Measurements of the Hall coefficients in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, ranging from the undoped ($x=p=0$) Mott insulator to overdoped compounds, exhibit a temperature dependence that offers insights into these compounds' electronic structure. We interpret these results using a model based on the theory of phase-separation dynamics, which begins at half-filled ($n=1$) and at a temperature $T_{\mathrm{PS}}\left(p\right)$, near the pseudogap temperature $T^{*}\left(p\right)$. The $n=1$ holes have low mobility and provide the modulations of the charge density waves (CDW). As doping increases from $p=0$, these modulations guide the additional $p$ holes to occupy alternating CDW domains. This charge inhomogeneity may facilitate the formation of localized superconducting amplitudes below the critical onset temperature $T_{\mathrm{c}}^{\max }\left(p\right)$. Using thermal activation expressions, along with quantum tunneling between the charge domains, we successfully reproduce all Hall coefficient measurements $R_{\mathrm{H}}(p,T)$ and highlight the relevant energies of the cuprates. The calculations confirm three significant electronic features: the phase-separating role of the pseudogap temperature, the superconducting state achieved through phase coherence, and the two types of charge carriers whose energies and mobilities become comparable at $p\approx 0.19$, where $T^{*}\left(p\right)\approx T_{\mathrm{c}}^{\max }\left(p\right)$. This results in a crossover from $n=p$ to $n=1+p$. These findings, along with the $R_{\mathrm{H}}(p,T)$ calculations from insulating to overdoped compounds, underscore the critical role of the electronic phase separation in the properties of cuprates.

Two matrix product states (MPS) are in the same phase in the presence of symmetries if they can be transformed into one another via symmetric short-depth circuits. We consider how symmetry-preserving measurements with feedforward alter the phase classification of MPS in the presence of global on-site symmetries. We demonstrate that, for all finite Abelian symmetries, any two symmetric MPS belong to the same phase. We give an explicit protocol that achieves a transformation between any two phases and that uses only a depth-two symmetric circuit, a single round of symmetric measurements, and a constant number of auxiliary systems per site. In the case of non-Abelian symmetries, symmetry protection prevents one from deterministically transforming symmetry-protected topological (SPT) states to product states directly via measurements, thereby complicating the analysis. Nonetheless, we provide protocols that allow for asymptotically deterministic transformations between the trivial phase, SPT phases, and GHZ phases of some non-Abelian nilpotent groups.

We investigated the electronic properties of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ by scanning tunneling microscopy and spectroscopy at low temperature. We obtained high-resolution quasiparticle interference data of the topological surface Dirac electrons at different energies. Spin-selective joint density of states calculations were performed for surface and bulk electronic states to interpret the observed quasiparticle interference data. The topological properties of our crystals are demonstrated by the absence of backscattering along with the linear energy dispersion of the dominant scattering vector. In addition, we detect nondispersive scattering modes which we associate with bulk-surface scattering and, thus, allow an approximate identification of the bulk energy gap range based on our quasiparticle interference data. Measurements of differential conductance maps in magnetic fields up to 15 T have been carried out, but no strong modifications could be observed.

We investigate the interplay between self-duality and spatially modulated symmetry of generalized $N$-state clock models, which include the transverse-field Ising model and ordinary $N$-state clock models as special cases. The spatially modulated symmetry of the model becomes trivial when the model's parameters satisfy a specific number-theoretic relation. We find that the duality is noninvertible when the spatially modulated symmetry remains nontrivial, and we show that this noninvertibility is resolved by introducing a generalized ${\mathbb{Z}}_N$ toric code, which manifests ultraviolet/infrared mixing, as the bulk topological order. In this framework, the boundary duality transformation corresponds to the boundary action of a bulk symmetry transformation, with the end point of the bulk symmetry defect realizing the boundary duality defect. Our results illuminate not only a holographic perspective on dualities but also a relationship between spatially modulated symmetry and ultraviolet/infrared mixing in one higher dimension.

