic approximation, predicted the $I\overline{4}3d$ phase as the ground state between 33 and 400 GPa, with the $\mathit{Fm}\overline{3}m$ phase considered thermodynamically metastable. Harmonic calculations also placed the minimum pressure for dynamical stability of the $\mathit{Fm}\overline{3}m$ phase as high as 290 GPa. However, recent experiments identified the $\mathit{Fm}\overline{3}m$ phase at 187 GPa. Contrasting these predictions, our study reveals that the $\mathit{Fm}\overline{3}m$ phase remains dynamically stable down to at least 145 GPa—approximately 145 GPa lower than harmonic estimates. Furthermore, while the $I\overline{4}3d$ phase is dynamically stable, it exhibits higher enthalpy than the $\mathit{Fm}\overline{3}m$ phase at 187 GPa, aligning with the experimental observations. We systematically investigate the structural, vibrational, and superconducting properties of the $\mathit{Fm}\overline{3}m \mathrm{Nb}{\mathrm{H}}_3$ under pressures ranging from 100 to 300 GPa, uncovering substantial modifications induced by the quantum and anharmonic effects. The calculated superconducting critical temperature ($T_{\mathrm{c}}$) from the McMillan equation (with ${\mu }^{*}=0.15$) for $\mathit{Fm}\overline{3}m \mathrm{Nb}{\mathrm{H}}_3$ at 187 GPa is 44 K, close to the measured value. These findings highlight the crucial role of quantum anharmonic effects in shaping the structural and vibrational properties of $\mathrm{Nb}{\mathrm{H}}_3$ at high pressures.

Driven by novel approaches and computational techniques, second-principles atomic potentials are nowadays at the forefront of computational materials science, enabling large-scale simulations of material properties with near-first-principles accuracy. However, their application to polar materials can be challenging, particularly when longitudinal-optical phonon modes are active on the material, as accurately modeling such systems requires incorporating the long-range part of the dipole-dipole interactions. In this study, we challenge the influence of these interactions on the properties of polar materials taking ${\mathrm{BaTiO}}_3$ as paradigmatic example. By comparing models with and without the long-range part of the electrostatic contributions in a systematic way, we demonstrate that even if these interactions are neglected, the models can still provide an overall good description of the material, though they may lead to punctual significant artifacts. Our results propose a pathway to identify when an atomistic potential may be inadequate and needs to be corrected through the inclusion of the long-range part of dipolar interactions.

Understanding the origin of unconventional magnetic order is a central theme in the research field of functional quantum materials for spin-dependent applications. In general, a paramagnetic (PM) to antiferromagnetic (AFM) transition is of thermodynamically second order in nature in the absence of a magnetic field. In the magnetically frustrated corrugated-honeycomb lattice compounds $(\mathrm{Ca},\mathrm{Sr}){\mathrm{Mn}}_2{\mathrm{P}}_2$, electrical resistivity $\rho$ measurements in the $ab$ plane are reported to exhibit sharp discontinuities at the respective PM to AFM ordering temperatures $T_{\mathrm{N}}=69.5$ and 53 K, respectively, signifying the unusual first-order nature of the AFM transition. To reveal the origin of such anomalous transitions, high-resolution linear thermal-expansion measurements are reported for both ${\mathrm{CaMn}}_2{\mathrm{P}}_2$ and ${\mathrm{SrMn}}_2{\mathrm{P}}_2$ in the $ab$ plane and along the $c$ axis using capacitance dilatometry. The thermal expansion measurements show a sharp discontinuity in $\mathrm{\Delta }L/L$ at $T_{\mathrm{N}}$, yielding a diverging behavior in the thermal expansion coefficient $\alpha \left(T\right)$ associated with strong magnetoelastic coupling, driving the first-order AFM transition in ${\mathrm{CaMn}}_2{\mathrm{P}}_2$. However, this effect is weaker in ${\mathrm{SrMn}}_2{\mathrm{P}}_2$, consistent with the magnetic entropy changes $S\left(T\right)$ obtained from the heat-capacity measurements. Temperature-dependent $ab$-plane x-ray diffraction measurements for ${\mathrm{CaMn}}_2{\mathrm{P}}_2$ near its $T_{\mathrm{N}}$ yield a volume thermal expansion coefficient consistent with literature data for other materials. The uniaxial pressure derivatives of $T_{\mathrm{N}}$ in the two compounds are found to be respectively opposite in sign, presumably due to the different magnetic structures.

