Quantum Oscillation Measurements Research Articles

Reply to “Comment on ‘Magnetotransport signatures of a single nodal electron pocket constructed from Fermi arcs' ”

In a recent manuscript, we showed how an electron pocket in the shape of a diamond with concave sides could potentially explain changes in sign of the Hall coefficient R_H in the underdoped high-Tc cuprates as a function of magnetic field and temperature. For simplicity, this Fermi surface is assumed to be constructed from arcs of a circle connected at vertices which is an idea borrowed from Banik and Overhauser. Such a diamond-shaped pocket is proposed to be the product of biaxial charge-density wave order, which was subsequently confirmed in x-ray scattering experiments. Since those x-ray scattering experiments were performed, the biaxial Fermi surface reconstruction scheme has garnered widespread support in the scientific literature. It has been shown to accurately account for the cross-section of the Fermi surface pocket observed in quantum oscillation measurements, the sign and behavior of the Hall coefficient, the size of the high magnetic field electronic contribution to the heat capacity and more recently the form of the angle-dependent magnetoresistance.In their comment, Chakravarty and Wang raise several important questions relating to the validity of the Hall coefficient we calculated for such a diamond-shaped Fermi surface pocket. These questions concern specifically (1) whether a change in sign of the Hall coefficient R_H with magnetic field and temperature is dependent on a `special' form for the rounding of the vertices, (2) whether a pocket of such a geometry can produce quantum oscillations in R_H in the absence of other Fermi surface sections and (3) whether a reconstructed Fermi surface consisting of a single pocket is less `natural' than one consisting of multiple pockets. Below we consider each of these in turn.

Cascade of Magnetic-Field-Induced Lifshitz Transitions in the Ferromagnetic Kondo Lattice Material YbNi_{4}P_{2}.

A ferromagnetic quantum critical point is thought not to exist in two- and three-dimensional metallic systems yet is realized in the Kondo lattice compound YbNi_{4}(P,As)_{2}, possibly due to its one-dimensionality. It is crucial to investigate the dimensionality of the Fermi surface of YbNi_{4}P_{2} experimentally, but common probes such as angle-resolved photoemission spectroscopy and quantum oscillation measurements are lacking. Here, we study the magnetic-field dependence of transport and thermodynamic properties of YbNi_{4}P_{2}. The Kondo effect is continuously suppressed, and additionally we identify nine Lifshitz transitions between 0.4 and 18T. We analyze the transport coefficients in detail and identify the type of Lifshitz transitions as neck or void type to gain information on the Fermi surface of YbNi_{4}P_{2}. The large number of Lifshitz transitions observed within this small energy window is unprecedented and results from the particular flat renormalized band structure with strong 4f-electron character shaped by the Kondo lattice effect.

Separation of electron and hole dynamics in the semimetal LaSb

We report investigations on the magnetotransport in LaSb, which exhibits extremely large magnetoresistance (XMR). Foremost, we demonstrate that the resistivity plateau can be explained without invoking topological protection. We then determine the Fermi surface from Shubnikov - de Haas (SdH) quantum oscillation measurements and find good agreement with the bulk Fermi pockets derived from first principle calculations. Using a semiclassical theory and the experimentally determined Fermi pocket anisotropies, we quantitatively describe the orbital magnetoresistance, including its angle dependence. We show that the origin of XMR in LaSb lies in its high mobility with diminishing Hall effect, where the high mobility leads to a strong magnetic field dependence of the longitudinal magnetoconductance. Unlike a one-band material, when a system has two or more bands (Fermi pockets) with electron and hole carriers, the added conductance arising from the Hall effect is reduced, hence revealing the latent XMR enabled by the longitudinal magnetoconductance. With diminishing Hall effect, the magnetoresistivity is simply the inverse of the longitudinal magnetoconductivity, enabling the differentiation of the electron and hole contributions to the XMR, which varies with the strength and orientation of the magnetic field. This work demonstrates a convenient way to separate the dynamics of the charge carriers and to uncover the origin of XMR in multi-band materials with anisotropic Fermi surfaces. Our approach can be readily applied to other XMR materials.