The electron spin decay lifetime in materials can be characterized by relaxation ($T_1$) and irreversible ($T_2$) and reversible ($T_2^{*}$) decoherence processes. Their interplay leads to a complex dependence of spin lifetimes on the direction and magnitude of magnetic fields, which is relevant for spintronics and quantum information applications. Here, we use real-time first-principles density matrix dynamics simulations to directly simulate Hahn echo measurements, disentangle dephasing from decoherence, and predict $T_1$, $T_2$, and $T_2^{*}$ spin lifetimes. We show that $g$-factor fluctuations lead to nontrivial magnetic field dependence of each of these lifetimes in inversion-symmetric crystals of ${\mathrm{CsPbBr}}_3$ and silicon, even when only intrinsic spin-phonon scattering is present. Most importantly, fluctuations in the off-diagonal components of the $g$ tensor lead to a strong magnetic-field dependence of even the $T_1$ lifetime in silicon. Our calculations elucidate the detailed role of anisotropic $g$ factors in determining the spin dynamics even in simple, low spin-orbit coupling materials such as silicon.

Magnetic skyrmion crystals with zero net skyrmion charge and zero topological Hall response are interesting candidate phases which can occur at a vanishing magnetic field in centrosymmetric systems. We study a minimal bilayer model of skyrmion crystals having opposite chirality and topological charge in the two layers, and show that it can host nearly flat electronic bands with quasiuniform Berry curvature and quantum metric. Using Hartree-Fock theory, we show that weak to moderate short-range electron interactions induce two distinct types of symmetry breaking patterns depending on the band dispersion: An intra-unit-cell charge density modulation from Chern band mixing or a layer-imbalanced phase with a nonzero ferroelectric polarization. Both phases break inversion symmetry leading to a spontaneous and large net topological Hall effect, with the phase diagram tunable by external electric fields. Our results may be relevant to centrosymmetric skyrmion materials such as ${\mathrm{Gd}}_2{\mathrm{PdSi}}_3$ and ${\mathrm{Gd}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ as well as artificially engineered heterostructures. We also discuss its relation to recent work on twisted transition metal dichalcogenide bilayers.

Linear photogalvanic effect (LPGE), a second-order nonlinear optical effect under the irradiation by linearly polarized light, stems usually from shift current due to the contribution of Berry curvature. For tilted Nodal-line semimetals, the LPGE from the shift current is excluded by $PT$ symmetry. Interestingly, it is found that the remarkable LPGE arises from the injection current, which is instead induced by quantum metric, a real part of quantum geometry. By employing the combining Keldysh-Floquet method, we derive a formula to calculate the quantum metric induced LPGE. The dependence of the photogalvanic response is discussed in detail on dispersion tilt, chemical potential, and nodal-line radius. The linear photogalvanic conductivity exhibits rich characteristic frequencies, which are closely related to the Fermi surface geometry, determined by the relative size of the tilt and the chemical potential. These features may serve as a diagnostic tool to characterize the systemic parameters. We also check that the quantum metric induced LPGE has no the fingerprint of the parity anomaly, different from the Berry curvature induced nonlinear responses or linear response.

We investigate theoretically the charge and valley current in a circular graphene quantum dot (GQD) illuminated by a linearly polarized light. The two leads connected to the GQD have an angle $\gamma$. The device in the noncolinear situation ($\gamma \ne 0$) lacks inversion symmetry, allowing a finite zero-bias photocurrent $\overline{I}$. We find that as $\gamma$ changes from $0^{\circ }$ to ${90}^{\circ }$, the maximum amplitude of the photocurrent $|\overline{I}|$ changes nomonotonously and depends on the boundary type. The valley current ${\overline{I}}^V$, calculated from the Floquet scattering theory, exhibits a weak dependence on $\gamma$ and is much larger than the photocurrent $|\overline{I}|$. A crude energy-valley locking in zigzag-edged graphene nanoribbons is vital for ${\overline{I}}^V$. The photocurrent $\overline{I}$ can be greatly tuned by the light intensity, photon energy, and polarization direction and varies nomonotonically with the device size. The valley current ${\overline{I}}^V$ shows a minor change with the light parameters and a remarkable increase with the device size. These findings could be helpful for the generation and optimization of photocurrents and valley currents in graphene-based devices.

