Quantum Oscillation Studies of the Fermi Surface of LaFePO
A. Carrington, A. I. Coldea, J. D. Fletcher, N. E. Hussey, C. M. J. Andrew, A. F. Bangura, J. G. Analytis, J. -H. Chu, A. S. Erickson, I. R. Fisher, R. D. McDonald
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Submitted to Physica C special issue on iron-pnictide superconductors
We review recent experimental measurements of the Fermi surface of the iron-pnictide superconductor LaFePO using quantum oscillation techniques. These studies show that the Fermi surface topology is close to that predicted by first principles density functional theory calculations, consisting of quasi-two-dimensional electron-like and hole-like sheets. The total volume of the two hole sheets is almost equal to that of the two electron sheets, and the hole and electron Fermi surface sheets are close to a nesting condition. No evidence for the predicted three dimensional pocket arising from the Fe $d_{z^2}$ band is found. Measurements of the effective mass suggest a renormalisation of around two, close to the value for the overall band renormalisation found in recent angle resolved photoemission measurements.
We report extensive measurements of quantum oscillations in the normal state of the Fe-based superconductor LaFePO, (Tc ~ 6 K) using low temperature torque magnetometry and transport in high static magnetic fields (45 T). We find that the Fermi surface is in broad agreement with the band-structure calculations with the quasiparticle mass enhanced by a factor ~2. The quasi-two dimensional Fermi surface consist of nearly-nested electron and hole pockets, suggesting proximity to a spin/charge density wave instability.
We perform charge self-consistent LDA+DMFT (density functional theory combined with dynamical mean field theory) calculations to study correlation effects on the Fermi surfaces of the iron pnictide superconductors LaFePO and LiFeP. We find a distinctive change in the topology of the Fermi surface in both compounds where a hole pocket with Fe dz^2 orbital character changes its geometry from a closed shape in LDA to an open shape upon inclusion of correlations.
Photoemission spectroscopy is used to investigate the electronic structure of the newly discovered iron-based superconductors LaFeAsO_{1-x}F_x and LaFePO_{1-x}F_x. Line shapes of the Fe 2p core-level spectra suggest an itinerant character of Fe 3d electrons. The valence-band spectra are generally consistent with band-structure calculations except for the shifts of Fe 3d-derived peaks toward the Fermi level. From spectra taken in the Fe 3p -> 3d core-absorption region, we have obtained the experimental Fe 3d partial density of states, and explained it in terms of a band-structure calculation wi…
We investigate the electronic structures of iron-based superconductors having perovskite-like blocking layers, %Ca$_4$Al$_2$O$_6$Fe$_2$(As$_{1-x}$P$_x$)$_2$ from first principles. Ca$_4$Al$_2$O$_6$Fe$_2$P$_2$ and Ca$_4$Al$_2$O$_6$Fe$_2$As$_2$ from first principles. Ca$_4$Al$_2$O$_6$Fe$_2$P$_2$ is found to have two hole-like Fermi surfaces around $Γ$, and one hole-like Fermi surface around M in the unfolded Brillouin zone. This is in contrast with LaFePO, where no Fermi surface is found around M. The relationship of their band structures and measured transition temperatures of superconductivity…
Recent measurements of Fermi surface with de Haas-van Alphen oscillations in LaFePO showed a shrinking of the Fermi pockets with respect to first-principle LDA calculations, suggesting an energy shift of the hole and electrons bands with respect to LDA. We show that these shifts are a natural consequence of the strong particle-hole asymmetry of electronic bands in pnictides, and that they provide an indirect experimental evidence of a dominant interband scattering in these systems.
