Antiferromagnetic spin fluctuations are the most promising candidate as the pairing glue of high critical temperature (Tc) superconductivity in cuprates. However, many-body states and intertwined orders have made it difficult to determine how electrons couple with fluctuating spins to form Cooper pairs. Recent experimental and theoretical studies have suggested spin fluctuation-driven quasiparticle band folding, but the relationship between the resultant Fermi pockets and superconductivity remains unclear. Here, using angle-resolved photoemission spectroscopy and numerical simulations, we show a proportional relationship between Tc and the quasiparticle weight of the incipient hole pocket near the nodal point in electron-doped Pr1−xLaCexCuO4±δ. Through complementary muon spin spectroscopy measurements, we uncover that the hole pocket forms only in the regime of the fluctuating antiferromagnetic ground state around a presumed quantum critical point. Our observations highlight the significance of the electron-spin fluctuation interaction in enhancing the hole pocket and consequently driving superconductivity. The authors study electron-doped cuprate superconductor Pr1−xLaCexCuO4-δ using ARPES and muon spin spectroscopy. They find that Tc is proportional to the quasiparticle weight of the hole pocket near the nodal points, which arises from Fermi-surface reconstruction associated with antiferromagnetic order.

We elucidate the ground state nature and low-energy spin dynamics of the $s=1/2$ near-perfect kagome antiferromagnet ${\mathrm{YCu}}_{3}{(\mathrm{OD})}_{6+x}{\mathrm{Br}}_{3\ensuremath{-}x}$ ($x=0.5$) using $^{63}\mathrm{Cu}$ nuclear quadrupole resonance (NQR) and muon spin relaxation/rotation ($\ensuremath{\mu}\mathrm{SR}$) techniques. Our combined $^{63}\mathrm{Cu}$ NQR and $\ensuremath{\mu}\mathrm{SR}$ data, along with the inverse Laplace transform analysis, reveal an inhomogeneous ground state comprising the majority of a gapless spin liquid intermingled with a minor fraction of spin singlets with varying energy gaps. Furthermore, the $^{63}\mathrm{Cu}$ NQR relaxation rate evinces distinct signatures of Dirac spinons, featuring a power-law dependence of $1/{T}_{1}\ensuremath{\sim}{T}^{\ensuremath{\eta}}$ with $\ensuremath{\eta}=1.35$ at temperatures below $0.13J$ ($\ensuremath{\cong}8\phantom{\rule{0.28em}{0ex}}\mathrm{K}$). Our results demonstrate that a kagome lattice endowed with specific exchange randomness provides a prominent platform for exploring Dirac fermions in magnetic insulators.

Exotic quantum many-body states, such as Haldane and spin liquid phases, can exhibit remarkable features like fractional excitations and non-Abelian statistics and offer new understandings of quantum entanglement in many-body quantum systems. These phases are classified by nonlocal correlators that can be directly measured in atomic analog quantum simulating platforms, such as optical lattices and Rydberg atom arrays. However, characterizing these phases in large systems is experimentally challenging because they are sensitive to local errors like atom loss, which suppress its signals exponentially. Additionally, protocols for systematically identifying and mitigating uncorrelated errors in analog quantum simulators are lacking. Here, we address these challenges by developing an error-correction method for large-scale neutral atom quantum simulators using optical lattices. Our error-correction method can distinguish correlated particle-hole pairs from uncorrelated holes in the Mott insulator. After removing the uncorrelated errors, we observe a dramatic improvement in the nonlocal parity correlator and find the perimeter scaling law. Furthermore, the error model provides a statistical estimation of fluctuations in site occupation, from which we measure the generalized brane correlator and confirm that it can be an order parameter for Mott insulators in two dimensions. Our work provides a promising avenue for investigating and characterizing exotic phases of matters in large-scale quantum simulators.