Origin of the extremely large magnetoresistance in the semimetal YSb

Electron-hole (e-h) compensation is a hallmark of multi-band semimetals with extremely large magnetoresistance (XMR) and has been considered to be the basis for XMR. Recent spectroscopic experiments, however, reveal that YSb with non-saturating magnetoresistance is uncompensated, questioning the e-h compensation scenario for XMR. Here we demonstrate with magnetoresistivity and angle dependent Shubnikov - de Haas (SdH) quantum oscillation measurements that YSb does have nearly perfect e-h compensation, with a density ratio of $0.95$ for electrons and holes. The density and mobility anisotropy of the charge carriers revealed in the SdH experiments allow us to quantitatively describe the magnetoresistance with an anisotropic multi-band model that includes contributions from all Fermi pockets. We elucidate the role of compensated multi-bands in the occurrence of XMR by demonstrating the evolution of calculated magnetoresistances for a single band and for various combinations of electron and hole Fermi pockets.

Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS

Whereas the discovery of Dirac- and Weyl-type excitations in electronic systems is a major breakthrough in recent condensed matter physics, finding appropriate materials for fundamental physics and technological applications is an experimental challenge. In all of the reported materials, linear dispersion survives only up to a few hundred millielectronvolts from the Dirac or Weyl nodes. On the other hand, real materials are subject to uncontrolled doping during preparation and thermal effect near room temperature can hinder the rich physics. In ZrSiS, angle-resolved photoemission spectroscopy measurements have shown an unusually robust linear dispersion (up to [Formula: see text]2 eV) with multiple nondegenerate Dirac nodes. In this context, we present the magnetotransport study on ZrSiS crystal, which represents a large family of materials (WHM with W = Zr, Hf; H = Si, Ge, Sn; M = O, S, Se, Te) with identical band topology. Along with extremely large and nonsaturating magnetoresistance (MR), [Formula: see text]1.4 [Formula: see text] 105% at 2 K and 9 T, it shows strong anisotropy, depending on the direction of the magnetic field. Quantum oscillation and Hall effect measurements have revealed large hole and small electron Fermi pockets. A nontrivial [Formula: see text] Berry phase confirms the Dirac fermionic nature for both types of charge carriers. The long-sought relativistic phenomenon of massless Dirac fermions, known as the Adler-Bell-Jackiw chiral anomaly, has also been observed.

Ideal charge-density-wave order in the high-field state of superconducting YBCO

The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa2Cu3O2 (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field ([Formula: see text]) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO2 planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to [Formula: see text], given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an "ideal" disorder-free cuprate.

Fermi Surface Reconstruction and Drop in the Hall Number due to Spiral Antiferromagnetism in High-T_{c} Cuprates.

We show that a Fermi surface reconstruction due to spiral antiferromagnetic order may explain the rapid change in the Hall number as recently observed near optimal doping in cuprate superconductors [Badoux etal., Nature (London) 531, 210 (2016)]. The single-particle spectral function in the spiral state exhibits hole pockets which look like Fermi arcs due to a strong momentum dependence of the spectral weight. Adding charge-density wave order further reduces the Fermi surface to a single electron pocket. We propose quantum oscillation measurements to distinguish between commensurate and spiral antiferromagnetic order. Similar results apply to certain metals in which topological order replaces antiferromagnetic order.

Compensated Semimetal LaSb with Unsaturated Magnetoresistance.

By combining angle-resolved photoemission spectroscopy and quantum oscillation measurements, we performed a comprehensive investigation on the electronic structure of LaSb, which exhibits near-quadratic extremely large magnetoresistance (XMR) without any sign of saturation at magnetic fields as high as 40T. We clearly resolve one spherical and one intersecting-ellipsoidal hole Fermi surfaces (FSs) at the Brillouin zone (BZ) center Γ and one ellipsoidal electron FS at the BZ boundary X. The hole and electron carriers calculated from the enclosed FS volumes are perfectly compensated, and the carrier compensation is unaffected by temperature. We further reveal that LaSb is topologically trivial but shares many similarities with the Weyl semimetal TaAs family in the bulk electronic structure. Based on these results, we have examined the mechanisms that have been proposed so far to explain the near-quadratic XMR in semimetals.

Experimental determination of the Fermi surface ofSr3Ir4Sn13

The stannide family of materials A3T4Sn13 (A = La,Sr,Ca, T = Ir,Rh) is interesting due to the interplay between a tunable lattice instability and phonon-mediated superconductivity with Tc ~ 5-7 K. In Sr3Ir4Sn13 a structural transition temperature T* ~ 147 K associated with this instability has been reported, which is believed to result from a superlattice distortion of the high temperature phase on cooling. Here we report the first experimental study of the electronic structure of a member of this material family - Sr3Ir4Sn13 through measurements of quantum oscillations and comparison with density functional theory calculations. Our measurements reveal good agreement with theory using the lattice parameters consistent with a body-centred cubic lattice of symmetry I-43d of the low temperature phase. The study of the fermiology of Sr3Ir4Sn13 we present here should help inform models of multiband superconductivity in the superconducting stannides.

