The full $H\text{−}T$ phase diagram in the nematic superconductor FeSe is mapped out using heat-capacity and thermal-expansion measurements down to 0.7 K and up to 30 T for both field directions. A clear thermodynamic signal of an underlying vortex-melting transition is found in both datasets and could be followed down to low temperatures. The existence of significant Gaussian thermal superconducting fluctuations is demonstrated by a scaling analysis, which also yields the mean-field upper critical field $H_{c2}\left(T\right)$. For both field orientations, $H_{c2}\left(T\right)$ shows Pauli-limiting behavior. Whereas the temperature dependence of the vortex-melting line is well described by the model of Houghton et al. [Phys. Rev. B 40, 6763 (1989)] down to the lowest temperatures for H $\perp$ FeSe layers, the vortex-melting line exhibits an unusual behavior for fields parallel to the planes, where the Pauli limitation is much stronger. Here, the vortex-melting anomaly is only observed down to $T^{*}\approx 2–3$ K, and then merges with the $H_{c2}\left(T\right)$ line as predicted by Adachi and Ikeda [Phys. Rev. B 68, 184510 (2003)]. Below $T^{*}$, $H_{c2}\left(T\right)$ also exhibits a slight upturn possibly related to the occurence of a Fulde-Ferrell-Larkin-Ovchinnikov state.

The spin-1/2 Kitaev model offers the exactly solvable example of quantum spin liquids. Possible material realizations of the spin-1/2 Kitaev systems and the prospect of using the Majorana fermion excitations for quantum computations have revolutionized quantum spin liquids research. Recently it has been suggested that higher-spin, especially spin-1, Kitaev exchange interactions can be realized in a variety of materials. Numerical computations on small clusters indicate that the ground state of the spin-1 Kitaev model may also be a quantum spin liquid. On the other hand, the nature of the ground state remains elusive since the spin-1 model is not exactly solvable in contrast to the spin-1/2 model. In this work, using the quantum-entanglement based tensor network approach, we construct an explicit ground-state wave function for the spin-1 Kitaev model, which is written only in terms of physical spin operators. We establish the existence of distinct topological sectors on a torus by constructing the minimally entangled states in the degenerate ground-state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the spin-1 Kitaev model is a gapped quantum spin liquid with $Z_2$ gauge structure and Abelian quasiparticles. We explain the subtle differences between the spin-1/2 and spin-1 Kitaev quantum spin liquids.

Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under development. In this paper, we study a general phenomenon in the space of $(1+1)\text{-dimensional}$ critical phases with fermionic degrees of freedom described by a continuous family of conformal field theories (CFTs), also known as the conformal manifold. Along a one-dimensional locus on the conformal manifold, there can be a transition point, across which the fermionic CFTs on the two sides differ by stacking an invertible fermionic topological order (IFTO), point by point along the locus. At every point on the conformal manifold, the order and disorder operators have power-law two-point functions, but their critical exponents cross over with each other at the transition point, where stacking the IFTO leaves the fermionic CFT unchanged. We call this continuous transition on the fermionic conformal manifold a topological transition. By gauging the fermion parity, the IFTO stacking becomes a Kramers-Wannier duality between the corresponding bosonic CFTs. Both the IFTO stacking and the Kramers-Wannier duality are induced by the electromagnetic duality of the $(2+1)\text{-dimensional}{\mathbb{Z}}_2$ topological order. We provide several examples of topological transitions, including the familiar Luttinger model of spinless fermions (i.e., the $c=1$ massless Dirac fermion with the Thirring interaction) and a class of $c=2$ examples describing $\text{U}\left(1\right)\times \text{SU}\left(2\right)$-protected gapless phases.