Utilizing the realistic continuum description of twisted bilayer MoTe2 and many-body exact diagonalization calculation, we establish that the second moir & eacute; band of twisted bilayer MoTe2, at a small twist angle of approximately 2 degrees, serves as an optimal platform for achieving the long-sought non-Abelian fractional quantum anomalous Hall states without the need for external magnetic fields. Across a wide parameter range, our exact diagonalization calculations reveal that the half-filled second moir & eacute; band demonstrates the ground state degeneracy and spectral flows, which are consistent with the Pfaffian state in the first Landau level. We further elucidate that the emergence of the non-Abelian state is deeply connected to the remarkable similarity between the second moir & eacute; band and the first Landau level. Essentially, the band not only exhibits characteristics akin to the first Landau level, 1 BZ d2k tr eta(k) 3 where eta ab(k) is the Fubini-Study metric of the band, but also that its projected Coulomb interaction closely mirrors the Haldane pseudopotentials of the first Landau level. Motivated by this observation, we introduce a metric of "first Landau level"-ness of a band, which quantitatively measures the alignment of the projected Coulomb interaction with the Haldane pseudopotentials in Landau levels. This metric is then compared with the global phase diagram of the half-filled second moir & eacute; band, revealing its utility in predicting the parameter region of the non-Abelian state. In addition, we uncover that the first and third moir & eacute; bands closely resemble the lowest and second Landau levels, revealing a remarkable sequential equivalence between the moir & eacute; bands and Landau levels. We finally discuss the potential implications on experiments.

We demonstrate that the mode number of Andreev bound states in bilayer graphene Josephson junctions can be modulated by in situ control of the superconducting coherence length. By exploiting the quadratic band dispersion of bilayer graphene, we control the Fermi velocity and thus the coherence length by the application of the electrostatic gating. Tunneling spectroscopy of Andreev bound states reveals a crossover from short to long Josephson junction regimes as the gate voltage is approached near the charge neutral point of bilayer graphene. Furthermore, quantitative analysis of Andreev spectrums for different mode numbers allows us to quantitatively estimate the phase-dependent Josephson current. Our work paves a new way to study multi-mode Andreev levels and to engineer Fermi velocity with bilayer graphene.

We present the magnetic, thermodynamic, and muon spin relaxation (mu SR) results of the dimer-based triangular antiferromagnet Ba6Y2Rh2Ti2O17-delta. The magnetic susceptibility data show the sub-Curie-Weiss behavior chi(T ) proportional to T -alpha chi below 100 K, suggesting random magnetism. The isothermal magnetization results reveal the presence of weakly interacting structural orphan spins about 6.1% at 2 K, arising from the oxygen deficiency. The comprehensive mu SR experiments exhibit the coexisting relaxing and nonrelaxing components along with the thermally activated behavior in the muon spin relaxation rate, reflecting the fluctuating orphan spins in the dimer singlet background. In addition, we observe the scaling behavior of M(H, T ) in H/T and Pz(t) in t/HLF with the scaling exponents alpha chi = alpha M = 0.75 and alpha mu = 0.72, respectively, but not for the magnetic specific heat data. The failure of the scaling relation in Cm(H, T )/T implies low-energy excitations dressed by the conventional orphan spins. Based on these observations, we find that the magnetic ground state resembles random singlets and discuss the possible configurations of the spin dimer unit Rh2O9. Our results shed light on the role of quenched disorder in the dimer-based frustrated magnets.

We elucidate the ground state nature and low-energy spin dynamics of the s = 1/2 near-perfect kagome antiferromagnet YCu3(OD)(6+x)Br3-x (x = 0.5) using Cu-63 nuclear quadrupole resonance (NQR) and muon spin relaxation/rotation / rotation (mu SR) techniques. Our combined Cu-63 NQR and mu SR data, along with the inverse Laplace transform analysis, reveal an inhomogeneous ground state comprising the majority of a gapless spin liquid intermingled with a minor fraction of spin singlets with varying energy gaps. Furthermore, the Cu-63 NQR relaxation rate evinces distinct signatures of Dirac spinons, featuring a power-law dependence of 1/T-1 similar to T-eta with eta = 1.35 at temperatures below 0.13 J (congruent to 8 K). Our results demonstrate that a kagome lattice endowed with specific exchange randomness provides a prominent platform for exploring Dirac fermions in magnetic insulators.

