An anisotropic metallic phase dubbed electronic nematic phase bounded by two consecutive metamagnetic transitions has been reported in the bilayer ruthenate Sr3Ru2O7. It has also been shown that the nematic and the accompanying metamagnetic transitions are driven by an effective momentum-dependent quadrupole-type interaction. Here, we study the microscopic origin of such an effective interaction. To elucidate the mechanism behind the spontaneous Fermi surface distortion associated with the nematic, we identify a simple tight binding model based on t2g orbitals, spin-orbit coupling and the rotation of RuO6 octahedra as starting point, consistent with the Fermi surface obtained from recent angle-resolved photoemission data. Within an extended Hubbard model the nematic state, characterized by an anisotropy between the bands near $(\pm π,0)$ and $(0,\pm π)$, then strongly competes with ferromagnetic order but pre-empts it via a finite nearest neighbor interaction. We discuss experimental means to confirm our proposal.
The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a spin density wave order in the presence of a magnetic field. We show that a cooperation of the nematicity and the magnetic field induces a finite coupling between the spin density wave and spin-triplet staggered flux orders. As a consequence of such a coupling, the magnon gap decreases as the magnetic field increases, and it eventually condenses beyond a crit…
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…
We report on $^{75}$As-NMR measurements in single crystalline BaFe$_{2}$(As$_{0.96}$P$_{0.04}$)$_{2}$ for magnetic fields parallel to the orthorhombic $[110]_{\rm o}$ and $[100]_{\rm o}$ directions above the structural transition temperature $T_{\rm S}\simeq121$ K. A large difference in the linewidth between the two field directions reveals in-plane anisotropy of the electric field gradient, even in the tetragonal phase. This provides microscopic evidence of population imbalance between As-$4p_{x}$ and $4p_{y}$ orbitals, which reaches $|n_x-n_y|/|n_x+n_y| \sim 15$\% at $T\rightarrow T_{\rm S}$…
We expose the theoretical mechanisms underlying disorder-induced nematicity in systems exhibiting strong fluctuations or ordering in the nematic channel. Our analysis consists of a symmetry-based Ginzburg-Landau approach and associated microscopic calculations. We show that a single featureless point-like impurity induces nematicity locally, already above the critical nematic transition temperature. The persistence of fourfold rotational symmetry constrains the resulting disorder-induced nematicity to be inhomogeneous and spatially average to zero. Going beyond the single impurity case, we dis…
In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced1. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within CuO2 unit cell. We analyze spectroscopic-imaging scanning tunn…
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…
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.
High-resolution angle-resolved photoelectron spectroscopy is used to examine the electronic band structure of FeTe$_{0.5}$Se$_{0.5}$ near the Brillouin zone center. A consistent separation of the $α_{1}$ and $α_{2}$ bands is observed with little $k_{z}$ dependence of the $α_{1}$ band. First-principles calculations for bulk and thin films demonstrate that the antiferromagnetic coupling between the Fe atoms and hybridization-induced spin-orbit effects lifts the degeneracy of the Fe $d_{xz}$ and $d_{yz}$ orbitals at the zone center leading to orbital ordering. These experimental and computational…
A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states, which, in many cases, are not independent competing phases, but instead display a complex intertwinement. In this review, we focus on a particular realization of intertwined orders: a primary phase characterized by a multi-component order parameter and a fluctuation-driven vestigial phase characterized by a composite order parameter. This concept has been widely employed to elucidate nematicity in iron-based and cuprate superconductors. Here we present a group-theoretical framework tha…
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
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…
Although the existence of nematic order in iron-based superconductors is now a well-established experimental fact, its origin remains controversial. Nematic order breaks the discrete lattice rotational symmetry by making the $x$ and $y$ directions in the Fe plane non-equivalent. This can happen because of (i) a tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking of an orbital symmetry, or (iii) a spontaneous development of an Ising-type spin-nematic order - a magnetic state that breaks rotational symmetry but preserves time-reversal symmetry. The Landau theory of phas…
The large anisotropy in the electronic properties across a structural transition in several correlated systems has been identified as the key manifestation of electronic nematic order, breaking rotational symmetry. In this context, FeSe is attracting tremendous interest, since electronic nematicity develops over a wide range of temperatures, allowing accurate experimental investigation. Here we combine angle-resolved photoemission spectroscopy and theoretical calculations based on a realistic multi-orbital model to unveil the microscopic mechanism responsible for the evolution of the electroni…
Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing. Nematic order breaks fourfold rotational symmetry in the iron plane, which is believed to be driven by either orbital or spin degrees of freedom. However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult. Here, we use neutron scattering to study structura…
