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Obstructed atomic insulator is recently proposed as an unconventional material, in which electric charge centers localized at sites away from the atoms. A half-filling surface state would emerge at specific interfaces cutting through these charge centers and avoid intersecting any atoms. In this article, we utilized angle-resolved photoemission spectroscopy and density functional theory calculations to study one of the obstructed atomic insulator candidates, NiP$_2$. A floating surface state with large effective mass that is isolated from all bulk states is resolved on the (100) cleavage plane, distinct from previously reported surface states in obstructed atomic insulators that are merged into bulk bands. Density functional theory calculation results elucidate that this floating surface state is originated from the obstructed Wannier charge centers, albeit underwent surface reconstruction that splits the half-filled obstructed surface state. Our findings not only shed lights on the spectroscopy study of obstructed atomic insulators and obstructed surface states, but also provide possible route for development of new catalysts., Comment: 21 pages, 5 figures

Recently, unconventional antiferromagnets that enable the splitting of electronic spins have been theoretically proposed and experimentally realized, where the magnetic sublattices containing moments pointing at different directions are connected by a novel set of symmetries. Such spin splitting (SS) is substantial, $k$-dependent, and independent of the spin-orbit coupling strength, making these magnets promising materials for antiferromagnetic spintronics. Here, combined with angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we perform a systematic study on CrSb, a metallic spin-split antiferromagnet candidate with $T_N$ = 703 K. Our data reveals the electronic structure of CrSb along both out-of-plane and in-plane momentum directions, which renders anisotropic $k$-dependent SS and agrees well with the calculational results. The magnitude of such SS reaches up to at least 0.8 eV at non-high-symmetry momentum points, which is significantly higher than the largest known SOC-induced SS. This compound expands the choice of materials in the field of antiferromagnetic spintronics and is likely to stimulate subsequent investigations of high-efficiency spintronic devices that are functional at room temperature., Comment: 14 pages, 4 figures

Symmetric mass generation (SMG) insulators are interaction-driven, featureless Mott insulating states in quantum many-body fermionic systems. Recent advancements suggest that zeros in the fermion Green's function could lead to non-vanishing negative optical conductivity in SMG insulators, even below the charge excitation gap. This study explores the origin of this unusual behavior through the lens of pole-zero duality, highlighting a critical issue where the current operator becomes unbounded, rendering the response function unphysical. By employing a lattice model, we derive a well-behaved lattice regularization of the current operator, enabling a detailed study of optical conductivity in SMG insulators. Utilizing both analytical and numerical methods, including strong-coupling expansions, we confirm that SMG insulators exhibit no optical conductivity at low energies below the charge gap, effectively resolving the paradox. This work not only deepens our understanding of quantum many-body phenomena but also lays a robust theoretical groundwork for future experimental explorations of SMG materials., Comment: 5 pages, 1 figure

Gauging a finite subgroup of a global symmetry can map conventional phases and phase transitions to unconventional ones. In this work, we study, as a concrete example, an emergent $\mathbb{Z}_2$-gauged system with global symmetry $U(1)$, namely, the $\mathbb{Z}_2$-gauged Bose-Hubbard model both in 1-D and in 2-D. In certain limits, there is an emergent mixed 't Hooft anomaly between the quotient $\tilde{U}(1)$ symmetry and the dual $\hat{\mathbb{Z}}_2$ symmetry. In 1-D, the superfluid phase is mapped to an intrinsically gapless symmetry-protected topological (SPT) phase, as supported by density-matrix renormalization group (DMRG) calculations. In 2-D, the original superfluid-insulator transition becomes a generalized deconfined quantum critical point (DQCP) between a gapless SPT phase, where a SPT order coexists with Goldstone modes, and a $\tilde{U}(1)$-symmetry-enriched topological (SET) phase. We also discuss the stability of these phases and the critical points to small perturbations and their potential experimental realizations. Our work demonstrates that partial gauging is a simple and yet powerful approach in constructing novel phases and quantum criticalities., Comment: v1: 16+$\varepsilon$ pages, 7 figures; v2: published version with one more appendix

