In-plane Electronic Anisotropy Research Articles

Synthesis and Modular Engineering of Porous Graphene Nanoarchitectures

Bottom-up nanoarchitectonics has demonstrated the capability to control structural parameters of nanomaterials with atomic precision. The surface-assisted synthesis of graphene-based one-dimensional nanostructures à la carte distinctly illustrates the power of this concept. However, despite impressive advances in the synthesis of 1D homostructures, advancing in structural complexity faces major challenges. However, despite impressive advances in the synthesis of 1D homostructures, advancing in structural complexity faces major challenges. The functionalization of edges in nanorib-bons, an effective strategy to tailor their electronic properties and chemical interactions, is a clear example. The concept of inserting the desired functional groups or dopants in the molecular precursor often fails due to their lack of stability during the reaction path. The fabrication of heterostructures is a second example, where the challenge lies on the control of the size and distribution of their com-ponents. A third one is extending the on-surface strategy to two-dimensional structures, where examples of long-range ordered nanoarchitectures are very limited.In this talk I will present different strategies that we have developed to overcome each one of this challenges. I will show introducing our method to synthesize a 2D nanoporous graphene, where the long-range order is achieved by the sequential growth of 1D building blocks and their posterior coupling [1]. I will continue presenting two modular strategies that lead to more complex nanoporous structures. The first consist on the molecular engineering of the coupling bridges. I will show an example where the introduction of phenyl groups in the bridges brings tunability of the quantum electronic coupling and the corresponding in-plane electronic anisotropy [2]. In a final example I will focus on intercalating different 1D ribbon components in periodic arrays for the formation of lateral heterostructure superlattices where the junction is defined with atomic precision [3]. One of the components being a N-doped ribbon, the heterostructure can also be seen as a nanoporous graphene sheet bearing N-doped pores.

In-plane electronic anisotropy revealed by interlayer resistivity measurements on the iron-based superconductor parent compound CaFeAsF

Both cuprates and iron-based superconductors demonstrate nematicity, defined as the spontaneous breaking of rotational symmetry in electron systems. The nematic state can play a role in the high-transition-temperature superconductivity of these compounds. However, the microscopic mechanism responsible for the transport anisotropy in iron-based compounds remains debatable. Here, we investigate the electronic anisotropy of CaFeAsF by measuring its interlayer resistivity under magnetic fields with varying field directions. Counterintuitively, the interlayer resistivity was larger in the longitudinal configuration ($B \parallel I \parallel c$) than in the transverse one ($B \perp I \parallel c$). The interlayer resistivity exhibited a so-called coherence peak under in-plane fields and was highly anisotropic with respect to the in-plane field direction. At $T$ = 4 K and $B$ = 14 T, the magnetoresistance $\Delta\rho/\rho_0$ was seven times larger in the $B \parallel b_o$ than in the $B \parallel a_o$ configuration. Our theoretical calculations of the conductivity based on the first-principles electronic band structure qualitatively reproduced the above observations but underestimated the magnitudes of the observed features. The proposed methodology can be a powerful tool for probing the nematic electronic state in various materials.

Specific heat of CeRhIn5 in high magnetic fields: Magnetic phase diagram revisited

${\mathrm{CeRhIn}}_{5}$ is a prototypical antiferromagnetic heavy-fermion compound, whose behavior in a magnetic field is unique. A magnetic field applied in the basal plane of the tetragonal crystal structure induces two additional phase transitions. When the magnetic field is applied along, or close to, the $c$ axis, a new phase characterized by a pronounced in-plane electronic anisotropy emerges at ${B}^{*}\ensuremath{\approx}$ 30 T, well below the critical field, ${B}_{c}\ensuremath{\simeq}$ 50 T, to suppress the antiferromagnetic order. The exact origin of this new phase, originally suggested to be an electronic-nematic state, remains elusive. Here we report low-temperature specific heat measurements in ${\mathrm{CeRhIn}}_{5}$ in high static magnetic fields up to 36 T applied along both the $a$ and $c$ axes. For fields applied along the $a$ axis, we confirmed the previously suggested phase diagram and extended it to higher fields. This allowed us to observe a triple point at $\ensuremath{\sim}30$ T, where the first-order transition from an incommensurate to commensurate magnetic structure merges into the onset of the second-order antiferromagnetic transition. For fields applied along the $c$ axis, we observed a small but distinct anomaly at ${B}^{*}$, which we discuss in terms of a possible field-induced transition, probably weakly first-order. We further suggest that the transition corresponds to a change of magnetic structure. We revise magnetic phase diagrams of ${\mathrm{CeRhIn}}_{5}$ for both principal orientations of the magnetic field based entirely on thermodynamic anomalies.

