Fermi surfaces of the topological semimetal CaSn$_{3}$ probed through de Haas van Alphen oscillations
K A M Hasan Siddiquee, Riffat Munir, Charuni Dissanayake, Xinzhe Hu, Swapnil Yadav, Yasumasa Takano, Eun Sang Choi, Duy Le, Talat S Rahman, Yasuyuki Nakajima
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7 pages, 7 figures, accepted for publication in Journal of Physics: Condensed Matter
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. In conjunction with density functional theory based calculations, the observed quantum oscillations frequencies indicate that the Fermi surfaces of CaSn$_{3}$ enclose an odd number of time-reversal-invariant momenta, satisfying one of the proposed criteria to realize topological superconductivity. Nonzero Berry phases extracted from the magnetic oscillations also support the nontrivial topological nature of CaSn$_{3}$.
We show how the de Haas-van Alphen effect can be used to directly measure the magnitude of spin-orbit coupling in non-centrosymmetric metals, such as CePt3Si and LaPt3Si.
Deploying a recently developed semiclassical theory of quasiparticles in the superconducting state we study the de Haas-van Alphen effect. We find that the oscillations have the same frequency as in the normal state but their amplitude is reduced. We find an analytic formulae for this damping which is due to tunnelling between semiclassical quasiparticle orbits comprising both particle-like and hole-like segments. The quantitative predictions of the theory are consistent with the available data.
We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along extremal orbits is relevant for the magnitude of the extra damping, thereby providing a support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which gives a good fit to the numerical results.
We present detailed results for the amplitude and field dependence of the de Haas-van Alphen (dHvA) signal arising from the electron-like $π$ sheet of Fermi surface in MgB_2. Our data and analysis show that the dip in dHvA amplitude when the field is close to the basal plane is caused by a beat between two very similar dHvA frequencies and not a spin-zero effect as previously assumed. Our results imply that the Stoner enhancement factors in MgB_2 are small on both the Sigma and Pi sheets.
Recently, Borisenko et al have posted a Comment (arXiv:1108.1159) where they suggest an alternative interpretation of our de Haas-van Alphen (dHvA) measurements on the superconductor LiFeAs. In our original paper (arXiv:1107.4375) we concluded that our measurements of the bulk Fermi surface were not consistent with the surface bands observed thus far by ARPES. Borisenko et al dispute this and suggest the two measurements are consistent if some of the orbits we observe are due to magnetic breakdown. We argue here that this scenario is inconsistent with the experimental data and therefore that o…
We report measurements of the Fermi surface (FS) of the ternary phosphide SrFe$_2$P$_2$ using the de Haas-van Alphen effect. The calculated FS of this compound is very similar to SrFe$_2$As$_2$, the parent compound of the high temperature superconductors. Our data show that the Fermi surface is composed of two electron and two hole sheets in agreement with bandstructure calculations. Several of the sheets show strong c-axis warping emphasizing the importance of three-dimensionality in the non-magnetic state of the ternary pnictides. We find that the electron and hole pockets have a different t…
We report measurements of the de Haas-van Alphen effect for single crystals of MgB$_2$, in magnetic fields up to 32 Tesla. In contrast to our earlier work, dHvA orbits from all four sheets of the Fermi surface were detected. Our results are in good overall agreement with calculations of the electronic structure and the electron-phonon mass enhancements of the various orbits, but there are some small quantitative discrepancies. In particular, systematic differences in the relative volumes of the Fermi surface sheets and the magnitudes of the electron-phonon coupling constants could be large eno…
Recent reports on quantum oscillations in MgB2 provide valuable information on three important aspects of this material: (1) electronic structure near the Fermi level, (2) disparity of the electron-phonon interaction between the two systems of bands (3) renormalization of spin susceptibility. However, extraction of most of this information requires highly accurate band structure calculations of the relevant quantities. In this paper we provide such calculations and use them to analyze the experimental data.