Topological superconductors are a class of unconventional superconducting materials featuring sub-gap zero-energy Majorana bound modes that hold promise as a building block for topological quantum computing. In this work, we study the realization of second-order topology that defines anomalous gapless boundary modes in a two-orbital superconductor with spin-orbital couplings. We reveal a time-reversal symmetry-breaking second-order topological superconducting phase with $d+id$-wave orbital-dependent paring without the need for the external magnetic field. Remarkably, this orbital-active $d$-wave paring gives rise to anomalous zero-energy Majorana corner modes, which is in contrast to conventional chiral $d$-wave pairing, accommodating one-dimensional Majorana edge modes. Our work not only reveals a unique mechanism of time-reversal symmetry breaking second-order topological superconductors but also bridges the gap between second-order topology and orbital-dependent pairings., Comment: 5+ pages, 5 figures

The Fermi surface symmetric mass generation (SMG) is an intrinsically interaction-driven mechanism that opens an excitation gap on the Fermi surface without invoking symmetry-breaking or topological order. We explore this phenomenon within a bilayer square lattice model of spin-1/2 fermions, where the system can be tuned from a metallic Fermi liquid phase to a strongly-interacting SMG insulator phase by an inter-layer spin-spin interaction. The SMG insulator preserves all symmetries and has no mean-field interpretation at the single-particle level. It is characterized by zeros in the fermion Green's function, which encapsulate the same Fermi volume in momentum space as the original Fermi surface, a feature mandated by the Luttinger theorem. Utilizing both numerical and field-theoretical methods, we provide compelling evidence for these Green's function zeros across both strong and weak coupling regimes of the SMG phase. Our findings highlight the robustness of the zero Fermi surface, which offers promising avenues for experimental identification of SMG insulators through spectroscopy experiments despite potential spectral broadening from noise or dissipation., Comment: 12 pages, 7 figures. 1 appendix

Spatial, momentum and energy separation of electronic spins in condensed matter systems guides the development of novel devices where spin-polarized current is generated and manipulated. Recent attention on a set of previously overlooked symmetry operations in magnetic materials leads to the emergence of a new type of spin splitting, enabling giant and momentum-dependent spin polarization of energy bands on selected antiferromagnets. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here, we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet MnTe$_2$, the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic (AFM) ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, stems from the intrinsic AFM order instead of spin-orbit coupling (SOC). Our finding demonstrates a new type of quadratic spin texture induced by time-reversal breaking, placing AFM spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials., Comment: Version 3, 49 pages, 4 main figures, 13 extended data figures and 2 extended data tables. Nature in press (2024)

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage, and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line, and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials., Comment: 32 pages, 15 figures

Symmetric mass generation is a novel mechanism to give gapless fermions a mass gap by non-perturbative interactions without generating any fermion bilinear condensation. The previous studies of symmetric mass generation have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this work, we generalize the concept of symmetric mass generation to Fermi liquid with a finite Fermi volume and discuss how to gap out the Fermi surfaces by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of Fermi surface symmetric mass generation in both (1+1)D and (2+1)D Fermi liquid systems when several Fermi surfaces together cancel the Fermi surface anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a non-perturbative interaction mechanism is the only way to gap out the Fermi surfaces. This symmetric Fermi surface reconstruction is in contrast to the conventional symmetry-breaking mechanism to gap the Fermi surfaces. As a side product, our model provides a pristine 1D lattice regularization for the (1+1)D U(1) symmetric chiral fermion model (e.g., the 3-4-5-0 model) by utilizing a lattice translation symmetry as an emergent U(1) symmetry at low energy. This opens up the opportunity for efficient numerical simulations of chiral fermions in their own dimensions without introducing mirror fermions under the domain wall fermion construction., Comment: 16 pages, 6 figures

We report successful growth of millimeter-sized high quality single crystals of V$_3$S$_4$, a candidate topological semimetal belonging to a low-symmetry space group and consisting of only low atomic number elements. Using density functional theory calculations and angle-resolved photoemission spectroscopy, we show that the nonmagnetic phase of monoclinic V$_3$S$_4$ hosts type-II Dirac-like quasiparticles which opens a sizable gap due to spin orbit coupling, as well as theoretical multiple nodal lines that are eliminated also by spin orbit coupling. These results suggest that relativistic effects give rise to profound modifications of the topological properties even in compounds with low-weight elements., Comment: 19 Pages, 3 Figures. To be published in Journal of Alloys and Compounds