We have investigated the element specific magnetic characteristics of single-crystal ${\mathrm{FeCr}}_2{\mathrm{S}}_4$ using x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD). We have found that the Fe $L_{2,3}$-edge XAS spectra do not exhibit clear multiplet structures, indicating strong hybridization between the Fe $3d$ and S $3p$ orbitals, leading to delocalized rather than localized electronic states. The Fe $3d$ and Cr $3d$ spin moments are antiferromagnetically coupled, consistent with the Goodenough-Kanamori rule. The orbital magnetic moments of Fe and Cr are determined to be −0.23 and −0.017 ${\mu }_{\mathrm{B}}$ /ion, respectively. The large orbital magnetic moment of Fe is due to the $d^6$ configuration under the relatively weak tetrahedra crystal field at the Fe site, and the delocalized Fe electrons maintain the orbital degree of freedom in spite of their itinerant nature. To understand phenomena such as the gigantic Kerr rotation, it is essential to consider not only the orbital degrees of freedom but also the role of spin-orbit coupling, which induces a finite orbital magnetic moment through $t_2$ and $e$ level hybridization under the tetrahedral crystal field. This finite orbital moment serves as a direct indicator of spin-orbit interaction strength and links element-specific orbital magnetism to the large Kerr rotation. On the other hand, the octahedral crystal-field splitting of the Cr $3d$ level is large enough to result in the quenching of the orbital moment of the Cr ion in ${\mathrm{FeCr}}_2{\mathrm{S}}_4$.

The Dzyaloshinskii-Moriya interaction (DMI) plays an important role in the spin-orbit torque (SOT)-driven magnetization switching and the chiral domain wall motion for energy-efficient spintronics. Topological insulators (TIs), a new class of quantum materials, can provide an enhanced SOT strength, resulting in a lower power consumption. However, DMI in the TI/ferromagnet heterostructures remains largely unexplored. Moreover, the synthesis of TI films using molecular beam epitaxy hinders their practical applications. Here, continuous ${\left(\mathrm{BiSb}\right)}_2{\mathrm{Te}}_3$ films are prepared using the industry-compatible magnetron sputtering technique. We observe a distinct DMI and left-handed Néel-type chiral domain walls in our sputtered ${\left(\mathrm{BiSb}\right)}_2{\mathrm{Te}}_3$-based devices. The DMI coefficient D is evaluated to be $\sim 97\mu \mathrm{J}/{\mathrm{m}}^2$, and the DMI significantly influences the behavior of chiral domain wall motion. We demonstrate efficient perpendicular magnetization switching of 3d ferromagnetic CoFeB through the giant SOT in ${\left(\mathrm{BiSb}\right)}_2{\mathrm{Te}}_3$; the current density is $1.36\times {10}^5\mathrm{A}/{\mathrm{cm}}^2$. Our work will advance the research on topological material-based DMI and domain wall dynamics.

We systematically investigate the impact of spin current $\left(J_{\mathrm{s}}\right)$ direction on terahertz (THz) emission intensity in Co/Al/Pt trilayer spintronic heterostructures. Contrary to the conventional expectations that reversing the $J_{\mathrm{s}}$ direction merely inverts the THz signal polarity without altering its magnitude, we observe a striking asymmetry: Pt/Al/Co trilayers generate THz signals that are over two orders of magnitude stronger than those from Co/Al/Pt stacks with reversed layer sequence. In contrast, Co/Pt bilayers and Cu-based trilayers show no such dependence, indicating that the effect is specific to Al-based systems. Moreover, the spin attenuation length in Al differs by a factor of $\sim 17$ depending on the $J_{\mathrm{s}}$ direction, and ferromagnetic resonance (FMR) measurements further reveal a corresponding anisotropy in the Gilbert damping coefficient $\left(\alpha \right)$. Cross-sectional high-resolution transmission electron microscopy measurements confirm that directional Pt-Al alloying occurs in Pt/Al/Co but is suppressed in Co/Al/Pt, which is responsible for the observed asymmetric THz signal. Our findings demonstrate that stacking-order-dependent interfacial alloying critically governs ultrafast spin transport and THz emission, offering new strategies for engineering efficient and tunable spintronic THz emitters.

