We study the critical behavior driven by potential quantum critical points (QCPs) termed as ${\tau }_{0,x,y,z}$-type QCPs beneath the superconducting dome of the $d$-wave cuprate superconductors. To comprehensively capture the distinct degrees of freedom in the vicinity of these QCPs, we construct a phenomenological effective theory based on the Landau-Ginzburg-Wilson framework and then employ the renormalization group approach to derive the coupled flow equations of all interaction parameters, incorporating all relevant one-loop corrections. Decoding these flow equations yields a series of unique properties arising from strong quantum fluctuations around QCPs. On one hand, the interaction parameters flow toward several fixed points (FPs) at certain critical energy scales. We identify two different types of FPs designated at the clean limit. FP-I is characterized by the divergence of the quadratic parameter and exhibits robustness against variations in interaction parameters. In contrast, FP-II is dominated by the cubic and quartic interaction parameters, and it is sensitive to initial conditions, leading to five subclasses: FP-IIA, FP-IIB, FP-IIC, FP-IID, and FP-IIE. In addition, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the ${\tau }_{x,z}$ QCPs, driving the system toward a preempted disorder-induced FP. On the other hand, we find that quantum fluctuations play a critical role in shaping the critical temperature ($T_c$) as the system approaches these QCPs. Near the ${\tau }_x$ QCP, $T_c$ is considerably suppressed for both FP-I and FP-II. In contrast, near the ${\tau }_0$ QCP, $T_c$ undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely, $T_c$ exhibits an increasing trend near the ${\tau }_y$ QCP, with a pronounced peak at $v_{\mathrm{\Delta }0}/v_{F0}\sim 0.25$. However, numerical analysis suggests that the ${\tau }_z$ QCP is unlikely to be physically realizable. Additionally, we realize that $T_c$ can also be modified by the emergence of disorder-induced FPs in the vicinity of the ${\tau }_x$ QCP. These findings would provide valuable insights into the critical low-energy properties of $d$-wave cuprate superconductors and related materials.

Interacting and open quantum systems can be formulated in terms of an effective non-Hermitian (NH) Hamiltonian; however, there are important constraints that must be satisfied by the effective action and the associated Green's functions. One common approach to many-body NH systems is to incorporate the anti-Hermitian part of the Hamiltonian directly in the Matsubara Green's function. Here, we show that such an approach is incompatible with the standard framework for systems with interactions. Furthermore, we furnish a consistent physical description for such systems by determining their distinction from conventional interacting physics, and find that they are described by pseudo-Hermitian quantum mechanics. In addition, we characterize the zero-temperature distribution functions within several frameworks for NH systems. As an application of our results, we consider the electromagnetic response of a NH quasiparticle Hamiltonian based on the ($1+1$)-dimensional NH Dirac model subject to various physical descriptions.

The ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ material family has emerged as a key platform for exploring magnetic topological phases, most notably exemplified by the experimental realization of the axion insulator state. The interplay between spin dynamics and axion states in topological magnets is anticipated to lead to rich phenomena that yet remain largely unexplored. In this work, we employ an antiferromagnetic spin-chain model to demonstrate that an external magnetic field induces perpendicular magnetic anisotropy. We find that an in-plane field stabilizes the antiferromagnetic order, whereas an out-of-plane field destabilizes it and triggers spin-flop transitions. Remarkably, near the surface spin-flop transition in even-layer ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ films, the axion insulator state undergoes a sharp switching behavior accompanied by distinct magnetoelectric responses. Furthermore, we propose that this switchable axionic magnetoelectric effect can be utilized to convert alternating magnetic field signals into measurable square-wave magneto-optical outputs, thereby realizing an axionic analog of a zero-crossing detector.

The zero-mode corner states in the gap of a two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid in large-sized systems. To reveal the higher-order topology of non-Hermitian systems, we establish a correspondence between the stable zero-mode singular states and the topologically protected corner states of energy spectrum in the thermodynamic limit. Within this framework, the number of zero-mode singular values is directly linked to the number of midgap corner states. The winding numbers in real space can be defined to count the number of stable zero-mode singular states. Our results formulate a bulk-boundary correspondence for both static and Floquet non-Hermitian systems, where topology arises intrinsically from the non-Hermiticity, even without symmetries.