Superconducting subphase in the layered perovskite ruthenateSr2RuO4in a parallel magnetic field

Magnetic torque measurements using a microcantilever have been performed to investigate the superconducting phase of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ down to 40 mK. For high-quality single crystals with the transition temperature $({T}_{\mathrm{c}})$ of 1.48--1.49 K, an abrupt jump of the torque signal is found near 1.5 T in field parallel to the conducting ${\mathrm{RuO}}_{2}$ planes below $\ensuremath{\sim}0.8\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The jump corresponds to the first order transition recently revealed by magnetocaloric and magnetization measurements [Yonezawa et al., Phys. Rev. Lett. 110, 077003 (2013); Kittaka et al., Phys. Rev. B 90, 220502(R) (2014)]. Furthermore, weak diamagnetic and irreversible signals are found to persist above the first order transition up to 1.85 T. The result indicates the presence of a subphase boundary separating low- and high-field phases in the superconducting phase. The high-field subphase disappears when the field is tilted from the conducting planes only by a few degrees. Quantum oscillation measurements are also reported to clarify the strong sample-quality dependence of the high-field subphase.

Quantum oscillations and the Fermi surface topology of the Weyl semimetal NbP

The Weyl semimetal NbP was found to exhibit topological Fermi arcs and exotic magneto-transport properties. Here, we report on magnetic quantum-oscillation measurements on NbP and construct the 3D Fermi surface with the help of band-structure calculations. We reveal a pair of spin-orbit-split electron pockets at the Fermi energy and a similar pair of hole pockets, all of which are strongly anisotropic. The Fermi surface well explains the linear magnetoresistance observed in high magnetic fields by the quantum-limit scenario. The Weyl points that are located in the $k_z \approx \pi/c$ plane are found to exist 5 meV above the Fermi energy. Therefore, we predict that the chiral anomaly effect can be realized in NbP by electron doping to drive the Fermi energy to the Weyl points.

Fermi surface reconstruction and quantum oscillations in underdopedYBa2Cu3O7−xmodeled in a single bilayer with mirror symmetry broken by charge density waves

Hole-doped high-temperature cuprate superconductors below optimum doping have small electron-like Fermi surfaces occupying a small fraction of the Brillouin zone. There is strong evidence that this is linked to charge density wave (CDW) order, which reconstructs the large hole-like Fermi surfaces predicted by band structure calculations . Recent experiments have revealed the structure of the two CDW components in the benchmark bilayer material YBa$_2$Cu$_3$O$_{7-x}$ in high field where quantum oscillation (QO) measurements are performed. We have combined these results with a tight-binding description of the bands in an isolated bilayer to give a minimal model revealing the essential physics of the situation. Here we show that this approach, combined with the effects of spin-orbit interactions and the pseudogap, gives a good qualitative description of the multiple frequencies seen in the QO observations in this material. Magnetic breakdown through weak CDW splitting of the bands will lead to a field-dependence of the QO spectrum and to the observed fourfold symmetry of the results in tilted fields.

Fragile charge order in the nonsuperconducting ground state of the underdoped high-temperature superconductors

The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3(6+δ). Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveals similar Fermi surface properties to YBa2Cu3(6+δ), despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa2Cu3(6+δ). Fermi surface reconstruction in YBa2Cu4O8 is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations.

Model of Electronic Structure and Superconductivity in Orbitally Ordered FeSe.

We provide a band structure with low-energy properties consistent with recent photoemission and quantum oscillation measurements on FeSe, assuming mean-field-like site- and/or bond-centered ferro-orbital ordering at the structural transition. We show how the resulting model provides a consistent explanation of the temperature dependence of the measured Knight shift and the spin-relaxation rate. Furthermore, the superconducting gap structure obtained from spin-fluctuation theory exhibits nodes on the electron pockets, consistent with the V-shaped density of states obtained by tunneling spectroscopy on this material, and the temperature dependence of the London penetration depth.

Nodal bilayer-splitting controlled by spin-orbit interactions in underdoped high-Tc cuprates.