Traditionally applied within equilibrium states, the charge-vortex dualities are expanded to address the complex dynamics of superfluids and ideal fluids under nonstatic conditions. We have constructed explicit mappings of finite temperature fluid dynamics to gauge theories, enabling a dual description where vortices in both superfluids and ideal fluids are interpreted as charges within these theories. We found that vortices in the normal component naturally exhibit mobility restrictions, as manifested by the symmetries and conservation laws. Next, we formulated the Liénard-Wiechert problem for the ideal fluid at finite temperature and extracted the wave dynamics in the system along with the speed of sound corrections for both fluid components. Finally, we computed the correlation functions for the gauge potentials, particularly elucidating explicit cross-correlations between the normal and superfluid components.

The interplay among Coulomb interaction, electron-phonon coupling, and phonon-phonon coupling has a significant impact on the low-energy behavior of three-dimensional type-I tilted Dirac semimetals. To investigate this phenomenon, we construct an effective theory, calculate one-loop corrections arising from all these interactions, and establish the coupled energy-dependent flows of all associated interaction parameters by adopting the renormalization-group approach. Deciphering such coupled evolutions allows us to determine a series of low-energy critical properties for these materials. At first, we present the low-energy tendencies of all interaction parameters. The tilting parameter exhibits distinct tendencies that depend heavily upon the initial anisotropy of fermion velocities. In comparison, the latter is mainly dominated by its initial value but is less sensitive to the former. Variations in these two quantities drive certain interaction parameters toward the strong anisotropy in the low-energy regime, indicating the screened interaction in specific directions, and others toward an approximate isotropy. Additionally, we observe that the tendencies of interaction parameters can be qualitatively clustered into three distinct types of fixed points, accompanied by the potential instabilities that induce an interaction-driven phase transition to a certain superconducting state. Furthermore, approaching these fixed points leads to the critical behavior of physical quantities, such as the density of states, compressibility, and specific heat, which exhibit quite different from their noninteracting counterparts and even deviate slightly from Fermi-liquid behavior. Our investigation sheds light on the intricate relationship between different types of interactions in these semimetals and provides useful insights into their fundamental properties.

Second-order phase transitions in metals are a longstanding question, often linked to charge-density waves, Peierls distortions, or Kohn anomalies in the phonon spectrum. Such a phase transition has recently been observed in cubic ${\mathrm{LaH}}_{10}$, a material that exhibits superconductivity with exceptionally high critical temperature up to 260 K. Previous work has shown that this phase is unstable below 200 GPa if quantum effects and anharmonicity are not present. Here, we study the instabilities occurring in this material at such pressures. Lowering the electronic temperature to 0 K softens the phonon branches along the $\mathrm{\Gamma }-X, K-\mathrm{\Gamma }, \mathrm{\Gamma }-L-U$, and $W-L-K$ directions. We relate these softenings to the linewidths predicted in the electronic high-temperature phonon band structure of ${\mathrm{LaH}}_{10}$ at specific wave vectors. The correspondence is striking: both functions are either large or small for all investigated wave vectors. In contrast, the Fermi nesting function, often invoked for such structural phase transitions, provides little insight. The phase transition in ${\mathrm{LaH}}_{10}$ is found to be similar to the one previously observed for paradigmatic charge-density-wave materials, $2H-{\mathrm{NbSe}}_2, {\mathrm{TaTe}}_4$, and $1T-{\mathrm{VSe}}_2$. Going beyond the observation of a simple coincidence between the softening and the linewidth, we highlight the similarities and differences between the equations describing the Fermi surface nesting function, the phonon linewidth, and the temperature dependence of the phonon frequencies. Furthermore, we analyze the contributions to the calculated phonon linewidth from the four electronic bands crossing the Fermi surface of ${\mathrm{LaH}}_{10}$. One specific intra-band contribution clearly dominates. However, the corresponding variation in the charge density of that specific band with temperature is negligible.

Recently, triangular lattice models have received a lot of attention since they can describe a number of strongly correlated materials that exhibit superconductivity and various magnetic and charge orders. In this research we present an extensive analysis of the charge-ordering phenomenon of the triangular-lattice extended Hubbard model with repulsive on-site and nearest-neighbor interaction, arbitrary charge concentration, and $\sqrt{3}\times \sqrt{3}$ supercell (3-sublattice assumption). The model is solved in the ground state with the mean-field approximation which allowed us to identify 8 charge-ordered phases and a large variety of phase transitions. An exotic pinball-liquid phase was found and described. Moreover, strong particle-hole asymmetry of the phase diagram is found to play an important role for triangular lattices. The detailed analysis of band structures, unavailable for more advanced methods, such as dynamical mean-field theory, allowed us to interpret the found triangular-lattice phases and provided great insight into the mechanisms behind the phase transitions that can also be met when correlation effects are taken into account. The complexity of the mean-field phase diagram showed the importance and usefulness of the results for further research with correlation effects included. Together with the atomic-limit approximation it can serve as both a starting point and a tool to interpret results.