The study of topological superconductivity is largely based on the analysis of mean-field Hamiltonians that violate particle number conservation and have only short-range interactions. Although this approach has been very successful, it is not clear that it captures the topological properties of real superconductors, which are described by number-conserving Hamiltonians with long-range interactions. To address this issue, we study topological superconductivity directly in the number-conserving setting. We focus on a diagnostic for topological superconductivity that compares the fermion parity $\mathcal{P}$ of the ground state of a system in a ring geometry and in the presence of zero versus ${\mathrm{\Phi }}_{\text{sc}}=\frac{h}{2e}\equiv \pi$ flux of an external magnetic field. A version of this diagnostic exists in any dimension and provides a ${\mathbb{Z}}_2$-invariant $\nu ={\mathcal{P}}_0{\mathcal{P}}_{\pi }$ for topological superconductivity. In this paper, we prove that the mean-field approximation correctly predicts the value of $\nu$ for a large family of number-conserving models of spinless superconductors. Our result applies directly to the cases of greatest physical interest, including $p$-wave and $p_x+i{p}_y$ superconductors in one and two dimensions, and gives strong evidence for the validity of the mean-field approximation in the study of (at least some aspects of) topological superconductivity.

We study electronic densities of states (DOS) of strongly disordered superconducting thin films of TiN. We find through scanning tunneling microscopy (STM) measurements that the DOS decreases towards the Fermi level in the normal phase obtained by applying magnetic fields. The DOS shows spatial fluctuations whose length scale is related to the energy-dependent decrease in the DOS close to the Fermi level and is similar in normal and superconducting phases. This shows that Coulomb interaction in disordered metals strongly influences the normal DOS and suggests that reduced Coulomb screening leads to spatial variations in the superconducting DOS.

Unconventional superconductivity has been discovered in a variety of doped quantum materials, including topological insulators and semimetals. A unifying property of these systems is strong orbital hybridization, which leads to pairing of states with nontrivial Bloch wave functions. In contrast to naive expectation, however, many of these superconductors are relatively resilient to disorder. Here we study the interplay of superconductivity and disorder in doped three-dimensional Dirac systems, which serve as a paradigmatic dispersion in quantum materials, using Abrikosov-Gor'kov theory. In this way, the role of disorder is captured by a single parameter $\mathrm{\Gamma }$, the pair scattering rate. In contrast to previous studies, we argue that interorbital scattering cannot be neglected due to the strong orbital hybridization in Dirac systems. We find that the robustness of different pairing states highly depends on the relative strength of the different interorbital scattering channels. In particular, we find that the “nematic” superconducting state, which is argued to be the ground state in many ${\mathrm{Bi}}_2{\mathrm{Se}}_3$-related compounds, is not protected from disorder in any way. The pair scattering rate in this case is at best smaller by a factor of 3 compared to systems without spin-orbit coupling. We also find that the odd-parity pairing state with total angular momentum zero (the B phase of superfluid ${}^3\mathrm{He}$) is protected against certain types of disorder, which include a family of time-reversal odd (magnetic) impurities. Namely, this odd-parity state is a singlet of partners under $\mathcal{CT}$ symmetry (rather than $\mathcal{T}$ symmetry in the standard Anderson's theory), where $\mathcal{C}$ and $\mathcal{T}$ are chiral and time-reversal symmetries, respectively. As a result, it is protected against any disorder potential that respects $\mathcal{CT}$ symmetry. Our procedure is very general and can be readily applied to different band structures and disorder configurations.

We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely, Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive crucial information about those models of fundamental importance in both classical and quantum physics, and to completely characterize their algebraic structure. Notably, we prove that the spectral gap can be obtained in polynomial computational time, which has strong implications in the context of adiabatic quantum computing with quantum spin chains. This quantity also characterizes the rate to stationarity of some important classical random processes such as interchange and exclusion processes. Reciprocally, we use results derived from the celebrated Bethe ansatz to obtain mathematical results about these graphs in the unweighted case. We also discuss extensions of this unifying framework to other systems, such as asymmetric exclusion processes—a paradigmatic model in nonequilibrium physics—or the more exotic non-Hermitian quantum systems.

