Rotational symmetry breaking at the incommensurate charge-density-wave transition in Ba(Ni,Co)$_2$(As,P)$_2$: Possible nematic phase induced by charge/orbital fluctuations
Michael Merz, Liran Wang, Thomas Wolf, Peter Nagel, Christoph Meingast, Stefan Schuppler
Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,\@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,\@ a non-magnetic analog of BaFe$_2$As$_2$ with a structural transition in the same temperature range,\@ share a common tetragonal aristotype crystal structure with space-group type $I4/mmm$.\@ In contrast to BaFe$_2$As$_2$ where collinear stripe magnetic order is found for the orthorhombic low-$T$ phase, a unidirectional charge density wave together with (distorted) zig-zag chains are observed for the triclinic low-$T$ phase of BaNi$_2$As$_2$.\@ Here we show that between the high- and low-$T$ phases of Ba(Ni,Co)$_2$(As,P)$_2$ an additional phase with broken fourfold symmetry and $d_{xz}$ orbital order exists which is a promising candidate for charge/orbital-fluctuation-induced nematicity. Moreover, our data suggest that the enhanced $T_{\rm c}$ found for Ba(Ni,Co)$_2$(As,P)$_2$ for higher Co or P substitution levels might result from suppression of the (distorted) zig-zag chains by reducing the contribution of the $d_{xy}$ orbitals.
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…
Recent discoveries of charge order and electronic nematic order in the iron-based superconductors and cuprates have pointed towards the possibility of nematic and charge fluctuations playing a role in the enhancement of superconductivity. The Ba1-xSrxNi2As2 system, closely related in structure to the BaFe2As2 system, has recently been shown to exhibit both types of ordering without the presence of any magnetic order. We report single crystal X-ray diffraction, resistance transport measurements, and magnetization of \BaSrLate, providing evidence that the previously reported incommensurate charg…
Electronic nematicity, the breaking of the crystal lattice rotational symmetry by the electronic fluid, is a fascinating quantum state of matter. Recently, BaNi$_2$As$_2$ has emerged as a promising candidate for a novel type of nematicity triggered by charge fluctuations. In this work, we scrutinize the electronic nematicity of BaNi$_2$(As$_{1-x}$P$_x$)$_2$ with $0 \leq x \leq 0.10$ using electronic transport measurements under strain. We report a large $B_{1g}$ elastoresistance coefficient that is maximized at a temperature slightly higher than the first-order triclinic transition, and that c…
Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO3, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists a…
Recent experimental and theoretical studies have highlighted the possible role of a electronic nematic liquid in underdoped cuprate superconductors. We calculate, within a model of d-wave superconductor with Hubbard correlations, the spin susceptibility in the case of a small explicitly broken rotational symmetry of the underlying lattice. We then exhibit how the induced spin response asymmetry is strongly enhanced by correlations as one approaches the instability to stripe order. In the disorder-induced stripe phase, impurities become spin nematogens with a C_2 symmetric impurity resonance st…
Motivated by recent reports of nematic order in twisted bilayer graphene (TBG), we investigate the impact of the triangular moiré superlattice degrees of freedom on nematicity. In TBG, the nematic order parameter is not Ising-like, as it is the case in tetragonal crystals, but has a 3-state Potts character related to the threefold rotational symmetry ($C_{3z}$) of the moiré superlattice. We find that even in the presence of static strain that explicitly breaks the $C_{3z}$ symmetry, the system can still undergo a nematic-flop phase transition that spontaneously breaks in-plane twofold rotation…
We show that unconventional nematic superconductors with multi-component order parameter in lattices with three-fold and six-fold rotational symmetries support a charge-$4e$ vestigial superconducting phase above $T_c$. The charge-$4e$ state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is non-superconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities…
Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory …
We study spin and charge susceptibilities in the d-wave superconducting state whose underlying electronic dispersion is anisotropic due to the formation of the electronic nematic order. We show that the amplitude of the incommensurate peaks in the spin susceptibility near (π,π) reveals a pronounced anisotropy in the momentum space. The relevance of our findings to the magnetic scattering pattern observed in a recent neutron scattering measurement on untwinned YBa_2Cu_3O_{6+x} is discussed. In the charge channel, we identify a well-defined collective mode at small momentum transfer with strong …
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…
Charge order in cuprate superconductors is a possible source of anomalous electronic properties in the underdoped regime. Intra-unit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context we investigate charge instabilities in the Emery model and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signalled by a divergence of the susceptibility. Our calculations reveal three different kinds of order: a commensurate ($q=0$) nematic order, and two incommensurate nematic p…
The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$ to…
A nematic superconductor can in principle support a vestigial order phase above its superconducting transition temperature, with rotational symmetry spontaneously broken while remain nonsuperconducting. We examine the condition for this vestigial nematic order to occur, within a Ginzburg-Landau theory with order parameter fluctuations included. Contrary to prior theoretical results, we found that this vestigial order actually requires very stringent conditions to be met: the material must be sufficiently deep in the nematic regime (i.e. far away from the boundary separating the nematic and chi…
We use scanning tunneling microscopy to investigate the doping dependence of quasiparticle interference (QPI) in NaFe1-xCoxAs iron-based superconductors. The goal is to study the relation between nematic fluctuations and Cooper pairing. In the parent and underdoped compounds, where four-fold rotational symmetry is broken macroscopically, the QPI patterns reveal strong rotational anisotropy. At optimal doping, however, the QPI patterns are always four-fold symmetric. We argue this implies small nematic susceptibility and hence insignificant nematic fluctuation in optimally doped iron pnictides.…
Electronic nematics, an electron orientational order which breaks the underlying rotational symmetry, have been observed in iron pnictide superconductors several years after their discovery. However, the universality of the doping dependence of this phase and its relation to other symmetry-breaking orders (such as superconductivity) in distinct families of iron pnictides, remain outstanding questions. Here we use torque magnetometry as a probe to study the rotational symmetry breaking in EuFe$_2$(As$_{1-x}$P$_x$)$_2$ without introducing external pressure. The nematic phase is found to prolifer…
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…
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 copper-oxide and iron-based high temperature (high-$T_{\rm c}$) superconductors, many physical properties exhibit in-plane anisotropy, which is believed to be caused by a rotational symmetry-breaking nematic order, whose origin and its relationship to superconductivity remain elusive. In many iron-pnictides, a tetragonal-to-orthorhombic structural transition temperature $T_{\rm s}$ coincides with the magnetic transition temperature $T_{\rm N}$, making the orbital and spin degrees of freedom highly entangled. NaFeAs is a system where $T_{\rm s}$ = 54 K is well separated from $T_{\rm N}$ = 42…
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…
The doped topological insulator $A_{x}\mathrm{Bi_{2}Se_{3}}$, with $A=\{\mathrm{Cu},\mathrm{Sr},\mathrm{Nb}\}$, becomes a nematic superconductor below $T_{c}\sim3-4\,\mathrm{K}$. The associated electronic nematic director is described by an angle $α$ and is experimentally manifested in the elliptical shape of the in-plane critical magnetic field $H_{c2}$. Because of the threefold rotational symmetry of the lattice, $α$ is expected to align with one of three high-symmetry directions corresponding to the in-plane nearest-neighbor bonds, consistent with a $Z_{3}$-Potts nematic transition. Here, w…
