在外加磁场中，双层化合物Sr $_3$ Ru $_2$ O $_7$的超纯晶体在低于临界温度$T^*$时经历变磁转变，该温度作为磁场$H$和Ru-O平面之间的角度的函数而变化。此外，当$H$垂直于平面时，$T^*$接近于零。然而，这一假定的“变磁量子临界点”被{ \it ab}平面中具有一阶电阻各向异性的超导流体相抢占。在具有中等强度局部库仑相互作用的“现实”双层模型中，准一维能带的范霍夫奇点附近的电子态密度存在急剧的发散，并且多个轨道的存在所允许的自旋-轨道耦合导致了平均场相图，该相图解释了许多这些实验观察到的现象。虽然自旋-轨道耦合不是太强，但它破坏了接近完美的费米面嵌套，从而抑制了自旋密度波（SDW）有序。
英文摘要：
In an externally applied magnetic field, ultra-pure crystals of the bilayer compound Sr$_3$Ru$_2$O$_7$ undergo a metamagnetic transition below a critical temperature, $T^*$, which varies as a function of the angle between the magnetic field $H$ and the Ru-O planes. Moreover, $T^*$ approaches zero when $H$ is perpendicular to the planes. This putative "metamagnetic quantum critical point", however, is preempted by a nematic fluid phase with order one resistive anisotropy in the {\it ab} plane. In a "realistic" bilayer model with moderate strength local Coulomb interactions, the existence of a sharp divergence of the electronic density of states near a van Hove singularity of the quasi-one-dimensional bands, and the spin-orbit couplings permitted by the presence of multiple orbitals result in a mean-field phase diagram which accounts for many of these experimentally observed phenomena. Although the spin-orbit coupling is not overly strong, it destroys the otherwise near perfect Fermi surface nesting and hence suppresses spin-density-wave (SDW) ordering.
We analyse various microscopic properties of the nematic fractional quantum Hall effect (FQHN) in the thermodynamic limit, and present necessary conditions required of the microscopic Hamiltonians for the nematic FQHE to be robust. Analytical expressions for the degenerate ground state manifold, ground state energies, and gapless nematic modes are given in compact forms with the input interaction and the corresponding ground state structure factors. We relate the long wavelength limit of the neutral excitations to the guiding center metric deformation, and show explicitly the family of trial w…
At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family…
Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-$T_c$ superconductors. Here, we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below $T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature $T^{\ast}$. Our result provides a microscopic evidence for int…
Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Carl Zeiss SMT GmbH（卡尔蔡司SMT有限公司）；Ariel University（阿里埃勒大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy (ARPES) with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe$_2$As$_2$ without interference from either twinning or magnetic order. We find that the nematic order parameter exhi…
Unveiling a nematic quantum critical point in multi-orbital systems
电子向列性，提出存在于一些过渡金属材料，可以有不同的微观起源。特别是，在Sr 3Ru 2 O 7中观察到的各向异性电阻率和元磁跳变与早先的提议一致，即各向同性-磁跳变一般是一阶的，并且当由磁场调谐时伴随着元磁。然而，其他引人注目的实验特征，如非费米液体电阻率和临界热力学行为意味着存在一个身份不明的量子临界点（QCP）。在这里，我们表明，轨道的自由度发挥了至关重要的作用，揭示了一个超临界QCP，即使它是蒙上阴影附近的亚临界转变在低温下。我们进一步提出了一个有限的温度相图，包括熵景观和讨论我们的研究结果中观察到的现象Sr 3Ru 2 O 7。
We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interaction. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It …
In this paper, we study theoretically the behaviors of the magnetic excitations(MEs) in the normal and nematic phases of iron pnictides. The normal state MEs exhibit commensurability to diamond and to square-like structure transition with the increase of energy. This structure transition persists in the spin and orbital scenarios of nematic phases, although the MEs show anisotropic behaviors due to the C4 symmetry breaking induced by the nematic orders. The MEs exhibit distinct energy evolution behaviors between the spin and orbital scenarios of nematicity. For the spinnematic scenario, the an…
We analyze theoretically the magnetic anisotropy in the nematic phase of FeSe by computing the spin and the orbital susceptibilities from the microscopic multiorbital model. In particular, we take into account both the $xz/yz$ and the recently proposed non-local $xy$ nematic ordering and show that the latter one could play a crucial role in reproducing the experimentally-measured temperature dependence of the magnetic anisotropy. This provides a direct fingerprint of the different nematic scenarios on the magnetic properties of FeSe.