The Drude model describes the free-electron conduction in simple metals, governed by the freedom that the mobile electrons have within the material. In strongly correlated systems, however, a significant deviation of the optical conductivity from the simple metallic Drude behavior is observed. Here, we investigate the optical conductivity of the heavy-fermion system $\mathrm{Ce}{\mathrm{Cu}}_{6-x}{\mathrm{Au}}_x$, using time-resolved, phase-sensitive terahertz spectroscopy. The terahertz electric field creates two types of excitations in heavy-fermion materials: First, the intraband excitations that leave the heavy quasiparticles intact. Second, the resonant interband transitions between the heavy and light parts of the hybridized conduction band that break the Kondo singlet. We find that the Kondo-singlet-breaking interband transitions do not create a Drude peak, while the Kondo-retaining intraband excitations yield the expected Drude response. This makes it possible to separate these two fundamentally different correlated contributions to the optical conductivity.

The existence of three generations of neutrinos (charged leptons/quarks) and their mass mixing are deep mysteries of our universe. It might indicate a profound internal structure of all elementary particles. It is well known that the history of neutrino physics can be traced back to Majorana's elegant work on a real solution of the Dirac equation—known as the Majorana fermion. Recently, Majorana's spirit returns in modern condensed matter physics—in the context of topological Majorana zero modes in certain classes of topological superconductors (TSCs). In this paper, we attempt to investigate the topological nature of the neutrino by assuming that a relativistic Majorana fermion can be divided into four topological Majorana zero modes at cutoff energy scale, e.g., planck scale. We begin with an exactly solvable $1\mathrm{D}$ lattice model which realizes a $T^2=-1$ time reversal symmetry protected TSC, and show that a pair of topological Majorana zero modes can realize a $T^4=-1$ time reversal symmetry. Moreover, we find that a pair of topological Majorana zero modes can also realize a $P^4=-1$ parity symmetry and even a nontrivial ${\overline{C}}^4=-1$ charge conjugation symmetry. Next, we argue that the origin of three generations of neutrinos (charged leptons and quarks) can be naturally explained as three distinguishable ways of forming a pair of complex fermions (with opposite spin polarizations) out of four topological Majorana zero modes, characterized by the $T^4=-1$, ${\left(TP\right)}^4=-1$, and ${\left(T\overline{C}\right)}^4=-1$ fractionalized symmetries that each complex fermion carries at cutoff energy scale. Finally, we use a semiclassical approach to compute the neutrino mass mixing matrix at leading order(LO), e.g., in the absence of $CP$ violation correction. We obtain ${\theta }_{12}=31.7^{\circ },{\theta }_{23}={45}^{\circ }$, and ${\theta }_{13}=0^{\circ }$, which is consistent with an $A_5$ flavor symmetry pattern (the golden ratio pattern). We further predict an exact mass ratio of the three mass eigenstates of neutrinos with $m_1/m_3=m_2/m_3=3/\sqrt{5}$ and an effective mass of neutrinoless double beta decay $m_{0\nu \beta \beta }=m_1/\sqrt{5}$.

Due to the exciton effects, two-dimensional materials have displayed strong light-matter interactions. Here, by considering many-body effects of electron-electron and electron-hole interactions, we provide a more accurate quasiparticle electronic structure, exciton, and optical absorption spectrum of Hittorf's phosphorene, a monolayer of Hittorf's (or violet) phosphorus obtained recently via exfoliation method. The fibrous nature of the crystal structure with twofold rotation symmetry leads to anisotropic electron-hole excitations, and an obvious dichroism in optical absorption is revealed over a wide spectral range. The first exciton state located at 2.4 eV is bright with a large binding energy of 0.9 eV and a lifetime of 18 ns. These unusual excitonic and optical properties demonstrate its potential applications in optoelectronics.

