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Congjun Wu

Publications and source records attributed to Congjun Wu.

At least 19 recordsLinked to original sources
arXiv2026

Space-time crystallography and symmetry-enforced dynamical phenomena in 2+1 dimensions

The concept of space group has long served as a fundamental framework for describing the physical properties of crystalline materials, from electronic bands to photonic dispersions. Recent advances in spatiotemporal control, including laser-driven lattices, dynamic photonic and phononic crystals, and dynamic optical lattices, necessitate the study of symmetries that intrinsically intertwine space and time. Standard Floquet theory primarily organizes temporal periodicity and does not by itself provide a general framework for classifying these intertwined space-time symmetries. Space-time groups include novel intertwined nonsymmorphic spatial-temporal symmetries such as time-glide reflection and time-screw rotation. Here, we establish the complete crystallography of (2+1)-dimensional space-time crystals, systematically classifying all 275 space-time groups into 7 crystal systems, 14 Bravais lattices, and 72 arithmetic crystal classes. We further develop the representation theory of space-time groups and show that these symmetries enforce dynamical phenomena without static counterparts, including handedness-flipping heterodyne responses and a novel "horizontal cone" arising from symmetry-enforced momentum degeneracy in space-time metamaterials. Our results establish space-time crystallography as a general framework for predicting and engineering symmetry-protected phenomena in driven quantum systems and time-modulated metamaterials.

cond-mat.mes-hall↗
arXiv2026

Topological Charge-2ne Superconductors

Charge-$4e$ superconductors are phases where quartets of electrons condense in the absence of Cooper pairing condensation. They exhibit distinctive signatures including fractional flux quantization and anomalous Josephson effects, and are actively being explored in strongly correlated systems, such as moiré materials. In this work we develop a general framework for topological charge-$2ne$ superconductors based on both wavefunction and field theory approaches. In particular, we generate topological charge-$2ne$ superconductors from charge-$2e$ ingredients, and by breaking the charge $U(1)$ symmetry in certain classes of quantum Hall states, in both spinless and spinful systems. Via bulk-edge correspondence, we further construct the corresponding edge conformal field theory and bulk topological quantum field theory for topological charge-$2ne$ superconductors that suggests fermionic nonabelian topological orders. Our results provide a unified low-energy description of the topological charge-$2ne$ superconductivity, offer a concrete platform for studying symmetry breaking and enrichment in interacting topological phases of matter, and have direct implications for experimental probes such as quasiparticle interferometry.

cond-mat.str-el↗
arXiv2026

Second-Chern Bounds in Non-Abelian Quantum Geometry

We study the quantum geometry of doubly degenerate energy levels in a four-dimensional parameter space. We find that the scalar quantum metric $g$ and the Berry curvature $F$ obey $(\operatorname{tr} g)^2/16\geq\sqrt{\det g}\geq |2\Tr(F\wedge F)-\Tr F\wedge \Tr F|/24$. The first inequality characterizes the anisotropy in the metric. The second determinant inequality measures the self-duality of the traceless $SU(2)$ part of the curvature under Hodge star operation and the algebraic closedness of the inter-level polarization amplitudes under $SU(2)$ rotations in the doubly degenerate levels. The saturation of the determinant bound imposes a quaternionic Cauchy-Riemann equation, analogous to the complex analyticity imposed by ideal-band conditions in two-dimensional Chern insulators. As examples, four-band Dirac Hamiltonians automatically saturate the determinant bound and possess a topological zero in $\operatorname{tr}(F\wedge F)$. We compare the differences between Kramers degeneracy and ordinary $U(2)$ degeneracy. In addition to the non-Abelian geometric bound, the latter also obeys an independent first-Chern bound.