This paper reviews quantum oscillation studies of iron-pnictide superconductors and related materials. These measurements give unique information regarding the full three dimensional topology of the Fermi surfaces and the renormalisation of the quasi-particle masses. The review will cover measurements of the 122 arsenide end members, XFe_2As_2 (X = Ba, Sr, Ca) which have a spin density wave ground state, but will concentrate on the phosphide end members (LaFePO and XFe2P2) which have a paramagnetic ground state and a Fermi surface topology which is similar to the higher Tc superconducting iron…
We have studied the angular dependent de Haas-van Alphen oscillations of LaRu$_2$P$_2$ using magnetic torque in pulsed magnetic fields up to 60T. The observed oscillation frequencies are in excellent agreement with the geometry of the calculated Fermi surface. The temperature dependence of the oscillation amplitudes reveals effective masses m*($α$)=0.71 and m*($β$)=0.99 m$_e$, which are enhanced over the calculated band mass by $λ^{cyc}$ of 0.8. We find a similar enhancement $λ^γ \approx 1$ in comparing the measured electronic specific heat ($γ= 11.5$ mJ/mol K$^2$) with the total DOS from band…
We have performed an angle-resolved photoemission spectroscopy (ARPES) study of the iron-based superconductor PrFeAsO_{0.7} and examined the Fermi surfaces and band dispersions near the Fermi level. Heavily hole-doped electronic states have been observed due to the polar nature of the cleaved surfaces. Nevertheless, we have found that the ARPES spectra basically agree with band dispersions calculated in the local density approximation (LDA) if the bandwidth is reduced by a factor of ~2.5 and then the chemical potential is lowered by ~70 meV. Comparison with previous ARPES results on LaFePO rev…
When a metal is subjected to strong magnetic field B nearly all measurable quantities exhibit oscillations periodic in 1/B. Such quantum oscillations represent a canonical probe of the defining aspect of a metal, its Fermi surface (FS). In this study we establish a new mechanism for quantum oscillations which requires only finite segments of a FS to exist. Oscillations periodic in 1/B occur if the FS segments are terminated by a pairing gap. Our results reconcile the recent breakthrough experiments showing quantum oscillations in a cuprate superconductor YBCO, with a well-established result of…
The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+δ}$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and positions of these three peaks are almost independent of doping. This pattern has been explained previously by rather special, exquisitely detailed, Fermi-surface reconstruction. We propose that these MQO have a different origin, and their frequencies are related to the bilayer and inter-bilayer electron hopping rather than directly to the areas of tiny Fermi-surface po…
We address quantum oscillation experiments in high Tc superconductors and the evidence from these experiments for a pseudogap versus a Fermi liquid phase at high magnetic fields. As a concrete alternative to a Fermi liquid phase, the pseudogap state we consider derives from earlier work within a Gor'kov-based Landau level approach. Here the normal state pairing gap in the presence of high fields is spatially non-uniform, incorporating small gap values. These, in addition to d-wave gap nodes, are responsible for the persistence of quantum oscillations. Important here are methodologies for disti…
It is shown that coherent scatterings by an ordered vortex lattice are critically enhanced for quasi particles moving in cyclotron orbits on the Fermi surface through vortex core regions, thus generating significant quasi-periodic oscillating contributions to the SC free energy as a function of the inverse magnetic field. The mean frequency of the oscillation provides a fingerprint of the vortex lattice geometry. Vortex-lattice disorder, tends to suppress this oscillatory component.
We have studied the electronic structure of electron-doped cuprate superconductors via measurements of high-field Shubnikov-de Haas oscillations in thin films. In optimally doped Pr$_{2-x}$Ce$_{x}$CuO$_{4\pmδ}$ and La$_{2-x}$Ce$_{x}$CuO$_{4\pmδ}$, quantum oscillations indicate the presence of a small Fermi surface, demonstrating that electronic reconstruction is a general feature of the electron-doped cuprates, despite the location of the superconducting dome at very different doping levels. Negative high-field magnetoresistance is correlated with an anomalous low-temperature change in scatter…
In the search of topological superconductors, nailing down the Fermiology of the normal state is as crucial a prerequisite as unraveling the superconducting pairing symmetry. In particular, the number of time-reversal-invariant momenta in the Brillouin zone enclosed by Fermi surfaces is closely linked to the topological class of time-reversal-invariant systems, and can experimentally be investigated. We report here a detailed study of de Haas van Alphen quantum oscillations in single crystals of the topological semimetal CaSn$_{3}$ with torque magnetometry in high magnetic fields up to 35 T. I…