We compute the resistivity anisotropy in the nematic phase of FeSe from the static solution of the multiorbital Boltzmann equation. By introducing disorder at the level of the microscopic multiorbital model we show that even elastic scattering by localized impurities may lead to non-trivial anisotropic renormalization of the electronic velocities, challenging the usual understanding of transport based only on cold- and hot-spots effects. Our model takes into account both the $xz/yz$ and the recently proposed $xy$ nematic ordering. We show that the latter one has a crucial role in order to repr…
Ultrafast techniques have emerged as promising methods to study and control quantum materials. To maintain the quantum nature of the systems under study, excess heating must be avoided. In this work, we demonstrate a method that employs the nonequilibrium laser excitation of planar stretching optical phonons in tetragonal systems to quench an electronic nematic state across a quantum phase transition. Appropriately tuned off-resonant pulses can perform a quantum quench of the system either into the nematic phase (red detuning) or out of it (blue detuning). The nonlinear coupling of this phonon…
我们发展了一个微观理论的电子相变接近各向同性费米液体在二维和三维。得到了有序状态下小振幅集体激发的显式表达式;值得注意的是，除了沿对称性所决定的特殊方向外，Goldstone模式（directorwave）是过阻尼的。在量子临界点，我们发现一个动力学指数的$z=3$，这意味着稳定的高斯不动点。过阻尼Goldstone模的主导微扰效应导致费米液体理论在α相的崩溃和费米表面周围强烈的角度依赖的电子自能。其它金属液晶相，{ \it} e. g.}一个量子六角体，表现类似。
We present $^{77}$Se-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\rm s}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperat…
Graphene-based moiré systems have attracted considerable interest in recent years as they display a remarkable variety of correlated phenomena. Besides insulating and superconducting phases in the vicinity of integer fillings of the moiré unit cell, there is growing evidence for electronic nematic order both in twisted bilayer graphene and twisted double-bilayer graphene (tDBG), as signaled by the spontaneous breaking of the threefold rotational symmetry of the moiré superlattices. Here, we combine symmetry-based analysis with a microscopic continuum model to investigate the structure of the n…
We study the interaction effect in a three dimensional Dirac semimetal and find that two competing orders, charge-density-wave orders and nematic orders, can be induced to gap the Dirac points. Applying a magnetic field can further induce an instability towards forming these ordered phases. The charge density wave phase is similar as that of a Weyl semimetal while the nematic phase is unique for Dirac semimetals. Gapless zero modes are found in the vortex core formed by nematic order parameters, indicating the topological nature of nematic phases. The nematic phase can be observed experimental…
Half-filled Landau levels form a zoo of strongly correlated phases. These include non-Fermi liquids (NFL), fractional quantum Hall (FQH) states, nematic phases, and FQH nematic phases. This diversity poses the question: what keeps the balance between the seemingly unrelated phases? The answer is elusive because the Halperin-Lee-Read (HLR) description that offers a natural departure point is inherent strongly coupled. But the observed nematic phases suggest nematic fluctuations play an important role. To study this possibility, we apply a recently formulated controlled double expansion approach…
Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive …
Motivated by growing indications for a distinct form of nematic correlations in the extremely hole doped iron pnictide compounds $A$Fe$_2$As$_2$ ($A$=K,Rb,Cs), we consider spin-driven nematic order in the general case of incommensurate magnetic fluctuations. We classify the nematic order parameters by broken mirror symmetries of the tetragonal $D_{4h}$ point group, and use this scheme to construct a general Ginzburg-Landau theory that links the nematic order to spatial pattern of magnetic fluctuations. Our analysis points to incommensurate magnetic fluctuations of wavevector $(q,q)$ as underly…
Despite its seemingly simple composition and structure, the pairing mechanism of FeSe remains an open problem due to several striking phenomena. Among them are nematic order without magnetic order, nodeless gap and unusual inelastic neutron spectra with a broad continuum, and gap anisotropy consistent with orbital selection of unknown origin. Here we propose a microscopic description of a nematic quantum spin liquid that reproduces key features of neutron spectra. We then study how the spin fluctuations of the local moments lead to pairing within a spin-fermion model. We find the resulting sup…