In-plane electronic anisotropy resulted from ordered magnetic moment in iron-based superconductors

We used polarization-resolved Raman scattering to study the magneto-elastic coupling in the parent compounds of several families of Fe-based superconductors (BaFe2As2, EuFe2As2, NaFeAs, LiFeAs, FeSe and LaFeAsO). We observe an emergent Ag-symmetry As phonon mode in the XY scattering geometry whose intensity is significantly enhanced below the magneto-structural transition only for compounds showing magnetic ordering. We conclude that the small lattice anisotropy is insufficient to induce the in-plane electronic polarizability anisotropy necessary for the observed phonon intensity enhancement, and interpret this enhancement below the Neel temperature in terms of the anisotropy of the magnetic moment and magneto-elastic coupling. We evidence a Fano line- shape in the XY scattering geometry resulting from a strong coupling between the Ag (As) phonon mode and the B2g symmetry-like electronic continuum. Strong electron-phonon coupling may be relevant to superconductivity.

Divergent Nematic Susceptibility near the Pseudogap Critical Point in a Cuprate Superconductor

Superconductivity is a quantum phenomenon caused by bound pairs of electrons. In diverse families of strongly correlated electron systems, the electron pairs are not bound together by phonon exchange but instead by some other kind of bosonic fluctuations. In these systems, superconductivity is often found near a magnetic quantum critical point (QCP) where a magnetic phase vanishes in the zero-temperature limit. Moreover, the maximum of superconducting transition temperature Tc frequently locates near the magnetic QCP, suggesting that the proliferation of critical spin fluctuations emanating from the QCP plays an important role in Cooper pairing. In cuprate superconductors, however, the superconducting dome is usually separated from the antiferromagnetic phase and Tc attains its maximum value near the verge of enigmatic pseudogap state that appears below doping-dependent temperature T*. Thus a clue to the pairing mechanism resides in the pseudogap and associated anomalous transport properties. Recent experiments suggested a phase transition at T*, yet, most importantly, relevant fluctuations associated with the pseudogap have not been identified. Here we report on direct observations of enhanced nematic fluctuations in (Bi,Pb)2Sr2CaCu2O8+d by elastoresistance measurements, which couple to twofold in-plane electronic anisotropy, i.e. electronic nematicity. The nematic susceptibility shows Curie-Weiss-like temperature dependence above T*, and an anomaly at T* evidences a second-order transition with broken rotational symmetry. Near the pseudogap end point, where Tc is not far from its peak in the superconducting dome, nematic susceptibility becomes singular and divergent, indicating the presence of a nematic QCP. This signifies quantum critical fluctuations of a nematic order, which has emerging links to the high-Tc superconductivity and strange metallic behaviours in cuprates.

Nematicity in chalcogenide parent compound Fe1+yTe probed by thermoelectric measurements

We present a study of the in-plane electronic transport anisotropy in the iron-chalcogenide parent compound Fe1.04Te. Measurements of the electrical resistivity, the thermoelectric power and the Nernst effect, were carried out in two configurations: across (index a) and along (index b) the uniaxial pressure. A comparison of the respective a- and b-indexed coefficients show that the in-plane electronic anisotropy emerges at a temperature significantly higher than the temperature of the structural/magnetic transition which is classified to be of the first order. The temperature evolution of the Nernst anisotropy suggests that the nematic phase occurring in Fe1+yTe is similar to the one observed in 122 iron-based superconductors.

Anisotropic Two-Dimensional Screening at the Surface of Black Phosphorus.

Electronic screening can have direct consequences for structural arrangements on the nanoscale, such as on the periodic ordering of adatoms on a surface. So far, such ordering phenomena have been explained in terms of isotropic screening of free electronlike systems. Here, we directly illustrate the structural consequences of anisotropic screening, making use of a highly anisotropic two-dimensional electron gas (2DEG) near the surface of black phosphorous. The presence of the 2DEG and its filling is controlled by adsorbed potassium atoms, which simultaneously serve to probe the electronic ordering. Using scanning tunneling microscopy, we show that the anisotropic screening leads to the formation of potassium chains with a well-defined orientation and spacing. We quantify the mean interaction potential utilizing statistical methods and find that the dimensionality and anisotropy of the screening is consistent with the presence of a band bending-induced 2DEG near the surface. The electronic dispersion of the 2DEG inferred by electronic ordering is consistent with that measured by angle-resolved photoemission spectroscopy.