Competing magnetic interactions and coupling to lattice degrees of freedom can stabilize complex spin orders in type-II multiferroic materials, leading to magnetically induced ferroelectricity. Here, we investigate the low-temperature crystal and magnetic structures of the spin-driven multiferroic ${\mathrm{FeVO}}_4$ using high-resolution synchrotron x-ray and neutron powder diffraction, complemented by macroscopic measurements. ${\mathrm{FeVO}}_4$ exhibits two successive antiferromagnetic transitions: an incommensurate collinear phase below $T_{\mathrm{N}1}\approx 21\mathrm{K}$, followed by an incommensurate noncollinear (NC) helical phase below $T_{\mathrm{N}2}\approx 15\mathrm{K}$. The magnetic order in these two phases is characterized by closely related incommensurate propagation vectors refined from powder neutron diffraction, indicating only a weak temperature dependence of the magnetic modulation. While both magnetic structures break inversion symmetry at the level of the magnetic modulation, ferroelectricity emerges only in the helical phase, where NC allows a finite spin chirality, consistent with spin-driven ferroelectricity commonly discussed within an inverse Dzyaloshinskii-Moriya framework. Subtle anomalies in lattice parameters observed near both magnetic transitions provide qualitative evidence of weak spin-lattice coupling, without detectable lowering of crystallographic symmetry. Together, these results establish a bulk-sensitive, temperature-dependent picture of how magnetic frustration, weak lattice responses, and NC spin order cooperate to stabilize the multiferroic ground state in ${\mathrm{FeVO}}_4$.

The reversal of the anomalous Hall effect (AHE) via low-power ferroelectric (FE) switching has recently attracted significant interest. However, a general symmetry-based design principle for such control remains absent. Here, we establish effective symmetry criteria for FE-switchable AHE in two-dimensional (2D) multiferroics without altering the magnetic configuration. By analyzing the transformation properties of Berry curvature under magnetic space group (MSG) symmetry operations associated with FE switching, we show that FE-switchable AHE in 2D multiferroics requires the following conditions (i) The MSG of the FE phase contains none of the symmetry operations belonging to the Berry curvature reversing set $S=\{T,2_{\parallel },n_{001}T,PT,m_{\perp },m_{001}T,S_{n}T\}$, thereby allowing a nonzero AHE. (ii) The MSG of the paraelectric phase contains at least one symmetry operation that not only belongs to the set $S$, but also maps the two symmetry-related FE states onto each other by reversing the FE polarization, thereby ensuring the simultaneous switching of both FE polarization and AHE. These criteria are validated by first-principles calculations in the in-plane FE VOBrI and out-of-plane FE ${\mathrm{Co}}_2{\mathrm{NF}}_2$ single layers, and further confirmed using a modified Kane–Mele model. Our results provide a practical symmetry-based guideline for designing and screening 2D multiferroics with FE-switchable AHE and Chern number $C$.

The transition from very weak to ultrastrong plasmon-polariton-phonon coupling in (surface) doped ${\mathrm{HfS}}_2$ multilayers has been investigated. A plasmon-polariton (PP) in a single-layer ${\mathrm{HfS}}_2$ interacts weakly with polar phonons, however in ${\mathrm{HfS}}_2$ multilayers ($N>25$) the PP-phonon splitting becomes ${\mathrm{\Omega }}_{\text{PP-Ph}}\ge {\omega }_{\text{LOx}}/3$, indicating ultrastrong PP-phonon coupling. A particularly interesting electrodynamic effect appears for $d>10\text{−}\mu \text{m}$-thick ${\mathrm{HfS}}_2$ slabs. Then the absorption spectrum is dominated by a series of infrared active cavity resonances that spatially and by frequency resemble ${\mathrm{HfS}}_2$ cavity modes; they are standing waves confined to the ${\mathrm{HfS}}_2$ film but also radiate into the surrounding vacuum. The intensity of cavity resonances is comparable with the intensity of evanescent surface plasmon polaritons, while their number and frequency can be tuned by changing the ${\mathrm{HfS}}_2$ surface doping and/or thickness $d$. These are also very robust modes, so they may be very useful for the development of multifunctional nanoscale and mesoscale photonic devices.