The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an $S=1$ generalized bilinear-biquadratic model with multi-neighbor interactions. We find a large parameter regime for a ($π$,0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C$_4$-symmetry-breaking quadrupolar phase is also provided by an unbiased den…
An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using nois…
Nematic superconductivity is a novel class of superconductivity characterized by spontaneous rotational-symmetry breaking in the superconducting gap amplitude and/or Cooper-pair spins with respect to the underlying lattice symmetry. Doped Bi2Se3 superconductors, such as CuxBi2Se3, SrxBi2Se3, and NbxBi2Se3, are considered as candidates for nematic superconductors, in addition to the anticipated topological superconductivity. Recently, various bulk probes, such as nuclear magnetic resonance, specific heat, magnetotransport, magnetic torque, and magnetization, have consistently revealed two-fold …
Due to the intertwining between electronic nematic and elastic degrees of freedom, lattice defects and structural inhomogeneities commonly found in crystals can have a significant impact on the electronic properties of nematic materials. Here, we show that defects commonly present at the surface of crystals generally shift the wave-vector of the nematic instability to a non-zero value, resulting in an incommensurate electronic smectic phase. Such a smectic state onsets above the bulk nematic transition temperature and is localized near the surface of the sample. We argue that this effect may e…
How superconductivity interacts with charge or nematic order is one of the great unresolved issues at the center of research in quantum materials. Ba$_{1-x}$Sr$_{x}$Ni$_{2}$As$_{2}$ (BSNA) is a charge ordered pnictide superconductor recently shown to exhibit a six-fold enhancement of superconductivity due to nematic fluctuations near a quantum phase transition (at $x_c=0.7$). The superconductivity is, however, anomalous, with the resistive transition for $0.4 < x< x_c$ occurring at a higher temperature than the specific heat anomaly. Using x-ray scattering, we discovered a new charge density w…
We study attractively interacting fermions on a square lattice with dispersion relations exhibiting strong spin-dependent anisotropy. The resulting Fermi surface mismatch suppresses the s-wave BCS-type instability, clearing the way for unconventional types of order. Unbiased sampling of the Feynman diagrammatic series using Diagrammatic Monte Carlo methods reveals a rich phase diagram in the regime of intermediate coupling strength. Instead of a proposed Cooper-pair Bose metal phase [A. E. Feiguin and M. P. A. Fisher, Phys. Rev. Lett. 103, 025303 (2009)] we find an incommensurate density wave …
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…
Recently, complex phase transitions accompanied by the rotational symmetry breaking have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various charge susceptibilities in an unbiased way, by applying the functional-renormalization-group method to the realistic $d$-$p$ Hubbard model. Without assuming the wavevector of the order parameter, we reveal that the most dominant instability is the uniform ($q = 0$) charge modulation on the $p_x$ and $p_y$ orbitals, which possesses the d-symmetry. This uniform nematic order triggers another nem…
We report a 75-As single crystal NMR investigation of LaFeAsO, the parent phase of a pnictide high Tc superconductor. We demonstrate that spin dynamics develop a strong two-fold anisotropy within each orthorhombic domain below the tetragonal-orthorhombic structural phase transition at T[TO]~156 K. This intermediate state with a dynamical breaking of the rotational symmetry freezes progressively into a spin density wave (SDW) below T[SDW]~142 K. Our findings are consistent with the presence of a spin nematic state below T[TO] with an incipient magnetic order.