cond-mat.mes-hall↗
arXiv2026

Orbital homology of p and t2g orbitals in models and materials

The nominal divide between $p$- and $d$-electron systems often obscures a deep underlying unity in condensed matter physics. This review elucidates the orbital homology between the $p$ and $t_{2g}$ orbital manifolds, establishing the correspondence that extends from minimal model Hamiltonians to the complex behaviors of real quantum materials. We demonstrate that despite their distinct atomic origins, these orbitals host nearly identical hopping physics and spin-orbit coupling, formalized through an effective ${l=1}$ angular momentum algebra for the $t_{2g}$ case. This equivalence allows one to transpose physical intuition and theoretical models developed for $p$-orbital systems directly onto the more complex $t_{2g}$ materials, and vice versa. We showcase how this paradigm provides a unified understanding of emergent phenomena, including non-trivial band topology, itinerant ferromagnetism, and unconventional superconductivity, across a wide range of platforms, from transition metal compounds, two-dimensional oxide heterostructures, and iron-based superconductors, to $p$-orbital ultracold gases. Ultimately, this $p$-$t_{2g}$ homology serves not only as a tool for interpretation but also as a robust design principle for engineering novel quantum states.

cond-mat.str-el↗
arXiv2026

Emergent Interfacial Magnetism in Epitaxial RuO$_2$

The magnetic ground state of the altermagnet candidate RuO$_2$ remains controversial, with magnetic signatures observed mainly in epitaxial films. Here we show, using first-principles calculations, that magnetism in epitaxial RuO$_2$ can emerge as an interfacial boundary phase at TiO$_2$/RuO$_2$ interfaces. While TiO$_2$-induced epitaxial strain alone does not make (001)-oriented RuO$_2$ magnetic, explicit TiO$_2$/RuO$_2$ interfaces stabilize sizable Ru moments confined to the first few Ru layers. Charge-density and orbital-resolved analyses reveal interfacial electronic reconstruction, and substrate doping provides a route to tune the induced moments. In symmetric TiO$_2$/RuO$_2$/TiO$_2$ heterostructures, the two magnetic interfaces couple through the metallic RuO$_2$ spacer, producing a thickness-dependent alternation between weak-ferromagnetic and compensated altermagnetic states. Our results identify interface engineering as a practical route to stabilize and control fragile magnetism in RuO$_2$.

cond-mat.mtrl-sci↗
arXiv2026

Many-body wave function and edge magnetization of an open $p+is$ superconducting chain

Although BCS wave functions for superconductors under periodic boundary conditions are well established, obtaining an explicit form of the many-body BCS wave function under open boundary condition is usually a nontrivial problem. In this work, we construct the exact BCS ground-state wave function of a one-dimensional spin-$\frac12$ superconductor with $p+is$ pairing symmetry under open boundary conditions for special sets of parameters. The spin magnetization on the edges is calculated explicitly using the obtained wave function. Our work is useful for obtaining deeper understandings of open $p+ is$ superconducting chains on a wave-function level.

cond-mat.supr-con↗
arXiv2026

Dynamical Generation of Rectified Electric Current

Rectification is a fundamental nonlinear transport process that converts an alternating drive into a direct current. In this work, we propose a general theoretical framework for electric current rectification triggered by a dynamical external drive that couples to an arbitrary well-defined operator of a periodic system, and which in the static limit forbids any steady current. In the dynamical regime, the finite frequency $Ω$ of the time-varying drive breaks time-translation invariance and injects energy into the system, enabling a second-order {\it nonlinear rectified} current that has no static counterpart. This rectification process has two distinct origins: (i) an impurity-scattering-modified distribution function at finite frequency, and (ii) a time-domain anomalous velocity stemming from a dynamical mixed Berry curvature. Both contributions persist when the driving frequency lies well below the optical transition gap. Applying our general theory to a buckled magnetic system subject to an out-of-plane oscillating electric field, we characterize the generated current as a {\it nonlinear magnetoelectric gyrotropic effect} and predict that the induced rectified current is sensitive to the magnetic order, thereby offering a feasible electrical probe of Néel order in non-coplanar antiferromagnets.

cond-mat.mes-hall↗
arXiv2026

Topological multicomponent superconductivity with sizable $s$-wave admixture in twisted bilayer cuprates