Understanding the superconducting properties of MgB_2 is based strongly on knowledge of its electronic structure. In this paper we review experimental measurements of the Fermi surface parameters of pure and Al-doped MgB_2 using the de Haas-van Alphen (dHvA) effect. In general, the measurements are in excellent agreement with the theoretical predictions of the electronic structure, including the strength of the electron-phonon coupling on each Fermi surface sheet. For the Al doped samples, we are able to measure how the band structure changes with doping and again these are in excellent agreem…
We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB_2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from 0.44-0.68 m_e. By comparing these with band masses calculated recently by three groups, we find that the electron-phonon coupling strength lam…
We report a de Haas-van Alphen (dHvA) study of the electronic structure of Al doped crystals of MgB$_2$. We have measured crystals with $\sim 7.5$% Al which have a $T_c$ of 33.6 K, ($\sim 14$% lower than pure MgB$_2$). dHvA frequencies for the $σ$ tube orbits in the doped samples are lower than in pure MgB$_2$, implying a $16\pm2%$ reduction in the number of holes in this sheet of Fermi surface. The mass of the quasiparticles on the larger $σ$ orbit is lighter than the pure case indicating a reduction in electron-phonon coupling constant $λ$. These observations are compared with band structure…
The de Haas-van Alphen-frequencies as well as the effective masses for a magnetic field parallel to the crystallographic c-axis are calculated within the local spin density approximation (LSDA) for MgB2 and TaB2. In addition, we analyze the plasma frequencies computed for each Fermi surface sheet. We find a large anisotropy of Fermi velocities in MgB2 in difference to the nearly isotropic behavior in TaB2. We compare calculations performed within the relativistic non-full potential augmented-spherical-wave (ASW) scheme and the scalar-relativistic full potential local orbital (FPLO) scheme. A s…
The de Haas-van Alphen (dHvA) signal arising from orbits on the $π$ Fermi surface sheet of the two-gap superconductor MgB$_2$ has been observed in the vortex state below $H_{c2}$. An extra attenuation of the dHvA signal, beyond those effects described in the conventional Lifshitz-Kosevich expression, is seen due to the opening of the superconducting gap. Our data show that the $π$ band gap is still present up to $H_{c2}$. The data are compared to current theories of dHvA oscillations in the superconducting state which allow us to extract estimates for the evolution of the $π$ band gap with mag…
Measurements of the de Haas - van Alphen effect have been carried out on the heavy fermion anti-ferromagnet CeRhIn5 at temperatures between 25 mK and 500 mK under pressure. We present some preliminary results of our measurements to track the evolution of the Fermi surface as the pressure induced superconducting transition is approached.
We report herein the nontrivial topological states in an intrinsic type-II superconductor BaSn5 (Tc ~ 4.4 K) probed via measuring the magnetizations, specific heat, de Haas-van Alphen (dHvA) effect and performing first principles calculations. The first principles calculations reveal a topological nodal ring structure centering at the H point in the kz = π plane of the Brillouin zone (BZ), which could be gapped by spin-orbit coupling (SOC), yielding rather small gaps below and above the Fermi level about 0.04 eV and 0.14 eV, respectively. The SOC also results in a pair of Dirac points along th…
We calculate the de Haas-van Alphen (dHvA) effect waveform using the canonical ensemble for different Fermi surface scenarios applicable to the underdoped cuprate superconductor YBa2Cu3O6.5, in which quantum oscillations have recently been observed. The harmonic content of the dHvA waveform of the principal F ~ 500 T frequency is consistent with the existence of a second thermodynamically dominant section of Fermi surface that acts primarily as a charge reservoir. Oscillations in the charge density to and from this reservoir are shown to potentially contribute to the observed large quantum osc…
In a recent preprint Putzke et al. argued that their dHvA data on LiFeAs are in good agreement with DFT calculations and contradict our ARPES results. Here we show that the situation is just the opposite.
A new algorithm for extracting de Haas-van Alphen frequencies and effective masses from calculated band energies is presented. The algorithm creates an interpolated k-space "super cell," which is broken into slices perpendicular to the desired magnetic field direction. Fermi surface orbits are located within each slice, and de Haas-van Alphen frequencies and effective masses are calculated. Orbits are then matched across slices, and extremal orbits determined. This technique has been successful in locating extremal orbits not previously noticed in the complicated topology of existing UPt3 band…
The three-dimensional Fermi surface morphology of superconducting BaFe_2(As_0.37}P_0.63)_2 with T_c=9K, is determined using the de Haas-van Alphen effect (dHvA). The inner electron pocket has a similar area and k_z interplane warping to the observed hole pocket, revealing that the Fermi surfaces are geometrically well nested in the (π,π) direction. These results are in stark contrast to the Fermiology of the non-superconducting phosphides (x=1), and therefore suggests an important role for nesting in pnictide superconductivity.
