Anisotropic Fermi Surface Research Articles

Conductance of a tunnel point contact of noble metals in the presence of a single defect

In a previous paper [Ye. S. Avotina et al., Phys. Rev. B 74, 085411 (2006)], the effect of Fermi surface anisotropy on the conductance of a tunnel point contact with a single point-like defect situated in its vicinity was investigated theoretically. The oscillatory dependence of the conductance on the distance between the contact and the defect was found for a general Fermi surface geometry. In the present paper the method developed in the cited work is applied to the calculation of the conductance of noble metal contacts. An original algorithm, which enables the computation of the conductance for any parametrically specified Fermi surface, is proposed. On this basis a pattern of the conductance oscillations, which can be observed by the method of scanning tunneling microscopy, is obtained for different orientations of the surface for the noble metals.

Atomic Layer Thermopile Materials: Physics and Application

New types of thermoelectric materials characterized by highly anisotropic Fermi surfaces and thus anisotropic Seebeck coefficients are reviewed. Early studies revealed that there is an induced voltage in high TC oxide superconductors when the surface of the films is exposed to short light pulses. Subsequent investigations proved that the effect is due to anisotropic components of the Seebeck tensor, and the type of materials is referred to atomic layer thermopile (ALT). Our recent studies indicate that multilayer thin films at the nanoscale demonstrate enhanced ALT properties. This is in agreement with the prediction in seeking the larger figure of merit (ZT) thermoelectric materials in nanostructures. The study of ALT materials provides both deep insight of anisotropic transport property of these materials and at the same time potential materials for applications, such as light detector and microcooler. By measuring the ALT properties under various perturbations, it is found that the information on anisotropic transport properties can be provided. The information sometimes is not easily obtained by other tools due to the nanoscale phase coexistence in these materials. Also, some remained open questions and future development in this research direction have been well discussed.

Gapless Fermi surfaces in superconductingCeCoIn5

According to Tanatar et al. [Phys. Rev. Lett. 95, 067002 (2005)], the low-temperature thermal conductivity in ${\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}\mathrm{Co}{\mathrm{In}}_{5}$, a multiband $d$-wave superconductor, reveals unexpected dependence on the concentration of defects as if one or more Fermi surface sheets remained ungapped below superconducting transition. The interior gap superfluidity mechanism, or unbalanced pairing, recently proposed by Liu and Wilczek [Phys. Rev. Lett. 90, 047002 (2003)] has been invoked as a possible origin of gaplessness. We indicate that the Fermi surface anisotropy in the real $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_{5}$ makes this explanation highly implausible. We emphasize the fundamental difference between unbalanced pairing of different Fermi entities and the formation of superconducting gaps on Fermi surfaces belonging to different bands. We also argue that interband interactions between electrons always induce a finite order parameter on all Fermi surfaces below the temperature of a superconducting transition. We calculate specific heat and thermal conductivity in a two-band model for a $d$-wave superconductor in the presence of defects. In our simple model, superconductivity originates on one Fermi surface, inducing a smaller gap on the other one. Impurities diminish the induced gap and increase the density of states, restoring rapidly the Wiedemann-Franz law for this Fermi surface. Our calculations are in agreement with experiment.

Self-energy corrections to anisotropic Fermi surfaces

The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper-oxide superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is nontrivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.

Analytical Formulation of the Local Density of States around a Vortex Core in Unconventional Superconductors

On the basis of the quasiclassical theory of superconductivity, we obtain a formula for the local density of states (LDOS) around a vortex core of superconductors with anisotropic pair-potential and Fermi surface in arbitrary directions of magnetic fields. Earlier results on the LDOS of d -wave superconductors and NbSe 2 are naturally interpreted within our theory geometrically; the region with high intensity of the LDOS observed in numerical calculations turns out to the enveloping curve of the trajectory of Andreev bound states. We discuss experimental results on YNi 2 B 2 C within the quasiclassical theory of superconductivity.