We present a numerical study of the field-angle resolved oscillations of the thermal conductivity and specific heat under rotated magnetic field in the $A_y$Fe$_{2-x}$Se$_2$ [$A$=K,Rb,Cs,(Tl,K)] superconductors, using realistic two-band Fermi surface parameterization. Our key finding is that even for isotropic pairing on an anisotropic Fermi surface, the thermodynamic quantities exhibit substantial oscillatory behavior in the superconducting state, even much below the upper critical field. Furthermore, in multiband systems the competition of anisotropies between two Fermi surfaces can cause a …
We present a study of the Fermi surface of KFe$_2$As$_2$ single crystals. Quantum oscillations were observed in magnetostriction measured down to 50 mK and in magnetic fields $H$ up to 14 T. For $H \parallel c$, the calculated effective masses are in agreement with recent de Haas-van Alphen and ARPES experiments, showing enhanced values with respect to the ones obtained from previous band calculations. For $H \parallel a$, we observed a small orbit at a cyclotron frequency of 64 T, characterized by an effective mass of $\sim 0.8 m_e$, supporting the presence of a three-dimensional pocket at th…
Within Bogoliubov-de Gennes theory, a semiclassical approximation is used to study quantum oscillations and to determine the Fermi surface area associated with these oscillations in a model of a $π$-striped superconductor, where the d-wave superconducting order parameter oscillates spatially with period 8 and zero average value. This system has a non-zero density of particle-hole states at the Fermi energy, which form Landau-like levels in the presence of a magnetic field, B. The Fermi surface is reconstructed via Andreev-Bragg scattering, and the semiclassical motion is along these Fermi surf…
Since the discovery of superconductivity in LaFePO in 2006, numerous iron-based superconductors have been identified within diverse structure families, all of which combine iron with a group-V (pnictogen) or group-VI (chalco- gen) element. Unconventional superconductivity is extremely rare among transition metal compounds outside these layered iron systems and the cuprates, and it is almost universally associated with highly anisotropic electronic properties and nearly 2D Fermi surface geometries. The iron-based intermetallic YFe$_2$Ge$_2$ features a 3D Fermi surface and a strongly enhanced lo…
According to the celebrated Onsagar-Lifshitz paradigm, the observation of Shubnikov de-Haas and de-Haas van Alphen (SdHvA) oscillations is an indication of the presence of `closed' orbit Fermi surface in the bulk. We present a real-space based calculation of SdHvA oscillations in generalized quasi-one-dimensional lattices by relaxing the quasi-classical approximations embedded in this decades old Onsagar-Lifshitz paradigm. We find that sizable quantum oscillation can arise from `open' Fermi surfaces as long as cyclotron orbits can form in real-space with finite, but not necessarily equal, elec…
We study underdoped high-Tc superconductors YBa2Cu3O6.5 and YBa2Cu4O8 using first-principles pseudopotential methods with additional Coulomb interactions at the Cu atoms, and obtain Fermi-surface pocket areas in close agreement with measured Shubnikov-de Haas and de Haas-van Alphen oscillations. With antiferromagnetic order in CuO2 planes, stable in the calculations, small hole pockets are formed near the so-called Fermi-arc positions in the Brillouin zone which reproduce the low-frequency oscillations. A large electron pocket, necessary for the negative Hall coefficient, is also formed in YBa…
We report on the direct probing of the Fermi surface in the bulk of the electron-doped superconductor Nd$_{2-x}$Ce$_x$CuO$_4$ at different doping levels by means of magnetoresistance quantum oscillations. Our data reveal a sharp qualitative change in the Fermi surface topology, due to translational symmetry breaking in the electronic system which occurs at a critical doping level significantly exceeding the optimal doping. This result implies that the $(π/a,π/a)$ ordering, known to exist at low doping levels, survives up to the overdoped superconducting regime.
We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a d-wave superconductor. Despite the angular dependence of the d-wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional s-wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-near…
We use quantum oscillation measurements to distinguish between spin and orbital components of the lowest energy quasiparticle excitations in YBa2Cu3O6.54, each of which couple differently to a magnetic field. Our measurements reveal the phase of the observed quantum oscillations to remain uninverted over a wide angular range, indicating that the twofold spin degeneracy of the Landau levels is virtually unaltered by the magnetic field. The inferred suppression of the spin degrees of freedom indicates a spin density-wave is responsible for creation of the small Fermi surface pockets in underdope…
We have observed Shubnikov-de Haas oscillations in FeSe. The Fermi surface deviates significantly from predictions of band-structure calculations and most likely consists of one electron and one hole thin cylinder. The carrier density is in the order of 0.01 carriers/ Fe, an order-of-magnitude smaller than predicted. Effective Fermi energies as small as 3.6 meV are estimated. These findings call for elaborate theoretical investigations incorporating both electronic correlations and orbital ordering.