We present a theory of a two-qubit gate with macroscopic singlet-triplet (ST) qubits in synthetic spin-one chains in InAsP quantum dot nanowires. The macroscopic topologically protected singlet-triplet qubits are built with two spin-half Haldane quasiparticles. The Haldane quasiparticles are hosted by a synthetic spin-one chain realized in chains of InAsP quantum dots embedded in an InP nanowire, with four electrons each. The quantum dot nanowire is described by a Hubbard-Kanamori (HK) Hamiltonian derived from an interacting atomistic model. Using exact diagonalization and matrix product states tools, we demonstrate that the low-energy behavior of the HK Hamiltonian is effectively captured by an antiferromagnetic spin-one chain Hamiltonian. Next, we consider two macroscopic qubits and present a method for creating a tunable coupling between the two macroscopic qubits by inserting an intermediate control dot between the two chains. Finally, we propose and demonstrate two approaches for generating highly accurate two-ST qubit gates: (1) by controlling the length of each qubit and (2) by employing different background magnetic fields for the two qubits.

Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively underexplored. Our work gives two definitions for replica topological order in mixed states, which involve $n$ copies of density matrices of the mixed state. Our framework categorizes topological orders in mixed states as either quantum, classical, or trivial, depending on the type of information that can be encoded. For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology. Using this formalism, we enumerate all the possible mixed state phases which result from applying a local decoherence channel to the toric code. In addition to the classical-topological phases that have been previously reported on, we also find mixed states exhibiting chiral topological order. We discuss the extent that our findings can be extrapolated to $n\to 1$ limit.

Extreme broadening previously observed in certain N x-ray fluorescence lines excited near the N K edge in nitrates has been observed in the S L x-ray fluorescence in sodium sulfate, ${\mathrm{Na}}_2{\mathrm{SO}}_4$. It is explained as a large imaginary self-energy corresponding to an anomalously short lifetime of quasiparticles in one of the valence bands of these compounds. Our latest measurement and the corresponding many-body theory indicate that this is a general effect not specific to nitrates.

The antiferromagnetic quantum Hall insulator (AFQHI), where one of the spin components is in the quantum Hall state and the other in the trivial state, is an established phase emerging as a result of the Hubbard repulsion in spinful quantum Hall systems. The stabilization of the AFQHI requires a charge order preventing the effect of the spin-flip transformation on the electronic state to be compensated by a space-group operation and is often induced via an ionic potential. While one would naively expect the nearest-neighbor (NN) density-density interaction favoring spontaneous charge order to result in qualitatively similar phenomena, an analysis of the Haldane-Hubbard model extended by the NN interaction finds no AFQHI. Here, by considering an extended version of the Harper-Hofstadter-Hubbard model, we go beyond the honeycomb structure and suggest that the realization of the AFQHI generically requires an explicit charge order and cannot be emerged through spontaneous charge order. We unveil how the AFQHI disappears upon approaching from the explicit to the spontaneous charge ordering limit. Our findings shine more light on the stabilization conditions of the AFQHI which can guide the future optical lattice experiments searching for this intriguing magnetic topological insulator phase.

We investigate localization and topological properties of a non-Hermitian generalization of the Aubry-André-Harper (AAH) model, which is the dimension reduction of the two-dimensional non-Hermitian quantum Hall model. Non-Hermiticity arises from the nonreciprocal hopping and the complex global phase. In the absence of nonreciprocal hopping, by applying Avila's global theory we analytically compute the localization length of states and determine phase diagrams. The complex global phase is in favor of the critical phase, whose transition to the localized phase falls outside the universality class of the classic AAH model. By mapping to the Hall model, we further demonstrate that the loop structure in spectrum originates from the spectral topology in the reduced dimension. When the nonreciprocal hopping is added, the localization is analytically studied by employing a similarity transformation, and phase diagrams are determined exactly. The system has boundary-dependent spectra and states because of the nontrivial spectral topology in the remaining physical dimension. The critical phase no longer exists, and the nonreciprocal hopping favors the extended phase when under the periodic boundary condition. Loops always exist in the complex spectrum but have distinct topological origins in different phases.

The ghost-Gutzwiller variational wave function within the Gutzwiller approximation is shown to stabilize a genuine paramagnetic Mott insulator in the half-filled single-band Hubbard model. This phase hosts quasiparticles that are crucial to the paramagnetic response without showing up in the single-particle spectrum, and, as such, they can be legitimately regarded as an example of Anderson's spinons. We demonstrate that these spinons at the interface with a metal reacquire charge by proximity effect and thus reemerge in the spectrum as a heavy-fermion band.