Signature of Fermi-surface anisotropy in point contact conductance in the presence of defects

In a previous paper (Avotina et al.,Phys. Rev. B Vol.71, 115430 (2005)) we have shown that in principle it is possible to image the defect positions below a metal surface by means of a scanning tunnelling microscope. The principle relies on the interference of electron waves scattered on the defects, which give rise to small but measurable conductance fluctuations. Whereas in that work the band structure was assumed to be free-electron like, here we investigate the effects of Fermi surface anisotropy. We demonstrate that the amplitude and period of the conductance oscillations are determined by the local geometry of the Fermi surface. The signal results from those points for which the electron velocity is directed along the vector connecting the point contact to the defect. For a general Fermi surface geometry the position of the maximum amplitude of the conductance oscillations is not found for the tip directly above the defect. We have determined optimal conditions for determination of defect positions in metals with closed and open Fermi surfaces.

Effect of the four-sheet Fermi surface on magnetoresistivity of MgB2

Recent experimental data of anisotropic magnetoresistivity measured in MgB2 films have shown an intriguing behaviour: the angular dependence of magnetoresistivity changes dramatically with temperature and disorder. In order to explain such phenomenology, in this work, we extend our previous analyses on multiband transverse magnetoresistivity in magnesium diboride, by calculating its analytic expression, assuming a constant anisotropic Fermi surface mass tensor. The calculation is done for arbitrary orientation of the magnetic field with respect to the crystalline axes and for the current density either perpendicular or parallel to the magnetic field. This approach allows to extract quite univocally the values of the scattering times in the s- and p- bands by fitting experimental data with a simple analytic expression. We also extend the analysis to the magnetoresistivity of polycrystalline samples, with an arbitrary angle between the current density and the magnetic field, taking into account the anisotropy of each randomly oriented grain. Thereby, we propose magnetoresistivity as a very powerful characterization tool to explore the effect of disorder by irradiation or selective doping as well as of phonon scattering in each one of the two types of bands, in single crystals and polycrystalline samples, which is a crucial issue in the study of magnesium diboride.

Fermi surface and thermoelectric power of (Bi1−x Sbx)2Te3<Ag, Sn> mixed crystals

The Fermi surface anisotropy of (Bi1−x Sbx)2Te3 single crystals (0.25 ≤ x ≤ 1) was studied by analyzing the angular dependence of the frequency of Shubnikov-de Haas oscillations and the effect of tin and silver doping on the thermoelectric power in these crystals in the temperature range 77 ≤ T ≤ 300 K. It was shown that silver doping of (Bi1−x Sbx)2Te3 mixed crystals produces acceptors, while silver in Bi2Te3 acts as a donor. Tin also exhibits acceptor properties. Both tin and silver doping of p-(Bi1−x Sbx)2Te3 mixed crystals decrease the thermoelectric power due to an increase in the hole concentration.

Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature Tc, the regionT c⪯ T ⪯ T* is a vast fluctuation regime.T c andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field Hc2 bounding the superconducting response and the pseudogap closing field Hpg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi2Sr2CaCu2O8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field Hc2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.

Hall effect in organic layered conductors

The Hall effect in organic layered conductors with a multisheeted Fermi surfaces was considered. It is shown that the experimental study of Hall effect and magnetoresistance anisotropy at different orientations of current and a quantizing magnetic field relative to the layers makes it possible to determine the contribution of various charge carriers groups to the conductivity, and to find out the character of Fermi surface anisotropy in the plane of layers

Control of the electronic state in a series of Pd(dmit) 2 salts, a strongly correlated electron system with a quasi-triangular lattice structure

Pressure effects on β′-type Pd(dmit) 2 anion radical salts, which belong to a strongly correlated electron system with a quasi-triangular lattice of dimerized Pd(dmit) 2 units, were studied with X-ray crystal structure analysis and resistivity measurements. The electronic state of this system is governed by various parameters including the effective on-site Coulomb energy on the dimer ( U eff.), the band width ( W), the degree of frustration, and the degree of band-filling. X-ray crystal structure analysis under hydrostatic pressure at low temperatures was performed for the Et 2Me 2P salt The tight-binding band calculations based on structural data indicate that the application of hydrostatic pressure reduces the electron correlation effect and leads the system from the Mott insulating state to the metallic state accompanied by the superconductivity. Further application of hydrostatic pressure induces another non-metallic behavior. This would originate from a partial nesting of the anisotropic Fermi surface associated with a structural transition which removes the glide plane and the two-fold axis. Based on cation dependence in the pressure effect, we propose a possible interplay of the correlation and the frustration, and discuss the uniaxial strain effect for this unique strongly correlated electron system.