Lattice regularization of chiral fermions has been a long-standing problem in physics. In this work, we present the density matrix renormalization group (DMRG) simulation of the 3-4-5-0 model of (1+1)D chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of (2+1)D lattice model of multi-layer Chern insulator, whose finite-width implies the quantum system is effectively (1+1)D. By introducing carefully designed two sets of six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation (SMG) mechanism. We show that the interaction-driven gapping transition is in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. We determine the evolution of Luttinger parameters before the transition, which confirms that the transition happens exactly at the point when the interaction term becomes marginal. As the mirror sector is gapped after the transition, we check that the fermions in the light chiral fermion sector remain gapless, which provides the desired lattice regularization of chiral fermions., Comment: 5 + 3 pages, Symmetric Mass Generation of the chiral fermion model arXiv:1307.7480

An unconventional superconductor is distinguished with two types of gap functions: unitary and non-unitary. This core subject has been concentrated on purely spin-triplet or singlet-triplet mixed superconductors. However, the generalization to a purely spin-singlet superconductor has remained primarily of theoretical interest, which requires at least a multi-orbital correlated electronic systems. In this work, we present a possible establishment of both unitary and non-unitary pairings for spin-singlet superconductors with two atomic orbitals. Then we investigate the effects of atomic spin-orbit coupling and find a new spin-orbit-coupled non-unitary superconductor that supports exotic phenomena. Remarkably, there are mainly three features. Firstly, the atomic spin-orbit coupling locks the electron spins to be out-of-plane, which could give birth to the Type II Ising superconductivity with a large in-plane upper critical field compared to the Pauli limit. Secondly, topological chiral or helical Majorana edge state could be realized even in the absence of external magnetic fields or Zeeman fields. In addition, a spin-polarized superconducting state could even be generated by spin-singlet non-unitary pairings with spontaneous time-reversal breaking, which severs as a smoking gun to detect this exotic state by measuring the spin-resolved density of states. Therefore, our work might pave a new avenue to spin-orbit-coupled superconductors with spin-singlet non-unitary pairing symmetries., Comment: 12 pages, 5 figures

We study superconductivity of electron systems with both spin and pseudospin-1/2 degrees of freedom. By solving linearized gap equations, we derive a weak coupling criterion for the even-parity spin-singlet pseudospin-triplet pairing. It can generally mix with the on-site s-wave pairing since both of them belong to the same symmetry representation ($A_{1g}$) and their mixture could naturally give rise to anisotropic intra-band pairing gap functions with or without nodes. This may directly explain why some of the iron-chalcogenide superconductors are fully gapped (e.g. FeSe thin film) and some have nodes (e.g. LaFePO and LiFeP). We also find that the anisotropy of gap functions can be enhanced when the principal rotation symmetry is spontaneously broken in the normal state such as nematicity, and the energetic stabilization of pseudospin-triplet pairings indicates the coexistence of nematicity and superconductivity. This could be potentially applied to bulk FeSe, where gap anisotropy has been experimentally observed., Comment: published version at Commun. Phys

Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors. When two superconducting gap functions with different symmetries compete, the relative phase channel ($\theta_-\equiv \theta_1-\theta_2$) exhibits an Ising-type $Z_2$ symmetry due to the second order Josephson coupling, where $\theta_{1,2}$ are the phases of two gap functions respectively. In contrast, the $U(1)$ symmetry in the channel of $\theta_+\equiv \frac{\theta_1+\theta_2}{2}$ is intact. The phase locking, i.e., ordering of $\theta_-$, can take place in the phase fluctuation regime before the onset of superconductivity, i.e. when $\theta_+$ is disordered. If $\theta_-$ is pinned at $\pm\frac{\pi}{2}$, then time-reversal symmetry is broken in the normal state, otherwise, if $\theta_-=0$, or, $\pi$, rotational symmetry is broken, leading to a nematic normal state. In both cases, the order parameters possess a 4-fermion structure beyond the scope of mean-field theory, which can be viewed as a high order symmetry breaking. We employ an effective two-component $XY$-model assisted by a renormalization group analysis to address this problem. As a natural by-product, we also find the other interesting intermediate phase corresponds to ordering of $\theta_+$ but with $\theta_-$ disordered. This is the quartetting, or, charge-4e, superconductivity, which occurs above the low temperature $Z_2$-breaking charge-2e superconducting phase. Our results provide useful guidance for studying novel symmetry breaking phases in strongly correlated superconductors., Comment: 7 pages + appendix, 2 figures. References are added