By performing density functional theory plus dynamical mean-field theory calculations, we systematically investigate the correlated electronic structure in the newly discovered monolayer-trilayer (ML-TL) phase of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ (1313-La327). Our calculated Fermi surfaces are in good agreement with the result of angle-resolved photoemission spectroscopy. We find that 1313-La327 is a multiorbital correlated metal. An orbital-selective Mott behavior is found in ML in our zero- and finite-temperature calculations. The ML Ni $3d_{z^2}$ orbital exhibits a Mott behavior, while the ML Ni $3d_{x^2-y^2}$ orbital is metallic due to self-doping. We also find a large static local spin susceptibility of ML Ni, suggesting that there is large spin fluctuation in 1313-La327. The TL Ni-$e_g$ orbitals possess electronic correlations similar to those in ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. The $e_g$ orbitals of the outer-layer Ni in TL show non-Fermi liquid behaviors. Besides, large weights of high-spin states are found in TL-outer Ni and ML Ni, implying Hundness. Under 16 GPa, a Lifshitz transition is revealed by our calculations and a La-related band crosses the Fermi level. Our work provides a theoretical reference for studying other potential mixed-stacked nickelate superconductors.

The anomalous Hall effect (AHE) generated by the extrinsic mechanism has attracted growing attention recently due to the potential to achieve colossal Hall response. Here, we report the magnetic and electrical transport properties of the hexagonal ferromagnet $\mathrm{PrCrG}{\mathrm{e}}_3$ single crystal. $\mathrm{PrCrG}{\mathrm{e}}_3$ undergoes the ferromagnetic transition at $T_{\mathrm{C}}\sim 80$ K with the Pr and Cr moments lying in the $ab$ plane. The spin reorientation transition happens at $T_{\mathrm{SR}}\sim 11$ K, with the direction of Cr moments shifting from the $ab$ plane to the $c$ axis. The relationship between longitudinal resistivity and temperature has a linear behavior in $20-80$ K due to strong phonon scattering. Large positive and unsaturated linear magnetoresistance is observed at low temperature, which is attributed to Lorentz force derived by applied field hindering the movement of the carriers. Hall results reveal that the majority carriers change from electrons to holes around $T_{\mathrm{C}}$, which may be ascribed to temperature-induced Lifshitz transition. Moreover, large AHE is obtained in $\mathrm{PrCrG}{\mathrm{e}}_3$, and scaling relation analysis proves that skew-scattering mechanism is predominant. Meanwhile, electron-phonon scattering plays a crucial role in the skew-scattering mechanism and becomes dominant above 20 K. Our results suggest $\mathrm{PrCrG}{\mathrm{e}}_3$ to be an excellent platform to study the extrinsic AHE mechanism.

Nonequilibrium states produced by electric and thermal voltages $(V,V_T)$ provide a straightforward insight into the underlying degrees of freedom of composite nanostructures, and they are of particular interest to probe Majorana bound states. Here we explore fluctuations of thermoelectric currents at finite frequencies $\omega$ in a quantum dot coupled to two interfering Majorana bound states. At small $V$ we find that in the emission spectra, the differential thermoelectric quantum noise $\partial S^{>}/\partial V_T$ shows an antiresonance, whereas in the absorption spectra Majorana interference induces an antiresonance-resonance pair. At large $V$ this pair is preserved, whereas the emission antiresonance turns into an antiresonance-resonance pair identical to the absorption one making $\partial S^{>}/\partial V_T$ antisymmetric in the frequency $\omega$. This antisymmetry distinguishes Majorana behavior from the one induced by Andreev bound states and does not break at higher temperatures, making it attractive for experiments on Majorana interference via thermoelectric fluctuation response.

Non-Hermiticity has greatly broadened the scope of research on topological materials, especially on topological metamaterial because of the flexibility in the introduction of designed loss/gain or active control wherein. This creates a new frontier—the non-Hermitian topological metamaterials. In this work, we report the realization of non-Hermitian Möbius insulators for acoustic waves by incorporating the designed loss into acoustic crystals. Associated with the Möbius insulators, features like wave localization, Möbius twist in momentum space with $4\pi$ periodicity, and projective translation eigenvalues in phase space, are demonstrated. More specifically, the skin effect of Möbius edge states is identified. We also extend our study to the three-dimensional case, and the Möbius hinge states and the associated skin effect are observed. With designed loss to achieve Möbius insulators and reveal the skin effect of Möbius edge states, our work provides an avenue toward the study of non-Hermitian topological physics.