Exotic quantum many-body states, such as Haldane and spin liquid phases, can exhibit remarkable features like fractional excitations and non-abelian statistics and offer new understandings of quantum entanglement in many-body quantum systems. These phases are classified by non-local correlators that can be directly measured in atomic analog quantum simulating platforms, such as optical lattices and Rydberg atom arrays. However, characterizing these phases in large systems is experimentally challenging because they are sensitive to local errors like atom loss, which suppress its signals exponentially. Additionally, protocols for systematically identifying and mitigating uncorrelated errors in analog quantum simulators are lacking. Here, we address these challenges by developing an error correction method for large-scale neutral atom quantum simulators using optical lattices. Our error correction method can distinguish correlated particle-hole pairs from uncorrelated holes in the Mott insulator. After removing the uncorrelated errors, we observe a dramatic improvement in the non-local parity correlator and find the perimeter scaling law. Furthermore, the error model provides a statistical estimation of fluctuations in site occupation, from which we measure the generalized brane correlator and confirm that it can be an order parameter for Mott insulators in two dimensions. Our work provides a promising avenue for investigating and characterizing exotic phases of matters in large-scale quantum simulators.

Engineering quantum states through light-matter interaction has created a paradigm in condensed-matter physics. A representative example is the Floquet-Bloch state, which is generated by time-periodically driving the Bloch wavefunctions in crystals. Previous attempts to realize such states in condensed-matter systems have been limited by the transient nature of the Floquet states produced by optical pulses1-3, which masks the universal properties of non-equilibrium physics. Here we report the generation of steady Floquet-Andreev states in graphene Josephson junctions by continuous microwave application and direct measurement of their spectra by superconducting tunnelling spectroscopy. We present quantitative analysis of the spectral characteristics of the Floquet-Andreev states while varying the phase difference of the superconductors, the temperature, the microwave frequency and the power. The oscillations of the Floquet-Andreev-state spectrum with phase difference agreed with our theoretical calculations. Moreover, we confirmed the steady nature of the Floquet-Andreev states by establishing a sum rule of tunnelling conductance4, and analysed the spectral density of Floquet states depending on Floquet interaction strength. This study provides a basis for understanding and engineering non-equilibrium quantum states in nanodevices.

Spin nematic (SN) is a magnetic analog of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid. Particularly intriguing is a valence-bond SN, in which spins are quantum entangled to form a multi-polar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here, we establish a SN phase in the square-lattice iridate Sr$_2$IrO$_4$, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet (AF) in the strong spin-orbit coupling limit. Upon cooling, the transition into the SN phase at T$_C$ $\approx$ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra, and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic (AF) phase below T$_N$ $\approx$ 230 K, and becomes directly observable through its interference with the AF order in resonant x-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic x-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a resonating-valence-bond-like quantum entanglement in the AF state. Taken together, our results reveal a quantum order underlying the N\'eel AF that is widely believed to be intimately connected to the mechanism of high temperature superconductivity (HTSC).

The modern theory of polarization establishes the bulk-boundary correspondence for the bulk polarization. In this paper, we attempt to extend it to a sum rule of the bulk quadrupole moment by employing a many-body operator introduced in Kang et al. [B. Kang, K. Shiozaki, and G. Y. Cho, Phys. Rev. B 100, 245134 (2019)] and Wheeler et al. [W. A. Wheeler, L. K. Wagner, and T. L. Hughes, Phys. Rev. B 100, 245135 (2019)]. The sum rule that we propose consists of the alternating sum of four observables, which are the phase factors of the many-body operator in different boundary conditions. We demonstrate its validity through extensive numerical computations for various noninteracting tight-binding models. We also observe that individual terms in the sum rule correspond to the bulk quadrupole moment, the edge-localized polarizations, and the corner charge in the thermodynamic limit on some models.