We investigate multicomponent superconductivity in twisted bilayer cuprates with order parameter $s+d_1 e^{iϕ_1}+d_2 e^{iϕ_2}$, where $s=s_1+s_2$ is the symmetric layer-resolved $s$-wave component and $d_i$ denotes the $d$-wave pairing in layer $i$. When $ϕ_1-ϕ_2\neq 0,π$, this three-component state breaks time-reversal and $C_4$ rotational symmetries and is topologically nontrivial. Combining Ginzburg--Landau analysis with self-consistent microscopic mean-field calculations, we show that this topological state is stabilized over a broad parameter regime. We further identify nematic Kerr anisotropy as a smoking-gun signature distinguishing it from $s+id$ and $d_1+e^{iϕ}d_2$ states. Our results show that a sizable $s$-wave component does not preclude chiral topological superconductivity, pointing to twisted cuprates as a more robust platform than previously appreciated.

cond-mat.supr-con↗
arXiv2026

Effective Theory of Fermion Quartet Condensation

We develop a theory of superconductivity (or superfluidity) based on condensed fermion quartets focusing on the dilute spin-$\frac{1}{2}$ systems at zero temperature. In the spirit of the Bardeen--Cooper--Schrieffer ansatz, a variational wavefunction is constructed such that, within the so-called ``dilute quartet approximation", it is the ground state of an effective quartic Hamiltonian. For a given two-body interaction in favor of quartetting, the gap parameter is suitably defined and the gap equation is also derived. As to the excited states, an intuitive physical picture based on a sixteen-dimensional ``occupation space" is depicted and the associated eigen-energies are obtained. This theory is applied to compute the superfluid fraction, which is found to be the same as in conventional superconductors, despite the interacting nature of the quartet problem.

cond-mat.supr-con↗
arXiv2026

Spin Quadrupolar orders in $d$-wave Unconventional Magnetism

Unconventional magnetism represents a class of metallic states whose Fermi surfaces exhibit spin-dependent splittings under the non-trivial representations of the rotation group. The $d$-wave $α$-phase unconventional magnetic state, commonly known as altermagnet, recently, has attracted significant attention. While these systems exhibit distinct anisotropic $d$-wave characteristics in momentum space, how this microscopic topology translates into the spin distributions in real space remains a question. In this work, we bridge the intrinsic spin quadrupolar ordering in momentum space to the real-space staggered magnetic distribution. By introducing a weak, non-magnetic periodic crystal potential into a $d$-wave unconventional magnetic state, the spin-charge cross susceptibility is calculated by using the linear response theory. We reveal that the interplay between the crystal potential and the intrinsic $d$-wave spin-splitting naturally induces a spatial spin quadrupole distribution without enlarging the unit cell. Our study thus provides a physical connection between momentum-space multipoles in the even partial wave channel and real-space spin multipole orders.

cond-mat.str-el↗
arXiv2026

Response tensor for the superconducting (Josephson) diode effect

We propose a response tensor $\mathbf{\hat χ}$ to characterize the non-reciprocal critical current response of the superconducting (Josephson) diode effect. It describes the coupling between the dipole component of the angular distribution of the critical current and the applied magnetic field -- an analogue to the Hall response in the normal state. In quasi-2D systems with Rashba spin-orbit coupling and point group symmetries $C_{3v}$, $C_{4v}$ or $C_{6v}$, this tensor takes a fully antisymmetric form. When nematicity is present, a symmetric contribution emerges, providing an indicator of the nematic order in the superconducting state. In contrast, for systems exhibiting Dresselhaus spin-orbit coupling with the $D_{2d}$ symmetry, the tensor becomes diagonal traceless, and nematicity brings in a trace part. Our analysis not only accounts for the superconducting diode effect under external applied or intrinsic effective magnetic fields, but also predicts the symmetry conditions for realizing the diode effect when the magnetic field is aligned with the current. Beyond this, the proposed tensor provides a promising tool for detecting nematicity and potential nematic transitions deep within the superconducting phase. It may also encode additional information about the underlying electronic structure and symmetry-breaking orders, warranting further experimental investigation.

cond-mat.supr-con↗
arXiv2026

Time-reversal symmetry breaking superconductivity in the presence of loop-current fluctuations