Nematic Fermi liquid arises when the system of interacting fermions spontaneously breaks the rotational symmetry while the translational symmetry is preserved. We consider a Nematic Fermi liquid of fermions with two distinct quantum numbers. Two quantum numbers represent the spin degrees of freedom or the layer degrees of freedom of the bilayer system. There are two director modes in this system: the in-phase and out-of-phase modes. We find that the out-of-phase (in-phase) mode mediates an attractive (repulsive) interaction between fermions with different quantum numbers. Pairing instability o…
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…
We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in BaNi$_2$As$_2$, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, $Q_{I-CDW}$. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around $Q_{I-CDW}$. The phonon continuously softens u…
The possibility is investigated that competition between fluctuations at different symmetry-related ordering wave vectors may affect the quantum phase transition between a fermi liquid and a longitudinal spin density wave state, in particular giving rise to an intermediate 'nematic' state with broken rotational symmetry but unbroken translational symmetry. At the marginal dimension the nematic transition is found to be preempted by a first order transition but a weak symmetry breaking field restores a second order magnetic transition with an intermediate regime in which correlations substantia…
Nematic states are characterized by rotational symmetry breaking without translational ordering. Recently, nematic superconductivity, in which the superconducting gap spontaneously lifts the rotational symmetry of the lattice, has been discovered. However the pairing mechanism and the mechanism determining the nematic orientation remain unresolved. A first step is to demonstrate control of the nematicity, through application of an external symmetry-breaking field, to determine the sign and strength of coupling to the lattice. Here, we report for the first time control of the nematic orientatio…
Unconventional superconductivity is characterized by the spontaneous symmetry breaking of the macroscopic superconducting wavefunction in addition to the gauge symmetry breaking, such as rotational-symmetry breaking with respect to the underlying crystal-lattice symmetry. Particularly, superconductivity with spontaneous rotational-symmetry breaking in the wavefunction amplitude and thus in bulk properties, not yet reported previously, is intriguing and can be termed "nematic" superconductivity in analogy to nematic liquid-crystal phases. Here, based on specific-heat measurements of the single-…
The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbar…
When a symmetry-breaking phase of matter is suppressed to a quantum critical point (QCP) at absolute zero, quantum-mechanical fluctuations proliferate. Such fluctuations can lead to unconventional superconductivity, as evidenced by the superconducting domes often found near magnetic QCPs in correlated materials. However, it remains unclear whether this superconductivity mechanism holds for QCPs of the electronic nematic phase, characterized by rotational symmetry breaking. Here, we demonstrate from systematic elastoresistivity measurements that nonmagnetic FeSe$_{1-x}$Te$_{x}$ exhibits an elec…
We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range charge-density wave order, but not superconducting or nematic order. We select three representative sets of input parameters and compute the corresponding charge-density wave structure factors using both large-$N$ techniques and classical Monte Carlo simulations. Where nematicity and superconductivity coexist at low temperature, the peak height of the charge-dens…
Motivated by the recent experiments suggesting the importance of nematicity in the phase diagrams of ironbased and cuprate high-Tc superconductors, we study the influence of nematicity on the collective modes inside the superconducting state in a non-equilibrium. In particular, we consider the signatures of collective modes in short-time dynamics of a system with competing nematic and s- and d-wave superconducting orders. In the rotationally symmetric state, we show that the Bardasis-Schrieffer mode, corresponding to the subdominant pairing, hybridizes with the nematic collective mode and merg…
A very fundamental and unconventional characteristic of superconductivity in iron-based materials is that it occurs in the vicinity of {\it two} other instabilities. Apart from a tendency towards magnetic order, these Fe-based systems have a propensity for nematic ordering: a lowering of the rotational symmetry while time-reversal invariance is preserved. Setting the stage for superconductivity, it is heavily debated whether the nematic symmetry breaking is driven by lattice, orbital or spin degrees of freedom. Here we report a very clear splitting of NMR resonance lines in FeSe at $T_{nem}$ =…
Nematic order is ubiquitous in liquid crystals and is characterized by a rotational symmetry breaking in an otherwise uniform liquid. Recently a similar phenomenon has been observed in some electronic phases of quantum materials related to high temperature superconductivity, particularly in the Fe-based superconductors. While several experiments have probed nematic fluctuations, they have been primarily restricted to the uniform nematic susceptibility, i.e. q = 0 fluctuations. Here, we investigate the behavior of finite-momentum nematic fluctuations by measuring transverse acoustic phonon mode…