An effective model of a two-band superconductor with full interband pairing is established based on doubly coupled Kitaev chains with a $\pi$-phase difference. Tunable Andreev bound states and quantized Andreev reflection are demonstrated. A hybrid qubit architecture is constructed, leveraging these bound states to synergize ultrafast microwave-driven Rabi oscillations in Andreev qubits with topologically protected quantum memory via Majorana zero modes. The resulting theoretically derived quantum memory and nontrivial fusion could offer supporting signatures for topological superconductivity. All theoretical results of our base model are directly reproduced within a realistic theoretical material model of an altermagnet-proximitized topological superconducting nanowire system.

We investigate analytically and numerically the effects of disorder on the helical edge of a two-dimensional topological insulator in the presence of a Zeeman field and superconductivity. Employing bosonization and a renormalization-group analysis, we study how impurity potentials modify charge- and spin-density wave correlations as well as superconducting pair correlations. Our results reveal that the Zeeman field controls the competition: in the attractive regime, it amplifies the superconducting gap, while in the repulsive regime, it stabilizes impurity effects by keeping the system longer in the relevant regime for disorder. We also find that disorder induces logarithmic suppression of density-wave correlations, while at the same time introducing positive logarithmic corrections that enhance superconducting pairing correlations and contribute to their stability. These effects directly modify the scaling of spin conductance, providing experimentally accessible signatures of the interplay between disorder and superconductivity in topological edge channels.

Surface-enhanced Raman scattering (SERS) has been considered as a powerful trace-level analytical technique for a diversity of fields. However, a molecule in the real world inevitably interacts with other molecules or external stimuli, which often results in obvious changes of its SERS spectrum, e.g., relative intensity, broadening/narrowing, shifting, splitting/merging of the peaks, emergence of new peaks and/or disappearance of existed peaks, etc. These bring fundamental challenges to SERS in solving real-world problems through recognition of the molecule's fingerprints, which has long been an open question in the field. We proposed here a virtual molecules (VMs) and virtual spectra method to deal with the molecule's interactions, and reformulated SERS with two concepts, i.e., cross-section function and relative scattering ability of molecules, which are valid for molecular systems with/without interactions. We established an approach to experimentally obtain the cross-section function and the relative scattering ability of VMs, by which the SERS behavior of molecular systems can be explicitly described by our formulation, with no need to recognize the molecule's fingerprints. These efforts consolidate the foundation of SERS, and push forward its applications as a powerful trace-level analytical technique in solving real-world problems.

We study topological effects in a one-dimensional plasmonic crystal formed by the screened plasmons emerging in a periodically modulated graphene sheet, placed on top of a metallic substrate. We develop the theory of quantization of screened plasmons, as appropriate for lossless graphene described by a Drude conductivity. By analyzing the resulting band structure, we show that the crystal sustains nontrivial topological bands, with quantized geometric phase. We further show that in a finite open system, edge states appear within the band gap, which undergo a topological phase transition and merge with bulk states as the modulation increases. Our work provides a robust theoretical framework for the study of band structure and topology of layered media and extends the possibilities for engineering two-dimensional materials with external modulation.

We uncover a previously overlooked contribution to the electro-optic Kerr rotation of reflected light, arising from the interplay of matter, the static electric field, and the magnetic component of light. This contribution remains nonzero even in isotropic, nonmagnetic, homogeneous systems. We derive analytical expressions for the Kerr rotation in both two-dimensional layers and semi-infinite systems. Within the relaxation-time approximation, we predict experimentally accessible signal magnitudes in metals. This inherent mechanism thereby opens opportunities for probing electronic properties in materials through Kerr spectroscopy.

Resonant parametric modulation is a major tool for studying magnetic systems. For a spin-1/2 chain in a strong magnetic field, the resulting excitations can be mapped onto fermionic excitations in the Kitaev chain. We show that the response to turning on the modulation reveals dynamical bulk aspects of the nontrivial topology of the closed chain. In the topological regime, depending on the turn-on rate, the system displays an absence of frequency dispersion of the time-averaged magnetization and an absence or a suppression of its spatial correlations near resonance. The transition between the topological and trivial regimes is controlled by the modulation frequency.