We report measurements of the de Haas-van Alphen (DHVA) effect and AC susceptibility in the layered organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The amplitude of the DHVA oscillations is attenuated over a wide field range above the irreversibility line, B_irr(B), below which a rigid flux lattice is formed. Thus the DHVA effect provides a unique probe of the superconducting fluctuations at high fields in this material. We compare our measurements with other determinations of the superconducting phase diagram of $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$.
Magnetic torque measurements have been performed on a KOs$_2$O$_6$ single crystal in magnetic fields up to 35.3 T and at temperatures down to 0.6 K. The upper critical field is determined to be $\sim$30 T. De Haas-van Alphen oscillations are observed. A large mass enhancement of (1+$λ$) = $m^* / m_{band}$ = 7.6 is found. It is suggested that, for the large upper critical field to be reconciled with Pauli paramagnetic limiting, the observed mass enhancement must be of electron-phonon origin for the most part.
The de Haas-van Alphen effect was observed in the underdoped cuprate YBa$_2$Cu$_3$O$_{6.5}$ via a torque technique in pulsed magnetic fields up to 59 T. Above an irreversibility field of $\sim$30 T, the magnetization exhibits clear quantum oscillations with a single frequency of 540 T and a cyclotron mass of 1.76 times the free electron mass, in excellent agreement with previously observed Shubnikov-de Haas oscillations. The oscillations obey the standard Lifshitz-Kosevich formula of Fermi-liquid theory. This thermodynamic observation of quantum oscillations confirms the existence of a well-de…
The de Haas - van Alphen (dHvA) effect in the cluster superconductor ZrB12 was studied by magnetic torque measurements in magnetic fields up to 28 T at temperatures down to 0.35 K. The dHvA oscillations due to orbits from the Neck sections and "Cubic Box" of the Fermi surface were detected. We measured cyclotron effective masses of 0.5m_0 for Neck section of the FS. The dHvA frequencies as well as the cyclotron effective masses were calculated using the full potential Linear Muffin-Tin Orbital (LMTO) method within the Generalized Gradient Approximation. Comparison of the angular dependence of …
We report on a band structure calculation and de Haas-van Alphen measurements of KFe$_2$As$_2$. Three cylindrical Fermi surfaces are found. Effective masses of electrons range from 6 to 18$m_e$, $m_e$ being the free electron mass. Remarkable discrepancies between the calculated and observed Fermi surface areas and the large mass enhancement ($\gtrsim 3$) highlight the importance of electronic correlations in determining the electronic structures of iron pnicitide superconductors.
The Landau expansion for the free energy of the superconducting mixed state near the upper critical field in powers of the square modulus of the order parameter averaged over Abrikosov lattice is derived. The analytical calculations has been carried out in frame of Gor'kov formalism for 3-dimensional isotropic BCS model beyond the limits of quasiclassical approximation, another words with Landau quantization of the quasiparticle energy levels taken into consideration. The derivation is performed at low temperature and high enough but finite crystal's purity. The effect of Pauli paramagnetic te…
By improving the experimental conditions and extensive data accumulation, we have achieved very high-precision in the measurements of the de Haas-van Alphen effect in the underdoped high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{6.5}$. We find that the main oscillation, so far believed to be single-frequency, is composed of three closely spaced frequencies. We attribute this to bilayer splitting and warping of a single quasi-2D Fermi surface, indicating that \emph{c}-axis coherence is restored at low temperature in underdoped cuprates. Our results do not support the existence of a larger…
Theory of quasiparticle spectra and the de Haas-van Alphen (dHvA) oscillation in type-II superconductors are developed based on the Bogoliubov-de Gennes equations for vortex-lattice states. As the pair potential grows through the superconducting transition, each degenerate Landau level in the normal state splits into quasiparticle bands in the magnetic Brillouin zone. This brings Landau-level broadening, which in turn leads to the extra dHvA oscillation damping in the vortex state. We perform extensive numerical calculations for three-dimensional systems with various gap structures. It is ther…
Here, we present a de Haas-van Alphen (dHvA) effect1 study on the newly discovered LaFeAsO1-xFx compounds2,3 in order to unveil the topography of the Fermi surface associated with their antiferromagnetic and superconducting phases, which is essential for understanding their magnetism, pairing symmetry and superconducting mechanism. Calculations 4 and surface-sensitive measurements 5,6,7 provided early guidance, but lead to contradictory results, generating a need for a direct experimental probe of their bulk Fermi surface. In antiferromagnetic LaFeAsO1-xFx 8,9 we observe a complex pattern in t…