Charge-$4e$ superconductivity as a novel phase of matter remains elusive so far. Here we show that charge-$4e$ phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect -- nematic vortex -- is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-$4e$ phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-…
The intra-unit-cell nematic phase is studied within the three-band Emery model of the cuprates with the use of the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF). According to our analysis the spontaneous $C_4$ symmetry breaking of the electronic wave function, leading to the nematic behavior, can appear due to electron correlations induced mainly by the onsite Coulomb repulsion, even in the absence of the corresponding intersite oxygen-oxygen repulsion term. The latter has been considered as the triggering factor of the nematic state formation in a numbe…
The exotic normal state of iron chalcogenide superconductor FeSe, which exhibits vanishing magnetic order and possesses an electronic nematic order, triggered extensive explorations of its magnetic ground state. To understand its novel properties, we study the ground state of a highly frustrated spin-$1$ system with bilinear-biquadratic interactions using unbiased large-scale density matrix renormalization group. Remarkably, with increasing biquadratic interactions, we find a paramagnetic phase between Néel and stripe magnetic ordered phases. We identify this phase as a candidate of nematic qu…
The electronic nematic responses in Fe-based superconductors have been observed ubiquitously in various experimental probes. One novel nematic character is the d-wave {\it bond} orbital-relevant nematic charge order which was firstly proposed by symmetry analysis and then conformed by angle-resolved photoemission spectroscopy. In this paper, we present a mechanism that the driving force of the orbital-relevant nematic charge order is the reduction of the large Hubbard energy in the particle-hole charge channel by virtual hopping processes. This is one scenario from strong-coupling consideratio…
We investigate quantum phase transitions and quantum coherence in infinite biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy. All considered coherence measures such as the $l_1$ norm of coherence, the relative entropy of coherence, and the quantum Jensen-Shannon divergence, and the quantum mutual information show consistently that singular behaviors occur for the spin-1 system, which enables to identity quantum phase transitions. For the spin-2 system, the relative entropy of coherence and the quantum mutual information properly detect no singular behavior in the whole sys…
The concept of a vestigial nematic order emerging from a "mother" spin or charge density-wave state has been applied to describe the phase diagrams of several systems, including unconventional superconductors. In a perfectly clean system, the two orders appear simultaneously via a first-order quantum phase transition, implying the absence of quantum criticality. Here, we investigate how this behavior is affected by impurity-free droplets that are naturally present in inhomogeneous systems. Due to their quantum dynamics, finite-size droplets sustain long-range nematic order but not long-range d…
Compatible Instability: Gauge Constraints of Elasticity Inherited by Electronic Nematic Criticality
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院）；Anthony J. Leggett Institute for Condensed Matter Theory, The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院安东尼·J·利格特凝聚态理论研究所）
The problem of interacting bosons in frustrated lattices is an intricate one due to the absence of a unique minimum in the single-particle dispersion where macroscopic number of bosons can condense. Here we consider a family of tight-binding models with macroscopically degenerate lowest energy band, separated from other bands by a gap. We predict the formation of exotic states that spontaneously break rotational symmetry at relatively low filling. These states belong to three nematic phases: Wigner crystal, supersolid, and superfluid. The Wigner crystal phase is established exactly at low fill…