A systematic structural investigation of $\mathrm{F}{\mathrm{e}}_2\mathrm{M}{\mathrm{o}}_3{\mathrm{O}}_8$ as a function of pressure, temperature, and magnetic field reveals that the $P{6}_{3}mc$ space group remains robust over a wide range of conditions. No changes in the long-range crystal structure are observed for pressures up to 10 GPa, temperatures between 11 K and 300 K, and magnetic fields up to 9 T. The magnetostructural response, quantified by $\mathrm{\Delta }c/c$, is determined for magnetic fields applied transverse to the crystallographic $c$ axis, demonstrating strong magnetoelastic coupling. The well-known magnetic-field-induced transition is confirmed to be first order and isostructural, occurring between two distinct altermagnetic states. Importantly, this transition can also be accessed using magnetic fields applied within the $\mathit{ab}$ plane. When expressed in terms of the $c/a$ ratio, the structural evolution under pressure (0–10 GPa) maps continuously onto that observed across the full Zn substitution range in $(\mathrm{F}{\mathrm{e}}_{1-y}\mathrm{Z}{\mathrm{n}}_y{)}_2\mathrm{M}{\mathrm{o}}_3{\mathrm{O}}_8\left(0\le y\le 1\right)$, indicating a common underlying structural control parameter. These results demonstrate that the $c$-axis lattice parameter is the primary structural degree of freedom governing magnetic behavior under external tuning parameters. More broadly, they indicate that magnetic order in this family of complex oxides ($A_2\mathrm{M}{\mathrm{o}}_3{\mathrm{O}}_8, A=\mathrm{Co},\mathrm{Mn},\mathrm{Ni}$) can be systematically tuned via pressure. This tunability highlights these materials as promising platforms for controllable magnetic switching, particularly in thin films integrated with piezoelectric substrates.

Hydrogen doping offers a versatile method to dynamically control the doping level of metal oxides over a wide range, yet it introduces strong lattice modulation whose structural details have been poorly investigated. Here, we elucidate the hydrogen-induced structural modulation in ${\mathrm{NdNiO}}_3$ thin films using synchrotron x-ray diffraction. While the strain relaxed pristine film exhibits a bulklike $\sqrt{2}\times \sqrt{2}\times 2$ structure, the hydrogen-induced insulating phase adopts a $1\times 1\times 2$ structure with some incommensurate modulation. Our results provide the first direct experimental evidence for hydrogen-induced formation of a superstructure in rare-earth nickelates.

${\mathrm{VO}}_2$ features concomitant structural and metal-insulator transitions. This poses a challenge for understanding the underlying mechanism: Is the transition triggered by a structural or by an electronic instability? The two scenarios are expected to produce very different pretransitional fluctuations above $T_{\mathrm{C}}$. By combining magnetic susceptibility, IR reflectivity, and x-ray diffuse scattering measurements, we observe that metallic ${\mathrm{VO}}_2$ features strong electronic and structural fluctuations toward the insulating monoclinic phase. By measuring resonant diffuse x-ray scattering across the vanadium $K$ edge, we search for a potential decoupling between electronic and structural ordering in these fluctuations, finding no evidence of it. While our results do not completely rule out pure electronic fluctuations, they constrain them, favoring the interpretation that the ${\mathrm{VO}}_2$ metal-insulator transition is triggered by a structural instability. Our work offers a unique approach to solve similar problems in other strongly correlated systems.

Several recent x-ray diffraction studies have focused on whether the high-pressure body-centered cubic (bcc) phase of zirconium undergoes an isostructural bcc-bcc transition at 58 GPa. The consensus of these studies is that there is no such transition and that a previous claim by Stavrou et al. resulted from issues with the pressure calibration. However, a close analysis of the data from one of the most recent of these diffraction studies by Anzellini et al. shows unremarked evidence of a discontinuity in both atomic volume and compressibility at 83 GPa indicating an isostructural transition is present. Unfortunately, no other previous studies have reached this pressure, and so the question of the bcc-bcc transition is still open. Here we describe a diffraction study of Zr to 240 GPa looking for a bcc-bcc isostructural transition. Our data show no evidence of any discontinuous change in volume or compressibility at 83 GPa. We observe no evidence of a $\beta \to {\beta }^{\prime }$ transition above 80 GPa, and suggest a possible cause of the discontinuity observed by Anzellini et al.