Quantum many-body scars have attracted much interest as a violation of the eigenstate thermalization hypothesis (ETH) due to recent experimental observation in Rydberg atoms and related theoretical studies. In this paper, we construct a model hosting exact Floquet quantum many-body scars, which violate the Floquet version of ETH. We consider two uniformly driven static Hamiltonians prohibiting neighboring up spins (Rydberg blockade) like the PXP model, and construct a binary drive composed of them. We show that there exists a four-dimensional subspace which completely avoids thermalization to infinite temperature and that any other states, including some special scar states reported in the static PXP model, are vulnerable to heating and relax to infinite temperature. We also construct a more generalized periodic drive composed of time-dependent PXP-type Hamiltonians showing exact Floquet quantum many-body scars and discuss possible experimental realization of the model in Rydberg atoms.

Recent theoretical studies have found quantum spin-liquid states with spinon Fermi surfaces upon the application of a magnetic field on a gapped state with topological order. We investigate the thermal Hall conductivity across this transition, describing how the quantized thermal Hall conductivity of the gapped state changes to an unquantized thermal Hall conductivity in the gapless spinon Fermi surface state. We consider two cases, both of potential experimental interest: the state with non-Abelian Ising topological order on the honeycomb lattice and the state with Abelian chiral spin-liquid topological order on the triangular lattice.

Thermalization of random-field Heisenberg spin chain is probed by time evolution of density correlation functions. Studying the impacts of average energies of initial product states on dynamics of the system, we provide arguments in favor of the existence of a mobility edge in the large system-size limit.

The proximity-induced moment (PIM) in heavy metal layers may play a significant role in heterostructured spintronic systems. In particular, the PIM of a heavy metal adjacent to a magnetic layer has been linked to interfacial spin transport behavior. Element-resolved x-ray magnetic measurements were used to investigate PIM in Pt layered with two different rare-earth (RE):$3d$ transition-metal (TM) ferrimagnetic alloys in which the net moment was dominated by either the RE or the TM at room temperature. We observed significant PIM in Pt confined to a 2-nm interfacial region for Pt/${\mathrm{Co}}_{77}{\mathrm{Gd}}_{23}$ and $\mathrm{Pt}/{\left({\mathrm{Fe}}_{50}{\mathrm{Co}}_{50}\right)}_{77}{\mathrm{Gd}}_{23}$ and, in both cases, the PIM was parallel to the TM sublattice rather than the RE or the net moment. Our results highlight the prominence of the $d-d$ mediated interactions between the Pt and the constituents of the ferrimagnetic RE:TM alloys over the net macroscopic moment.

We study quantum dynamics of a dark soliton in a one-dimensional Bose gas in an optical lattice within the truncated Wigner approximation. Previous work has revealed that in the absence of quantum fluctuations, dynamical stability of the dark soliton significantly depends on whether its phase kink is located at a lattice site or a link of two neighboring sites. It has also shown that the dark soliton is unstable in a regime of strong quantum fluctuations regardless of the phase-kink position. To bridge the gap between the classical and strongly quantum regimes, we investigate the dynamical stability of the dark soliton in a regime of weak quantum fluctuations. We find that the position dependence of the dynamical stability gradually diminishes and eventually vanishes as the strength of quantum fluctuations increases. This classical-to-quantum crossover of the soliton stability remains even in the presence of a parabolic trapping potential. We suggest that the crossover behavior can be used for experimentally diagnosing whether the instability of a dark soliton is due to quantum fluctuations or classical dynamical instability.

We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene. The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that minimally twisted bilayer graphene realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps. We identify the FTIs by analyzing the nontrivial spectral flow in the Hofstadter butterfly, and by explicitly computing the chiral edge states. Our theory paves the way for an effective practical realization of FTIs in equilibrium solid-state systems.

A central question on Kitaev materials is the effects of additional couplings on the Kitaev model, which is proposed to be a candidate for realizing topological quantum computations. However, two spatial dimensions typically suffer the difficulty of lacking controllable approaches. In this work, using a combination of powerful analytical and numerical methods available in one dimension, we perform a comprehensive study on the phase diagram of a one-dimensional version of the spin-1/2 Kitaev-Heisenberg-Gamma model in its full parameter space. A strikingly rich phase diagram is found with nine distinct phases, including four Luttinger liquid phases, a ferromagnetic phase, a Néel ordered phase, an ordered phase of distorted-spiral spin alignments, and two ordered phases, which both break a $D_3$ symmetry albeit in different ways, where $D_3$ is the dihedral group of order six. Our work paves the way for studying one-dimensional Kitaev materials and may provide hints to the physics in higher-dimensional situations.