The highest superconducting transition temperatures in the cuprates are achieved in bilayer and trilayer systems, highlighting the importance of interlayer interactions for high Tc. It has been argued that interlayer hybridization vanishes along the nodal directions by way of a specific pattern of orbital overlap. Recent quantum oscillation measurements in bilayer cuprates have provided evidence for a residual bilayer-splitting at the nodes that is sufficiently small to enable magnetic breakdown tunneling at the nodes. Here we show that several key features of the experimental data can be understood in terms of weak spin-orbit interactions naturally present in bilayer systems, whose primary effect is to cause the magnetic breakdown to be accompanied by a spin flip. These features can now be understood to include the equidistant set of three quantum oscillation frequencies, the asymmetry of the quantum oscillation amplitudes in c-axis transport compared to ab-plane transport, and the anomalous magnetic field angle dependence of the amplitude of the side frequencies suggestive of small effective g-factors. We suggest that spin-orbit interactions in bilayer systems can further affect the structure of the nodal quasiparticle spectrum in the superconducting phase. PACS numbers: 71.45.Lr, 71.20.Ps, 71.18.+y

Development of non-metallic diamond anvil cell and quantum oscillation measurement of CePt2ln7 in a pulsed-magnet

In order to combine the extreme conditions of high pressure and magnetic field, we have developed a non-metallic diamond anvil cell to avoid Joule-heating in a pulsed-magnetic field. Although the cell is deformed with loading, a maximum pressure of ~ 8.5 GPa can be applied. Quantum oscillation measurements using tunnel diode oscillator have been performed for heavy fermion antiferromagnet CePt2In7 in a pulsed field and at ambient pressure. The detail of the pressure cell and field-induced Fermi surface changes of CePt2In7 are discussed.

Diagnosing a strong topological insulator by quantum oscillations

We show how quantum oscillation measurements of surface states in an insulator may allow to diagnose a strong topological insulator and distinguish it from its weak or topologically trivial counterpart. The criterion is defined by the parity of the number of fundamental frequencies in the surface-state quantum oscillation spectrum: an even number of frequencies implies a weak or a topologically trivial insulator, whereas an odd number points to a strong topological insulator. We also discuss various aspects and issues related to applying this criterion in practice.

Quantum Oscillations in Hole-Doped Cuprates

One of the leading challenges of condensed matter physics in the past few decades is an understanding of the high-temperature copper-oxide superconductors. Although the d-wave character of the superconducting state is well understood, the normal state in the underdoped regime has eluded understanding. Here, we review the past few years of quantum oscillation measurements performed in the underdoped cuprates that have culminated in an understanding of the normal ground state of these materials. A nodal electron pocket created by charge order is found to characterize the normal ground state in YBa2Cu3O6+δand is likely universal to a majority of the cuprate superconductors. An open question remains regarding the origin of the suppression of the antinodal density of states at the Fermi energy in the underdoped normal state, either from mainly charge correlations or, more likely, from mainly pairing and/or magnetic correlations that precede charge order.

Quantum oscillations inEuFe2As2single crystals

Quantum oscillation measurements can provide important information about the Fermi surface (FS) properties of strongly correlated metals. Here, we report a Shubnikov-de Haas (SdH) effect study on the pnictide parent compounds EuFe$_{2}$As$_{2}$ (Eu122) and BaFe$_{2}$As$_{2}$ (Ba122) grown by In-flux. Although both members are isovalent compounds with approximately the same density of states at the Fermi level, our results reveal subtle changes in their fermiology. Eu122 displays a complex pattern in the Fourier spectrum, with band splitting, magnetic breakdown orbits, and effective masses sistematically larger when compared to Ba122, indicating that the former is a more correlated metal. Moreover, the observed pockets in Eu122 are more isotropic and 3D-like, suggesting an equal contribution from the Fe $3d$ orbitals to the FS. We speculate that these FS changes may be responsible for the higher spin-density wave ordering temperature in Eu122.

Tunable line node semimetals

Weyl semimetals are examples of a new class of topological states of matter, which are gapless in the bulk with protected surface states. Their low-energy sector is characterized by massless chiral fermions, which are robust against translationally invariant perturbations. A variant of these systems has two nondegenerate bands touching along lines rather than points. A proposal to realize such a phase involves alternating layers of topological insulators and magnetic insulators, where the magnetization lies perpendicular to the symmetry axis of the heterostructure. The shape, size, and the dispersion in the vicinity of the nodal lines varies with the strength of the magnetization, offering a new knob to control the properties of the system. In this paper, we map out the evolution of the nodal lines and the dependence of the conductivity on magnetization and identify signatures of the low-energy sector in quantum oscillation measurements.