We report a de Haas-van Alphen (dHvA) oscillation study of the 111 iron pnictide superconductors LiFeAs with T_c ~18K and LiFeP with T_c~5K. We find that for both compounds the Fermi surface topology is in good agreement with density functional band-structure calculations and shows quasi-nested electron and hole bands. The effective masses generally show significant enhancement, up to ~3 for LiFeP and ~5 for LiFeAs. However, one hole Fermi surface in LiFeP shows a very small enhancement, as compared with its other sheets. This difference probably results from k-dependent coupling to spin fluct…
Recent observations of slow magneto-oscillations in some underdoped cuprate superconductors are one of the most striking discoveries in the field of superconductivity since many probes of underdoped cuprates clearly point to a non Fermi-liquid normal state. We show that a large magnitude and strong magnetic-field dependence of the residual resistance invalidate the conventional interpretation of the magneto-oscillations as a normal-state dHvA effect. We propose that the oscillations are most likely caused by a quantum interference of vortex and crystal lattice modulations of the order paramete…
Comprehensive magnetic-field-orientation dependent studies of the susceptibility and de Haas-van Alphen effect have been carried out on single crystals of the filled skutterudites PrOs$_4$As$_{12}$ and LaOs$_4$As$_{12}$ using magnetic fields of up to 40~T. Several peaks are observed in the low-field susceptibility of PrOs$_4$As$_{12}$, corresponding to cascades of metamagnetic transitions separating the low-field antiferromagnetic and high-field paramagnetic metal (PMM) phases. The de Haas-van Alphen experiments show that the Fermi-surface topologies of PrOs$_4$As$_{12}$ in its PMM phase and L…
LiFeAs is unique among the arsenic based Fe-pnictide superconductors because it is the only nearly stoichiometric compound which does not exhibit magnetic order. This is at odds with electronic structure calculations which and a very stable magnetic state and predict cylindrical hole- and electron-like Fermi surface sheets whose geometry suggests spin uctuations and a possible instability toward long-range ordering at the nesting vector. In fact, a complex magnetic phase-diagram is indeed observed in the isostructural NaFeAs compound. Previous angle resolved photoemission (ARPES) experiments r…
We have performed de Haas-van Alphen (dHvA) measurements of the heavy-fermion superconductor CeCoIn$_5$ down to 2 mK above the upper critical field. We find that the dHvA amplitudes show an anomalous suppression, concomitantly with a shift of the dHvA frequency, below the transition temperature $T_{\rm n}=20$ mK. We suggest that the change is owing to magnetic breakdown caused by a field-induced antiferromagnetic (AFM) state emerging below $T_{\rm n}$, revealing the origin of the field-induced quantum critical point (QCP) in CeCoIn$_5$. The field dependence of $T_{\rm n}$ is found to be very w…
We report a critical analysis of the electronic structures and de Haas-van Alphen (dHvA) quantities of the heavy-fermion superconductors CeCoIn$_5$, CeRhIn$_5$, and CeIrIn$_5$. The electronic structures are investigated {\it ab initio} on the basis of full-potential band-structure calculations, adopting both the scalar- and fully relativistic formulations within the framework of the local spin-density approximation (LSDA). In contrast to another recent study, in which a pronounced change of the Fermi surface due to relativistic effects and therefore the importance of relativistic interactions …
The recent confirmation of closed Fermi surface in the high temperature cuprates via de Haas-van Alphen and Shubnikov-de haas oscillations calls for a theoretical investigation of the origin of such oscillations. We study de Haas-van Alphen oscillations and magnetic breakdown in the context of ortho-II high temperature cuprates to understand the origin of the multiple frequencies. We find that the magnetic breakdown is highly sensitive not only to the ortho-II potential, but also to the Fermi surface topology, and is thus useful to distinguish between various theoretical proposals related to q…
The negative-U impurity stripes confining the edge channels of semiconductor quantum wells are shown to allow the effective cooling inside in the process of the spin-dependent transport. The aforesaid promotes also the creation of composite bosons and fermions by the capture of single magnetic flux quanta on the edge channels under the conditions of low sheet density of carriers, thus opening new opportunities for the registration of the quantum kinetic phenomena in weak magnetic fields at high temperatures up to the room temperature. As a certain version noted above we present the first findi…