Spontaneous symmetry breaking has been a paradigm to describe the phase transitions in condensed matter physics. In addition to the continuous electromagnetic gauge symmetry, an unconventional superconductor can break discrete symmetries simultaneously, such as time reversal and lattice rotational symmetry. In this work we report a characteristic in-plane 2-fold behaviour of the resistive upper critical field and point-contact spectra on the superconducting semimetal PbTaSe2 with topological nodal-rings, despite its hexagonal lattice symmetry (or D_3h in bulk while C_3v on surface, to be preci…
We derive from a microscopic model the effective theory of nematic order in a system with a spontaneous quantum anomalous Hall effect in two dimensions. Starting with a model of two-component fermions (a spinor field) with a quadratic band crossing and short range four-fermion marginally relevant interactions we use a 1/N expansion and bosonization methods to derive the effective field theory for the hydrodynamic modes associated with the conserved currents and with the local fluctuations of the nematic order parameter. We focus on the vicinity of the quantum phase transition from the isotropi…
Ordered phases such as charge- and spin-density wave state accompany either full or partial gapping of Fermi surface (FS) leading a metal-insulator or metal-metal transition (MMT). However, there are examples of MMT without any signatures of symmetry breaking. One example is Na$_2$Ti$_2$Sb$_2$O, where a partial gapping of FS is observed but a density wave ordering has not been found. Here we propose a microscopic mechanism of such a MMT which occurs due to a momentum dependent spin-orbit coupled molecular orbital polarization. Since a molecular $d$ orbital polarization is present due to a smal…
Electronic nematicity, proposed to exist in a number of transition metal materials, can have different microscopic origins. In particular, the anisotropic resistivity and meta-magnetic jumps observed in Sr3Ru2O7 are consistent with an earlier proposal that the isotropic-nematic transition is generically first order and accompanied by meta-magnetism when tuned by a magnetic field. However, additional striking experimental features such as a non-Fermi liquid resistivity and critical thermodynamic behavior imply the presence of an unidentified quantum critical point (QCP). Here we show that orbit…
The spin S=$\frac{1}{2}$ Kitaev honeycomb model has attracted significant attention, since emerging candidate materials have provided a playground to test non-Abelian anyons. The Kitaev model with higher spins has also been theoretically studied, as it may offer another path to a quantum spin liquid. However, a microscopic route to achieve higher spin Kitaev models in solid state materials has not been rigorously derived. Here we present a theory of the spin S=1 Kitaev interaction in two-dimensional edge-shared octahedral systems. Essential ingredients are strong spin-orbit coupling in anions …
We report the observation of an antipolar phase in cubic GaNb$_4$S$_8$ driven by an unconventional microscopic mechanism, the cooperative Jahn-Teller effect of Nb$_4$S$_4$ molecular clusters. The assignment of the antipolar nature is based on sudden changes in the crystal structure and a strong drop of the dielectric constant at $T_\mathrm{JT}=31$\,K, also indicating the first-order nature of the transition. In addition, we found that local symmetry lowering precedes long-range orbital ordering, implying the presence of a dynamic Jahn-Teller effect in the cubic phase above $T_\mathrm{JT}$. Bas…
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…
Coupled-wire constructions offer particularly simple and powerful models to capture the essence of strongly correlated topological phases of matter. They often rely on effective theories valid in the low-energy and strong coupling limits, which impose severe constraints on the physical systems where they could be realized. We investigate the microscopic relevance of a class of coupled-wire models and their possible experimental realization in cold-atom experiments. We connect with earlier results and prove the emergence of fractional quantum Hall states in the limit of strong inter-wire tunnel…
We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of …
Quantum spin liquids are long-range entangled phases whose magnetic correlations are determined by strong quantum fluctuations. While an overarching principle specifying the precise microscopic coupling scenarios for which quantum spin-liquid behavior arises is unknown, it is well-established that they are preferably found in spin systems where the corresponding classical limit of spin magnitudes $S\rightarrow\infty$ exhibits a macroscopic ground state degeneracy, so-called classical spin liquids. Spiral spin liquids represent a special family of classical spin liquids where degenerate manifol…
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…
FeSe is arguably the simplest, yet the most enigmatic, iron-based superconductor. Its nematic but non-magnetic ground state is unprecedented in this class of materials and stands out as a current puzzle. Here, our NMR measurements in the nematic state of mechanically detwinned FeSe reveal that both the Knight shift and the spin-lattice relaxation rate 1/T_1 possess an in-plane anisotropy opposite to that of the iron pnictides LaFeAsO and BaFe2As2. Using a microscopic electron model that includes spin-orbit coupling, our calculations show that an opposite quasiparticle weight ratio between the …
FeSe, despite being the structurally simplest compound in the family of iron-based superconductors, shows an astoundingly rich interplay of physical phenomena including nematicity and pressure-induced magnetism. Here, we present a microscopic study of these two phenomena by high-energy x-ray diffraction and time-domain Mössbauer spectroscopy on FeSe single crystals over a wide temperature and pressure range. The topology of the pressure-temperature phase diagram is a surprisingly close parallel to the well-known doping-temperature phase diagram of BaFe2As2 generated through partial Fe/Co and B…