Crystalline anisotropy associated with a second antiferromagnetic phase in the absence of spin density wave in the heavily hydrogen-doped LaFeAsO1−xHx (x∼0.5)

Electronic and magnetic properties of the heavily H-doped LaFeAsO1−xHx (x∼0.5) were studied in the framework of the density functional theory combined with the dynamical mean field theory. We found a stripe-like-ordered structure of hydrogen and oxygen atoms, as the ground state, in a 2 a×2b×c supercell, with the same configuration as the antiferromagnetic order. The new configuration could explain the existing experimental results related to the heavily H-doped LaFeAsO1−xHx, such as the in-plane electronic anisotropy and the nonuniform magnetic behavior. A significant anisotropy was observed between Fe-3dxz (xz) and Fe-3dyz (yz) orbitals in the ground state in the absence of the pseudogap resulting from the spin density wave phase, which was found to originate from the crystalline anisotropy. Magnetic moments were not spatially uniform and were sensitive to the crystal configuration. We found that the nonuniform magnetic behavior is associated with the As–Fe–As bond angle in the structure. Our findings would clarify the importance of crystal details and orbital degrees of freedom in iron-based superconductors.

Strong anisotropy and its electric tuning for brownmilleriteSrCoO2.5films with different crystal orientations

Brownmillerite oxides ($A\mathrm{B}{\mathrm{O}}_{2.5}$) with long-range ordering of oxygen vacancies own a distinct superstructure formed by alternately stacked octahedral $\mathrm{B}{\mathrm{O}}_{6}$ and tetrahedral $\mathrm{B}{\mathrm{O}}_{4}$ planes. The one-dimensional oxygen vacancy channels within $\mathrm{B}{\mathrm{O}}_{4}$ layers usually lead to high ionic conductivity of brownmillerite oxides, demonstrating great application potential in solid-oxide fuel cells, the oxygen separation membrane, and catalyzers. Here, high quality brownmillerite-$\mathrm{SrCo}{\mathrm{O}}_{2.5}$ films have been epitaxially grown on differently oriented substrates by pulsed laser deposition. The anisotropic structural and physical properties of (110)- and (111)-oriented $\mathrm{SrCo}{\mathrm{O}}_{2.5}$ films were systematically investigated. We found, unlike the out-of-plane (001)-oriented $\mathrm{SrCo}{\mathrm{O}}_{2.5}$ films, the $\mathrm{Co}{\mathrm{O}}_{6}$ and $\mathrm{Co}{\mathrm{O}}_{4}$ planes would alternately stack along one of the [100] and [010] axes for (110)-oriented films and one of the [100], [010], and [001] axes for (111)-oriented films, forming coexisting crystal domains with different orientations. More importantly, the superstructure of these films could be reversibly tuned by alternately applying an electric field along two orthogonal directions, switching between an ordered and a disordered state. Corresponding to structural anisotropy, strong in-plane electronic anisotropy of the (110)-oriented $\mathrm{SrCo}{\mathrm{O}}_{2.5}$ film was revealed, which was also electrically tunable like the superstructure. This work demonstrates the approaches to modify the ionic conduction channels of brownmillerite oxides, opening avenues towards electrically tunable oxygen separation membrane and catalyzers.

Enhanced Hybridization Sets the Stage for Electronic Nematicity in CeRhIn_{5}.

High magnetic fields induce a pronounced in-plane electronic anisotropy in the tetragonal antiferromagnetic metal CeRhIn_{5} at H^{*}≳30 T for fields ≃20° off the c axis. Here we investigate the response of the underlying crystal lattice in magnetic fields to 45T via high-resolution dilatometry. At low fields, a finite magnetic field component in the tetragonal ab plane explicitly breaks the tetragonal (C_{4}) symmetry of the lattice revealing a finite nematic susceptibility. A modest a-axis expansion at H^{*} hence marks the crossover to a fluctuating nematic phase with large nematic susceptibility. Magnetostriction quantum oscillations confirm a Fermi surface change at H^{*} with the emergence of new orbits. By analyzing the field-induced change in the crystal-field ground state, we conclude that the in-plane Ce 4f hybridization is enhanced at H^{*}, in agreement with the in-plane lattice expansion. We argue that the nematic behavior observed in this prototypical heavy-fermion material is of electronic origin, and is driven by the hybridization between 4f and conduction electrons which carries the f-electron anisotropy to the Fermi surface.

π-Plasmon Dispersion in Free-Standing Monolayer Graphene Investigated by Momentum-Resolved Electron Energy-Loss Spectroscopy

The {\pi}-plasmon dispersion in graphene was scrutinized by momentum(q)-resolved electron energy-loss spectroscopy with an improved q resolution and found to display the square root of q dispersion characteristic of the collective excitation of two-dimensional electron systems, in contrast with previous experimental and theoretical studies which reported a linear q dispersion. Our theoretical elaborations on the q-dependent spectra affirm this square root of q relation and further unveil an in-plane electronic anisotropy. The physical property of the {\pi} plasmon is thoroughly compared to that of the two-dimensional plasmon due to carriers of the Dirac fermions. A clear distinction between the {\pi} plasmon and the two-dimensional Dirac plasmon was demonstrated, clarifying the common notion on correlating the linearly-dispersed Dirac cones to the linear dispersion of the {\pi} plasmon previously reported.