Vortex-lattice symmetry nearTcinYNi2B2C

Detailed high-resolution small-angle neutron diffraction measurements have been used to determine the structural phase diagram of the vortex lattice (VL) in $\mathrm{Y}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ with $\mathbit{H}\ensuremath{\Vert}\mathbit{c}$. At low temperatures $(T⪡{T}_{c})$ the first-order 45\ifmmode^\circ\else\textdegree\fi{} reorientation transition at a field ${H}_{1}(T)$ and second-order rhombic to square transition, ${H}_{2}(T)$ have previously been described by the effects of Fermi surface (FS) anisotropy and nonlocality. ${H}_{1}(T)$ decreases while ${H}_{2}(T)$ increases with increasing temperature. Measurements of the VL structure as close to the upper critical field ${T}_{c2}(H)$ as is currently experimentally feasible show no evidence of significant upward curvature or reentrance of ${H}_{2}$ that is expected when thermal fluctuations suppress nonlocality. For fields ${H}_{1}(T)<H<{H}_{2}(T)$ the VL remains rhombic and shows no sign of becoming hexagonal close to ${T}_{c2}(H)$. Our data suggest that an underlying electronic asymmetry, other than FS and nonlocal effects and likely due to an anisotropic superconducting gap, controls the VL structure close to ${T}_{c2}(H)$.

Anisotropic Diamagnetic Response in Type-II Superconductors with Gap and Fermi-Surface Anisotropies

The effects of anisotropic gap structures on a diamagnetic response are investigated in order to demonstrate that the field-angle-resolved magnetization [ML(chi)] measurement can be used as a spectroscopic method to detect gap structures. Our microscopic calculation based on the quasiclassical Eilenberger formalism reveals that ML(chi) in a superconductor with a fourfold gap displays a fourfold oscillation reflecting the gap and Fermi-surface anisotropies, and the sign of this oscillation changes at a field between Hc1 and Hc2. As a prototype of unconventional superconductors, magnetization data for borocarbides are also discussed.

Ab initiocalculations ofHc2in type-II superconductors: Basic formalism and model calculations

Detailed Fermi-surface structures are essential to describe the upper critical field ${H}_{c2}$ in type-II superconductors, as first noticed by and Hohenberg and Werthamer [Phys. Rev. 153, 493 (1967)] and shown explicitly by Butler for high-purity cubic Niobium [Phys. Rev. Lett. 44, 1516 (1980)]. We derive an ${H}_{c2}$ equation for classic type-II superconductors that is applicable to systems with anisotropic Fermi surfaces and/or energy gaps under arbitrary field directions. It can be solved efficiently by using Fermi surfaces from ab initio electronic-structure calculations. Thus, it is expected to enhance our quantitative understanding on ${H}_{c2}$. Based on the formalism, we calculate ${H}_{c2}$ curves for Fermi surfaces of a three-dimensional tight-binding model with cubic symmetry, an isotropic gap, and no impurity scatterings. It is found that, as the Fermi surface approaches to the Brillouin zone boundary, the reduced critical field $h*(T∕{T}_{c})$, which is normalized by the initial slope at ${T}_{c}$, is enhanced significantly over the curve for the spherical Fermi surface with a marked upward curvature. Thus, the Fermi-surface anisotropy can be a main source of the upward curvature in ${H}_{c2}$ near ${T}_{c}$.

Ab Initio Calculations of Hc2 for Nb, NbSe2, and MgB2

We report on quantitative calculations of the upper critical field $H_{c2}$ for clean type-II superconductors Nb, NbSe$_{2}$, and MgB$_{2}$ using Fermi surfaces from {\em ab initio} electronic structure calculations. The results for Nb and NbSe$_2$ excellently reproduce both temperature and directional dependences of measured $H_{c2}$ curves without any adjustable parameters, including marked upward curvature of NbSe$_{2}$ near $T_{c}$. As for MgB$_2$, a good fit is obtained for a $\pi / \sigma$ gap ratio of $\sim 0.3$, which is close to the value from a first-principles strong-coupling theory [H. J. Choi \textit{et al}. Nature, \textbf{418} 758 (2002)]. Our results indicate essential importance of Fermi surface anisotropy for describing $H_{c2}$.