Topological materials which are also superconducting are of great current interest, since they may exhibit a non-trivial topologically-mediated superconducting phase. Although there have been many reports of pressure-tuned or chemical-doping-induced superconductivity in a variety of topological materials, there have been few examples of intrinsic, ambient pressure superconductivity in a topological system having a stoichiometric composition. Here, we report that the pure intermetallic CaSn3 not only exhibits topological fermion properties but also has a superconducting phase at 1.178 K under a…
We have completely determined the Fermi surface in KFe$_2$As$_2$ via de Haas-van Alphen (dHvA) measurements. Fundamental frequencies $ε$, $α$, $ζ$, and $β$ are observed in KFe$_2$As$_2$. The first one is attributed to a hole cylinder near the X point of the Brillouin zone, while the others to hole cylinders at the $Γ$ point. We also observe magnetic breakdown frequencies between $α$ and $ζ$ and suggest a plausible explanation for them. The experimental frequencies show deviations from frequencies predicted by band structure calculations. Large effective masses up to 19 $m_e$ for $B \parallel c…
We report the first observation of the de Haas-van Alphen (dHvA) effect in the novel spin-triplet superconductor UTe2 using high quality single crystals with the high residual resistivity ratio (RRR) over 200. The dHvA frequencies, named alpha and beta, are detected for the field directions between c and a-axes. The frequency of branch beta increases rapidly with the field angle tilted from c to a-axis, while branch alpha splits, owing to the maximal and minimal cross-sectional areas from the same Fermi surface. Both dHvA branches, alpha and beta reveal two kinds of cylindrical Fermi surfaces …
Measurements of the de Haas-van Alphen effect in CexLa1-xRhIn5 reveal that the Ce 4f electrons remain localized for all x, with the mass enhancement and progressive loss of one spin from the de Haas-van Alphen signal resulting from spin fluctuation effects. This behavior may be typical of antiferromagnetic heavy fermion compounds, inspite of the fact that the 4f electron localization in CeRhIn5 is driven, in part, by a spin-density wave instability.
The quasi-two-dimensional organic superconductor beta-(BEDT-TTF)_2SF_5CH_2CF_2SO_3 (T_c approx 4.4 K)shows very strong Shubnikov-de Haas (SdH) oscillations which are superimposed on a highly anomalous steady background magnetoresistance, R_b. Comparison with de Haas- van Alphen oscillations allow a reliable estimate of R_b which is crucial for the correct extraction of the SdH signal. At low temperatures and high magnetic fields insulating behavior evolves. The magnetoresistance data violate Kohler's rule, i.e., cannot be described within the framework of semiclassical transport theory, but co…
Energy spectrum of electrons (holes) doped into a two-dimensional antiferromagnetic insulator is quantized in an external magnetic field of arbitrary direction. A peculiar dependence of de Haas-van Alphen (dHvA) or Shubnikov-de Haas (SdH) magneto-oscillation amplitudes on the azimuthal in-plane angle from the magnetization direction and on the polar angle from the out-of-plane direction is found, which can be used as a sensitive probe of the antiferromagnetic order in doped Mott-Hubbard, spin-density wave (SDW), and conventional band-structure insulators.
We report a study of the de Haas-van Alphen effect in the normal state of the ferromagnetic superconductor ZrZn2. Our results are generally consistent with an LMTO band structure calculation which predicts four exchange-split Fermi surface sheets. Quasiparticle effective masses are enhanced by a factor of about 4.9 implying a strong coupling to magnetic excitations or phonons. Our measurements provide insight in to the mechanism for superconductivity and unusual thermodynamic properties of ZrZn2.
We report the observation of the de Haas-van Alphen effect in IrTe2 measured using torque magnetometry at low temperatures down to 0.4 K and in high magnetic fields up to 33T. IrTe2 undergoes a major structural transition around 283 K due to the formation of planes of Ir and Te dimers that cut diagonally through the lattice planes, with its electronic structure predicted to change significantly from a layered system with predominantly three-dimensional character to a tilted quasi-two dimensional Fermi surface. Quantum oscillations provide direct confirmation of this unusual tilted Fermi surfac…
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.
We report the Shubnikov-de Haas (SdH) oscillations observed in the vortex liquid state of the quasi two dimensional organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The SdH oscillations can be observed down to about 5 T at 0.5 K, where the flux flow resistivity becomes as small as about 30 % of the normal state value. Below the upper critical field $H_{\rm c2}$ of about 7 T, the additional damping of the SdH oscillation amplitude appears, as well as that of the de Haas-van Alphen (dHvA) oscillations, with respect to the normal state one which is described with the standard Lifshitz-Ko…
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…
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…