The nature of the pseudogap and its relationship with superconductivity are one of the central issues of cuprate superconductors. Recently, a possible scenario has been proposed that the pseudogap state is a distinct phase characterized by spontaneous rotational symmetry breaking called "nematicity" based on transport and magnetic susceptibility measurements, where the symmetry breaking was observed below the pseudogap temperature $T^*$. Here, we report a temperature-dependent ARPES study of nematicity in slightly overdoped Bi${}_{1.7}$Pb${}_{0.5}$Sr${}_{1.9}$CaCu${}_2$O${}_{8+δ}$ triggered by…
The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBS) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken $C_4$ rotational symmetry. One of the few stoichiometric IBS, lithium iron arsenide, superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, usi…
Spontaneous rotational-symmetry breaking in the superconducting state of doped $\mathrm{Bi}_2\mathrm{Se}_3$ has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal $\mathrm{Sr}_{0.1}\mathrm{Bi}_2\mathrm{Se}_3$ provides unequivocal evidence of a two-fold rotational symmetry in the superconducting gap by a \emph{bulk thermodynamic} probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's …
If the topological insulator Bi$_{2}$Se$_{3}$ is doped with electrons, superconductivity with $T_{\rm c}\approx3-4\:{\rm K}$ emerges for a low density of carriers ($n\approx10^{20}{\rm cm}^{-3}$) and with a small ratio of the superconducting coherence length and Fermi wave length: $ξ/λ_{F}\approx2\cdots4$. These values make fluctuations of the superconducting order parameter increasingly important, to the extend that the $T_{c}$-value is surprisingly large. Strong spin-orbit interaction led to the proposal of an odd-parity pairing state. This begs the question of the nature of the transition i…
Recent nuclear magnetic resonance and specific heat measurements have provided concurring evidence of spontaneously broken rotational symmetry in the superconducting state of the doped topological insulator Cu$_x$Bi$_2$Se$_3$. This suggests that the pairing symmetry corresponds to a two-dimensional representation of the $D_{3d}$ crystal point group, and that Cu$_x$Bi$_2$Se$_3$ is a nematic superconductor. In this work, we present a comprehensive study of the upper critical field $H_{c2}$ of nematic superconductors within Ginzburg-Landau (GL) theory. Contrary to typical GL theories which have a…
Massachusetts Institute of Technology（麻省理工学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Institute for Materials Science（国立材料研究所）；Princeton University（普林斯顿大学）
The superconducting behavior of the topological semimetal CaSn$_{3}$ was investigated by means of magnetotransport and muon spectroscopy $μ$SR measurements, both providing strong evidence of nematic behavior. Magnetotransport detects an anisotropic upper critical field, characterized by a twofold symmetry about $C_{4}$ axis, thus breaking the rotational symmetry of the underlying cubic lattice. Transverse-field $μ$SR data support such picture, with the muon depolarization rate depending strongly on the magnetic field direction, here applied along the [110] or [001] crystal directions. In the f…
Understanding superconductivity requires detailed knowledge of the normal electronic state from which it emerges. A nematic electronic state that breaks the rotational symmetry of the lattice can potentially promote unique scattering relevant for superconductivity. Here, we investigate the normal transport of superconducting FeSe$_{1-x}$S$_x$ across a nematic phase transition using high magnetic fields up to 69 T to establish the temperature and field-dependencies. We find that the nematic state is an anomalous non-Fermi liquid, dominated by a linear resistivity at low temperatures that can tr…
The recent study of $^{77}$Se nuclear magnetic resonance (NMR) in a $β$-FeSe single crystal proposed that ferro-orbital order breaks the $90^\circ$ $C_4$ rotational symmetry, driving nematic ordering. Here, we report an NMR study of the impact of small strains generated by gluing on nematic state and spin fluctuations. We observe that the local strains strongly affect the nematic transition, considerably enhancing its onset temperature. On the contrary, no effect on low-energy spin fluctuations was found. Furthermore we investigate the interplay of the nematic phase and superconductivity. Our …
We present the strain and temperature dependence of an anomalous nematic phase in optimally doped BaFe$_2$(As,P)$_2$. Polarized ultrafast optical measurements reveal broken 4-fold rotational symmetry in a temperature range above $T_c$ in which bulk probes do not detect a phase transition. Using ultrafast microscopy, we find that the magnitude and sign of this nematicity vary on a ${50{-}100}~μ$m length scale, and the temperature at which it onsets ranges from 40 K near a domain boundary to 60 K deep within a domain. Scanning Laue microdiffraction maps of local strain at room temperature indica…