Recent experiments have revealed incommensurate charge density wave (CDW) in the pseudogap regime in underdoped cuprates, e.g. YBa$_2$Cu$_3$O$_{6+δ}$ and HgBa$_2$CuO$_{4+δ}$. However, its relationship with the pseudogap is still controversial. In this work, we take a phenomenological synthesis of the doped resonating valence bond (RVB) state and the CDW order. Starting from the Yang-Rice-Zhang Green's function ansatz for the doped RVB state [Phys. Rev. B {\bf 73}, 174501 (2006)], in which the Fermi surface is partially truncated into four nodal hole-like Fermi pockets by the antinodal RVB gap,…
We argue that the low- frequency quantum oscillations observed recently in the vortex state of underdoped ortho II-YBCO have the same origin as in other strongly correlated electronic systems. Superconductivity driven by strong interactions on several Fermi surfaces creates proximity gaps on the other. The gap transferred on a small-sized pocket from larger Fermi surfaces is small. In case of unconventional pairing symmetry the induced gap is proportional to ratio of the oscillations' frequencies for small and large Fermi surfaces. The gap is in inverse proportion to mass enhancement on the la…
In this paper we explore whether the quantum oscillation signals recently observed in ortho-II YBa$_2$Cu$_3$O$_{6.5}$ may be explained by conventional density functional band-structure theory. Our calculations show that the Fermi surface of YBa$_2$Cu$_3$O$_{6.5}$ is extremely sensitive to small shifts in the relative positions of the bands. With rigid band shifts of around 30 meV small tubular pockets of Fermi surface develop around the Y point in the Brillouin zone. The cross-sectional areas and band masses of the quantum oscillatory orbits on these pockets are close to those observed. The di…
We study the crossover from strong to weak localization of hard-core bosons on a two dimensional honeycomb lattice in a magnetic field, as motivated by recent experiments on structured films. Taking into account long range Coulomb interactions among the bosons, an effective mobility edge in the excitation spectrum of the insulating Bose glass is identified as the (intensive) energy scale at which excitations become nearly delocalized. Within the forward scattering approximation in the bosonic hopping we find the effective mobility edge $ε_c$ to oscillate periodically with the magnetic flux per…
We report an angular quantum oscillation study of Tl_2Ba_2CuO_{6+delta} for two different doping levels (Tc = 10K and 26 K) and determine the Fermi surface size and topology in considerable detail. Our results show that Fermi liquid behavior is not confined to the edge of the superconducting dome and is robust up to at least T_c^{max}/3.5. Superconductivity is found to survive up to a larger doping p_c = 0.31 than in La_{2-x}Sr_xCuO_4. Our data imply that electronic inhomogeneity does not play a significant role in the loss of superconductivity and superfluid density in overdoped cuprates, and…
When immersed in a see of cold electrons, local impurities give rise to density modulations known as Friedel oscillations. In spite of the generality of this phenomenon, the exact shape of these modulations is usually computed only for non-interacting electrons with a quadratic dispersion relation. In actual materials, one needs to take into account several additional factors, such as (i) the details of the band structure, (ii) the lifetime of quasiparticles, (iii) in superconductors, the presence of a pairing gap. Studying how these effects influence Friedel oscillations is a viable way to ac…
We propose a quantum oscillation experiment by which the rotation of an underdoped YBa2Cu3O6+x sample about two different axes with respect to the orientation of the magnetic field can be used to infer the shape of the in-plane cross-section of corrugated Fermi surface cylinder(s). Deep corrugations in the Fermi surface are expected to give rise to nodes in the quantum oscillation amplitude that depend on the magnitude and orientation of the magnetic induction B. Because the symmetry of electron and hole cyclinders within the Brillouin zone are expected to be very different, the topology can p…
Despite the fact that 1111-type iron arsenides hold the record transition temperature of iron-based superconductors, their electronic structures have not been studied much because of the lack of high-quality single crystals. In this study, we completely determine the Fermi surface in the antiferromagnetic state of CaFeAsF, a 1111 iron-arsenide parent compound, by performing quantum oscillation measurements and band-structure calculations. The determined Fermi surface consists of a symmetry-related pair of Dirac electron cylinders and a normal hole cylinder. From analyses of quantum-oscillation…
Despite twenty years of research, the phase diagram of high transition- temperature superconductors remains enigmatic. A central issue is the origin of the differences in the physical properties of these copper oxides doped to opposite sides of the superconducting region. In the overdoped regime, the material behaves as a reasonably conventional metal, with a large Fermi surface. The underdoped regime, however, is highly anomalous and appears to have no coherent Fermi surface, but only disconnected "Fermi arcs". The fundamental question, then, is whether underdoped copper oxides have a Fermi s…
$ $The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $Φ$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor--normal-metal--superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/Φ$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower $\propto 1/\sqrtΦ$ when the magnetic length $l_m=\sqrt{\hbar/eB}$ drops…