In flat-band systems, destructive interference leads to the localization of noninteracting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighboring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum $l=1$ states of a diamond-chain lattice, wherein an effective $\pi$ flux may yield a completely flat single-particle energy landscape. In the weakly interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

We present a joint theoretical and experimental study of the oxygen $K$-edge spectra for $\mathrm{La}\mathrm{Fe}{\mathrm{O}}_3$ and homovalent Ni-substituted $\mathrm{La}\mathrm{Fe}{\mathrm{O}}_3$ ($\mathrm{La}{\mathrm{Fe}}_{0.75}{\mathrm{Ni}}_{0.25}{\mathrm{O}}_3$), using first-principles simulations based on density-functional theory with extended Hubbard functionals and x-ray absorption near edge structure (XANES) measurements. Ground-state and excited-state XANES calculations employ Hubbard onsite $U$ and intersite $V$ parameters determined from first principles and the Lanczos recursive method to obtain absorption cross sections, which allows for a reliable description of XANES spectra in transition-metal compounds in a very broad energy range, with an accuracy comparable to that of hybrid functionals but at a substantially lower cost. We show that standard gradient-corrected exchange-correlation functionals fail in capturing accurately the electronic properties of both materials. In particular, for $\mathrm{La}{\mathrm{Fe}}_{0.75}{\mathrm{Ni}}_{0.25}{\mathrm{O}}_3$ they do not reproduce its semiconducting behavior and provide a poor description of the pre-edge features at the O $K$ edge. The inclusion of Hubbard interactions leads to a drastic improvement, accounting for the semiconducting ground state of $\mathrm{La}{\mathrm{Fe}}_{0.75}{\mathrm{Ni}}_{0.25}{\mathrm{O}}_3$ and for good agreement between calculated and measured XANES spectra. We show that the partial substitution of Ni for Fe affects the conduction-band bottom by generating a strongly hybridized $\mathrm{O}\left(2p\right)\text{−}\mathrm{Ni}\left(3d\right)$ minority-spin empty electronic state. The present work, based on a consistent correction of self-interaction errors, outlines the crucial role of extended Hubbard functionals to describe the electronic structure of complex transition-metal oxides such as $\mathrm{La}\mathrm{Fe}{\mathrm{O}}_3$ and $\mathrm{La}{\mathrm{Fe}}_{0.75}{\mathrm{Ni}}_{0.25}{\mathrm{O}}_3$ and paves the way to future studies on similar systems.

Semiconductor Rashba nanowires are quasi-one-dimensional systems that have large spin-orbit (SO) coupling arising from a broken inversion symmetry due to an external electric field. There exist parametrized multiband models that can describe accurately this effect. However, simplified single band models are highly desirable to study geometries of recent experimental interest, since they may allow to incorporate the effects of the low dimensionality and the nanowire electrostatic environment at a reduced computational cost. Commonly used conduction band approximations, valid for bulk materials, greatly underestimate the SO coupling in zinc-blende crystal structures and overestimate it for wurtzite ones when applied to finite cross-section wires, where confinement effects turn out to play an important role. We demonstrate here that an effective equation for the linear Rashba SO coupling of the semiconductor conduction band can reproduce the behavior of more sophisticated eight-band $\mathrm{k}·\mathrm{p}$ model calculations. This is achieved by adjusting a single effective parameter that depends on the nanowire crystal structure and its chemical composition. We further compare our results to the Rashba coupling extracted from magnetoconductance measurements in several experiments on InAs and InSb nanowires, finding excellent agreement. This approach may be relevant in systems where Rashba coupling is known to play a major role, such as in spintronic devices or Majorana nanowires.