Orbitally and magnetically induced anisotropy in iron-based superconductors

Recent experimental developments in the iron pnictides have unambiguously demonstrated the existence of in-plane electronic anisotropy in the absence of the long-range magnetic order. Such anisotropy can arise from orbital ordering, which is described by an energy splitting between the two otherwise degenerate ${d}_{xz}$ and ${d}_{yz}$ orbitals. By including this phenomenological orbital order into a five-orbital Hubbard model, we obtain the mean-field solutions where the magnetic order is determined self-consistently. Despite sensitivity of the resulting states to the input parameters, we find that a weak orbital order that places the ${d}_{yz}$ orbital slightly higher in energy than the ${d}_{xz}$ orbital, combined with intermediate on-site interactions, produces band dispersions that are compatible with the photoemission results. In this regime, the stripe antiferromagnetic order is further stabilized and the resistivity displays the observed anisotropy. We also calculate the optical conductivity and show that it agrees with the temperature evolution of the anisotropy seen experimentally.

Symmetry-breaking orbital anisotropy observed for detwinned Ba(Fe 1- x Co x ) 2 As 2 above the spin density wave transition

Nematicity, defined as broken rotational symmetry, has recently been observed in competing phases proximate to the superconducting phase in the cuprate high-temperature superconductors. Similarly, the new iron-based high-temperature superconductors exhibit a tetragonal-to-orthorhombic structural transition (i.e., a broken C 4 symmetry) that either precedes or is coincident with a collinear spin density wave (SDW) transition in undoped parent compounds, and superconductivity arises when both transitions are suppressed via doping. Evidence for strong in-plane anisotropy in the SDW state in this family of compounds has been reported by neutron scattering, scanning tunneling microscopy, and transport measurements. Here, we present an angle-resolved photoemission spectroscopy study of detwinned single crystals of a representative family of electron-doped iron-arsenide superconductors, Ba(Fe 1- x Co x ) 2 As 2 in the underdoped region. The crystals were detwinned via application of in-plane uniaxial stress, enabling measurements of single domain electronic structure in the orthorhombic state. At low temperatures, our results clearly demonstrate an in-plane electronic anisotropy characterized by a large energy splitting of two orthogonal bands with dominant d xz and d yz character, which is consistent with anisotropy observed by other probes. For compositions x > 0, for which the structural transition ( T S ) precedes the magnetic transition ( T SDW ), an anisotropic splitting is observed to develop above T SDW , indicating that it is specifically associated with T S . For unstressed crystals, the band splitting is observed close to T S , whereas for stressed crystals, the splitting is observed to considerably higher temperatures, revealing the presence of a surprisingly large in-plane nematic susceptibility in the electronic structure.

In-plane electronic anisotropy in underdopedBa(Fe1−xCox)2As2revealed by partial detwinning in a magnetic field

We present results of angle-dependent magnetoresistance measurements and direct optical images of underdoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ which reveal partial detwinning by action of a 14T magnetic field. Driven by a substantial magneto-elastic coupling, this result provides evidence for an electronic origin of the lattice distortion in underdoped iron pnictides. The observed anisotropy in these partially detwinned samples implies a substantial in-plane electronic anisotropy in the broken symmetry state, with a smaller resistivity along the antiferromagnetic ordering direction.

Magnetic properties of Bi2212 single crystals with Bi:Sr:Ca:Cu = 2:2:1:2

Bi2212 single crystals having various cation compositions were grown by the floating zone method and evaluated their magnetic properties and resistivity after control of oxygen content by post-annealing. The in-plane anisotropy in the normal state resistivity of Bi2212 single crystals systematically increased with approaching cation compositions to be stoichiometric, 2:2:1:2. This means that disorders in modulation structure due to cation nonstoichiometry strongly affects the in-plane electronic anisotropy of Bi2212. On the magnetic phase diagram under H// c, large differences were not found in the second peak behavior and first order transition (FOT) line of the vortex system between the cation stoichiometric and nonstoichiometric single crystals, while strong bulk pinning was effective up to the FOT line for the former crystals with their irreversibility lines just on the FOT line. In addition, the entropy change of the vortex at the FOT of cation stoichiometric crystals was apparently larger than that of conventional ones. These suggest that more homogeneous and strong superconductivity occurs in the cation stoichiometric “Bi2212” crystals.