We study the quantum quench of the Yukawa-Sachdev-Ye-Kitaev model and one of its random hopping extensions with $q$ fermions and one boson. Several equilibrium properties are computed for general $q$ with different parameter scaling within the large-$N$ dynamical mean-field scheme. The non-Fermi liquid quench dynamics are studied by integrating the Kadanoff-Baym equations for switching off the random hopping term with constant Yukawa coupling or quenching to different final Yukawa couplings. The postquench oscillations and relaxation dynamics are insensitive to the quench amplitudes deep inside the non-Fermi liquid phase. With weak hopping coupling quenches, we find universal thermalization dynamics similar to the SYK model; however, with two temperatures and two distinct relaxation rates for bosons and fermions, both signal Planckian relaxations without quasiparticles, as in strange metals.

The Kondo effect arises from many-body interactions between localized magnetic impurities and conduction electrons, affecting electronic properties at low temperatures. In this study, we investigate the Kondo effect within a two-dimensional electron gas subjected to strong spin-orbit coupling in and out of the persistent spin helix regime, a state characterized by a long spin lifetime due to SU(2) symmetry recovery. Using the numerical renormalization group approach, we systematically analyze the influence of spin-orbit coupling strength and the orientation of an external magnetic field on the spectral properties of the impurity. Our findings reveal an intriguing interplay between spin-orbit coupling and the magnetic field, leading to key phenomena such as splitting of the hybridization function, asymmetry in the spectral function of the impurity, and significant tunability of the Kondo temperature due to spin-orbit. These results provide valuable insights into the delicate balance between spin-orbit and external magnetic field effects in quantum impurity systems, contributing to a deeper understanding of spintronics and quantum manipulation in low-dimensional materials.

This study presents a theoretical investigation of the thermoelectric properties of three-dimensional magnetic topological insulators (TIs), with a focus on the role of exchange interactions between magnetic dopants. The presence of these magnetic atoms on the TI surface modulates the local magnetic order, which in turn alters the electronic band structure and surface transport phenomena. Magnetic correlations, such as those arising from ferromagnetic or antiferromagnetic exchange, promote cluster formation, magnetic domain structures, and spin fluctuations, all of which critically influence thermoelectric responses. Using extensive Monte Carlo simulations based on Ising and Heisenberg models of these surface exchange interactions, we analyze how magnetic clustering, particularly near the surface critical temperature, affects relaxation dynamics, electrical and thermal resistivity, the Seebeck coefficient, and the thermoelectric figure of merit. Our results demonstrate that exchange-driven magnetic clustering enhances the scattering of Dirac surface states, thereby increasing the thermoelectric power factor. Specifically, optimized interlayer and intralayer exchange interactions can elevate the surface thermopower beyond levels observed in conventional spin-based thermoelectric materials. These findings highlight the significant potential of magnetic TIs for thermoelectric applications and provide a foundation for future experimental and theoretical studies of magnetic correlations in topologically nontrivial systems.

The Mott regime with finite $U$ offers a promising platform for exploring phases of matter, such as quantum spin liquids (QSL) that exhibit fractionalization and emergent gauge field. Here, we provide a wavefunction, dubbed ancilla wavefunction, to capture both charge and spin (gauge) fluctuations in QSLs at finite $U$. The ancilla wavefunction can unify the Fermi liquid and Mott insulator phases with a single variation parameter $\mathrm{\Phi }$ tuning the charge gap. As $\mathrm{\Phi }\to \infty$, the wavefunction reduces to the Gutzwiller-projected state, while at $\mathrm{\Phi }=U/2$, it is effectively equivalent to applying an inverse Schrieffer-Wolff transformation to the Gutzwiller-projected state. This wavefunction can be numerically simulated in the matrix product state representation, and its performance is supported by numerical results for both one- and two-dimensional Hubbard models. Besides, we propose the possibility of a narrow regime of fractional Fermi-liquid phase between the usual Fermi liquid and the Mott insulator phases close to the metal-insulator transition, a scenario typically overlooked by the conventional slave rotor theory. Our ancilla wavefunction offers a conceptual framework and a powerful numerical tool for understanding Mott physics.