We construct new many-body invariants for 2D Chern and 3D chiral hinge insulators characterizing quantized pumping of bulk dipole and quadrupole moments. The many-body invariants are written entirely in terms of many-body ground state wave functions on a torus geometry with twisted boundary conditions and a set of unitary operators. We present a number of supporting arguments for the invariants via topological field theory interpretation, adiabatic pumping argument, and direct mapping to free-fermion band indices. Therefore, the invariants explicitly encircle several different pillars of theoretical descriptions of topological phases. Furthermore, our many-body invariants are written in forms which can be directly employed in various numerics including the exact diagonalization and the density-matrix renormalization group simulations. We finally confirm our invariants by numerical computations including an infinite density-matrix renormalization group on quasi-one-dimensional systems.

Engineering quantum states through light-matter interaction has created a new paradigm in condensed matter physics. A representative example is the Floquet-Bloch state, which is generated by time-periodically driving the Bloch wavefunctions in crystals. Previous attempts to realise such states in condensed matter systems have been limited by the transient nature of the Floquet states produced by optical pulses, which masks the universal properties of non-equilibrium physics. Here, we report the generation of steady Floquet Andreev (F-A) states in graphene Josephson junctions by continuous microwave application and direct measurement of their spectra by superconducting tunnelling spectroscopy. We present quantitative analysis of the spectral characteristics of the F-A states while varying the phase difference of superconductors, temperature, microwave frequency and power. The oscillations of the F-A state spectrum with phase difference agreed with our theoretical calculations. Moreover, we confirmed the steady nature of the F-A states by establishing a sum rule of tunnelling conductance, and analysed the spectral density of Floquet states depending on Floquet interaction strength. This study provides a basis for understanding and engineering non-equilibrium quantum states in nano-devices.

Stacking two-dimensional van der Waals (vdW) materials rotated with respect to each other show versatility for studying exotic quantum phenomena. In particular, anisotropic layered materials have great potential for such twistronics applications, providing high tunability. Here, we report anisotropic superconducting order parameters in twisted Bi2Sr2CaCu2O8+x (Bi-2212) vdW junctions with an atomically clean vdW interface, achieved using the microcleave-and-stack technique. The vdW junctions with twist angles of 0° and 90° showed the maximum Josephson coupling, comparable to that of intrinsic Josephson junctions. As the twist angle approaches 45°, Josephson coupling is suppressed, and eventually disappears at 45°. The observed twist angle dependence of the Josephson coupling can be explained quantitatively by theoretical calculation with the d-wave superconducting order parameter of Bi-2212 and finite tunneling incoherence of the junction. Our results revealed the anisotropic nature of Bi-2212 and provided a novel fabrication technique for vdW-based twistronics platforms compatible with air-sensitive vdW materials.

We report the magnetic susceptibility, specific heat, and muon spin relaxation results of the 5d(1) double perovskite Ba2YWO6. The dc magnetic susceptibility shows two distinct Curie-Weiss regimes and a sub-Curie-Weiss increase T-n with n = 0.75(1) for T = 3-100 K, alluding to the presence of random magnetism. The ac magnetic susceptibility reveals a spin freezing at T-f similar to 0.3 K with the activation energy of Delta/k(B) = 27.6 K. The specific heat data exhibit the pseudogap behavior at 25 K and the subsequent power-law dependence with decreasing temperature, indicating the gradual spin freezing with the quenching of orbital fluctuations. However, the muon spin relaxation data display only a weak muon spin depolarization with lacking long-range magnetic ordering down to 26 mK. Taken together, our results suggest that Ba2YWO6 is the proximate realization of a random spin-orbit dimer state.