Loop currents have been proposed in various superconductors and recently confirmed in kagome materials, raising a fundamental question regarding their intrinsic connection to superconductivity. Here, we study a sign-problem-free bilayer $t-J_{\perp}-V$ model hosting a spontaneous interlayer loop-current parent state, and explore the interplay between loop-current fluctuations and superconductivity using unbiased projector quantum Monte Carlo simulations. Near half-filling, unbiased interlayer interactions induce spontaneous loop currents that break time-reversal symmetry. Upon hole doping, the loop-current order is suppressed, and interlayer $s$-wave superconductivity emerges where loop-current fluctuations become dominant. We establish a phase diagram revealing a transition from the loop-current parent to a superconducting state, reminiscent of the evolution from an antiferromagnetic parent to superconductivity in cuprates. Strikingly, a coexisting regime emerges near the phase boundary, yielding time-reversal-symmetry-breaking superconductivity. Our study reveals an intrinsic connection between loop currents and superconductivity, and identifies a promising mechanism for time-reversal symmetry breaking in superconductors. Furthermore, our results offer insights into unconventional superconductivity in loop-current systems and establish a minimal theoretical framework for understanding time-reversal symmetry breaking in bilayer correlated electron systems.

cond-mat.supr-con↗
arXiv2026

Superconductivity in bilayer La$_3$Ni$_2$O$_7$: A review focusing on the strong-coupling Hund's rule assisted pairing mechanism

Discovery of high-$T_c$ superconductivity (SC) in the bilayer nickelate series La$_3$Ni$_2$O$_7$ have attracted substantial interest, providing a new platform for exploring unconventional SC. Certain experimental evidence has pointed to a correlated electronic nature, which is the driving force responsible for its high critical temperature ($T_c$). This work reviews the SC in La$_3$Ni$_2$O$_7$, with a particular focus on theoretical understanding of its pairing mechanism driven by this strong-coupling, Hund-assisted scenario. The electronic landscape is governed by two $E_g$-orbitals within the bilayer structure of NiO$_2$ planes. The $3d_{z^2}$ orbital is nearly half-filled and exhibits a stronger localized character, while the $3d_{x^2-y^2}$ is approximately quarter-filled and remains highly itinerant. The localized $3d_{z^2}$ orbitals experience robust interlayer hybridization, mediated by the $2p_z$ orbitals of the inner apical oxygen atoms. This hybridization generates a strong interlayer antiferromagnetic (AFM) exchange. In the strong coupling regime, Hund's rule coupling aligns the spins of the two $E_g$ orbitals on the same nickel site. The strong interlayer AFM exchange is effectively transferred to the itinerant $3d_{x^2-y^2}$ orbital, generating an effective coupling $J_{\perp}$ within this orbital. This mechanism is captured by a minimal strong-coupling bilayer $t$-$J$-$J_{\perp}$ model for the $3d_{x^2-y^2}$ band. Driven by $J_{\perp}$, $3d_{x^2-y^2}$ electrons can form interlayer Cooper pairs, leading to an extended $s$-wave pairing SC with high $T_c$. Meanwhile, the strongly localized $3d_{z^2}$ electrons tend to form interlayer rung singlets. Due to a lack of phase coherence, these singlets do not directly participate in the SC condensate, but instead give rise to a pseudogap phase.

cond-mat.supr-con↗
arXiv2026

Chiral finite-momentum superconductivity in the tetralayer graphene

Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene, we investigate the pairing mechanism arising from the density-density interactions within the random-phase approximation. This approach successfully highlights the dominance of the chiral $p$-wave pairing between electrons with the same spin and valley index at low densities, while also predicting the superconducting range in agreement with experimental findings. Furthermore, we examine the characteristics of distinct superconducting regions: SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations, whereas SC4 displays zero-momentum spin-singlet superconductivity.