Modulated vortex lattice in high fields and gap nodes

The mean field vortex phase diagram of a quasi-two-dimensional superconductor with a nodal $d$-wave pairing and with strong Pauli spin depairing is studied in the parallel field case in order to examine the effect of gap nodes on the stability of a Fulde-Ferrell-Larkin-Ovchinnikov- (FFLO-) like vortex lattice. We find through a heuristic argument and a model calculation with a fourfold anisotropic Fermi surface that the FFLO-like state is relatively suppressed as the field approaches a nodal direction. When taking account of available experimental results together, the present result strongly suggests that the pairing symmetry of ${\text{CeCoIn}}_{5}$ should be of ${d}_{xy}$ type.

Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors

Quasiclassic Uzadel equations for two-band superconductors in the dirty limit with the account of both intraband and interband scattering by nonmagnetic impurities are derived for any anisotropic Fermi surface. From these equations the Ginzburg-Landau equations, and the critical temperature $T_c$ are obtained. An equation for the upper critical field, which determines both the temperature dependence of $H_{c2}(T)$ and the orientational dependence of $H_{c2}(\theta)$ as a function of the angle $\theta$ between ${\bf H}$ and the c-axis is obtained. It is shown that the shape of the $H_{c2}(T)$ curve essentially depends on the ratio of the intraband electron diffusivities $D_1$ and $D_1$, and can be very different from the standard one-gap dirty limit theory. In particular, the value $H_{c2}(0)$ can considerably exceed $0.7T_cdH_{c2}/dT_c$, which can have important consequences for applications of $MgB_2$. A scaling relation is proposed which enables one to obtain the angular dependence of $H_{c2}(\theta)$ from the equation for $H_{c2}$ at ${\bf H}\| c$. It is shown that, depending on the relation between $D_1$ and $D_2$, the ratio of the upper critical field $H_{c2}^\|/H_{c2}^\perp$ for ${\bf H}\| ab$ and ${\bf H}\perp ab$ can both increase and decrease as the temperature decreases. Implications of the obtained results for $MgB_2$ are discussed.

Superconductivity of SrTiO $ \mathsf {_{3-\delta}}$

Superconducting SrTiO_{3-\delta} was obtained by annealing single crystalline SrTiO_3 samples in ultra high vacuum. An analysis of the V(I) characteristics revealed very small critical currents I_c which can be traced back to a unavoidable doping inhomogeneity. R(T) curves were measured for a range of magnetic fields B at I<<I_c, thereby probing only the sample regions with the highest doping level. The resulting curves B_{c2}(T) show upward curvature, both at small and strong doping. These results are discussed in the context of bipolaronic and conventional superconductivity with Fermi surface anisotropy. We conclude that the special superconducting properties of SrTiO_{3-\delta} can be related to its Fermi surface and compare this finding with properties of the recently discovered superconductor MgB_2.

Fermi surface and low temperature structure in (DMET-TSeF)2Au(CN)2

The title compound is one of the DMET-TSeF salts which are quasi-one-dimensional organic metals at room temperatures. We show that the compound has a closed Fermi surface using the angle-dependent magnetoresistance oscillation (AMRO) method together with magnetoresistance and magnetization quantum oscillation measurements at low temperatures. By the X-ray measurement, we confirm that the structural phase transition observed around 180 K is related to the anomaly observed in the temperature dependence of the resistivity [1]. The nesting vector has the direction of 0.5a*+0.5c*. The obtained low temperature closed Fermi surface has about 4 % of the first Brillouin zone area. The AMRO data show the existence of a very anisotropic Fermi surface where the diameter perpendicular to the most conducting a direction is about 0.5 c*. The possible origin of the low temperature closed Fermi surface is discussed and the relation to the ordering of anion molecules is considered as the probable reason.

Vortex lattice structures in tetragonal BCS superconductors due to Fermi surface anisotropy

We investigate vortex lattice (VL) structures of tetragonal strongly type II BCS superconductors in the clean limit for the case H||c. Anisotropy of the Fermi surface is assumed small and treated as a perturbation. Location of the line in the T–B plane separating square and rhombic VLs is found.