cond-mat.supr-con↗
arXiv2026

Collective Nuclear Polaritons with Coherent and Tunable Excitation Dynamics

We propose collective nuclear polaritons formed by hybridizing a 229Th nuclear ensemble with a vacuum-ultraviolet cavity mode generated via four-wave mixing, achieving a collective light-matter coupling that scales as $\sqrt{N}$. In the strong-coupling regime the system displays vacuum Rabi oscillations, indicating the hybridization between cavity photons and nuclear excitations. In the superradiant regime, the stored excitation is released in a cooperative burst with peak intensity scaling as $N^2$. The emission lifetime shrinks from thousands of seconds to the millisecond scale and remains tunable. Detuning sweeps across the polariton avoided crossing allow adiabatic conversion of the photonic excitation into a collective nuclear excitation, enabling reversible quantum storage. Our results demonstrate that cavity-mediated nuclear polaritons enable deterministic lifetime engineering and coherent quantum storage in nuclear systems.

quant-ph↗
arXiv2026

Kinetic Energy Driven Ferromagnetic Insulator

We construct a minimal model of interacting fermions establishing a ferromagnetic insulating phase. It is based on the Hubbard model on a trimerized triangular lattice in the regime of $t\gg |t^\prime|>0$ with $t$ and $t^\prime$ the intra- and inter-trimer hopping amplitudes, respectively. At the $\frac{1}{3}$-filling, each trimer becomes a triplet spin-1 moment, and the inter-trimer superexchange is ferromagnetic with $J =- \frac{2}{27}\frac{t^{\prime 2}}{t}$ in the limit of $U/t=+\infty$. As $U/t$ becomes finite, the antiferromagnetic superexchange competes with the ferromagnetic one. The system enters into a frustrated antiferromagnetic insulator when $λ>U/t\gg 1$ where $λ$ is a constant at the order of 10. In contrast, a similar analysis to the trimerized Kagome lattice shows that only the antiferromagnetic superexchange exists at $\frac{1}{3}$-filling.

cond-mat.str-el↗
arXiv2026

Possible Liquid-Nitrogen-Temperature Superconductivity Driven by Perpendicular Electric Field in the Single-Bilayer Film of La$_3$Ni$_2$O$_7$ at Ambient Pressure

Recently, high-temperature superconductivity (HTSC) is found in the La$_3$Ni$_2$O$_7$/SrLaAlO$_4$ ultrathin film with critical temperature $T_c$ above the McMillan limit at ambient pressure (AP). It is eager to enhance $T_c$ of La$_3$Ni$_2$O$_7$ at AP. We propose that a perpendicular electric field strongly enhances $T_c$ in the single-bilayer film of La$_3$Ni$_2$O$_7$ at AP. Under electric field, the layer with lower potential energy will accept electrons flowing from the other layer to fill in the Ni-$3d_{x^2-y^2}$ orbitals, as the nearly half-filled Ni-$3d_{z^2}$ orbital cannot accommodate more electrons. With the enhancement of the filling fraction in the $3d_{x^2-y^2}$ orbitals in this layer, the interlayer $s$-wave pairing is suppressed, but the intralayer $d$-wave pairing in this layer is strongly enhanced. We numerically verify this idea and yield that an imposed voltage of about $0.1\sim0.2$ volt between layers is enough to realize liquid-nitrogen-temperature HTSC in this single bilayer at AP. Our results appeal for experimental verification.

cond-mat.supr-con↗
arXiv2026

Incompressible quantum liquid on the four-dimensional sphere

The study of quantum Hall effect (QHE) is a foundation of topological physics, inspiring extensive explorations of its high-dimensional generalizations. Notably, the four dimensional (4D) QHE has been experimentally realized in synthetic quantum systems, including cold atoms, photonic lattices, and metamaterials. However, the many-body effect in the 4D QHE system remains poorly understood. In this study, we explore this problem by formulating the microscopic wavefunctions inspired by Laughlin's seminal work. Employing a generalized pseudo-potential framework, we derive an exact microscopic Hamiltonian consisting of two-body projectors that annihilate the microscopic wavefunctions. Diagonalizations on a small size system show that the quasi-hole states remain zero energy while the quasi-particle states exhibit a finite gap, in consistency with an incompressible state. Furthermore, the pairing distribution is calculated to substantiate the liquid-like nature of the wavefunction. Our work provides a preliminary understanding to the fractional topological states in high dimension.

cond-mat.str-el↗