The superconductor iron selenide (FeSe) is of intense interest owing to its unusual nonmagnetic nematic state and potential for high-temperature superconductivity. But its Cooper pairing mechanism ...has not been determined. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the electronic bands surrounding the G = (0, 0) and X = (p/aFe, 0) points of FeSe and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless and that they exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique, we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing that, in FeSe, is based preferentially on electrons from the dyz orbitals of the iron atoms.
High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave ...(CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states
(
) within the halo surrounding Bi
Sr
CaCu
O
vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric
(
) modulations with wave vectors
and
, with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO
unit-cell periodicity and coexisting with its secondary CDWs.
The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus ...generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold (6)Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a 'pair density wave' state. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi2Sr2CaCu2O8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. This phenomenology is consistent with Ginzburg-Landau theory when a charge density wave with d-symmetry form factor and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.
Full text
Available for:
IJS, KISLJ, NUK, SBMB, UL, UM, UPUK
The concept of intermediate asymptotics for the solution of an evolution equation with initial data and a related solution obtained without initial conditions was introduced by G.N. Barenblatt and ...Ya.B. Zeldovich in the context of extending the concept of strict determinism in statistical physics and quantum mechanics. Here, according to V.P. Maslov, to axiomatize the mathematical theory, we need to know the conditions satisfied by the initial data of the problem. We show that the correct solvability of a problem without initial conditions for fractional differential equations in a Banach space is a necessary, but not sufficient, condition for intermediate asymptotics. Examples of intermediate asymptotics are given.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
According to Ptolemy’s theorem, the product of the lengths of the diagonals of a quadrilateral inscribed in a circle on the Euclidean plane equals the sum of the products of the lengths of opposite ...sides. This theorem has various generalizations. In one of the generalizations on the plane, a quadrilateral is replaced with an inscribed hexagon. In this event the lengths of the sides and long diagonals of an inscribed hexagon is called Ptolemy’s theorem for a hexagon or Fuhrmann’s theorem. Casey’s theorem is another generalization of Ptolemy’s theorem. Four circles tangent to this circle appear instead of four points lying on some fixed circle whilst the lengths of the sides and diagonals are replaced by the lengths of the segments tangent to the circles. If the curvature of the Lobachevsky plane is
, then in the analogs of the theorems of Ptolemy, Fuhrmann and Casey for the polygons inscribed in a circle or circles tangent to one circle, the lengths of the corresponding segments, divided by 2, will be under the signs of hyperbolic sines. In this paper, we prove some theorems that generalize Casey’s theorem and Fuhrmann’s theorem on the Lobachevsky plane. The theorems involve six circles tangent to some line of constant curvature. We prove the assertions that generalize these theorems for the lengths of tangent segments. If, in addition to the lengths of the segments of the geodesic tangents, we consider the lengths of the arcs of the tangent horocycles, then there is a correspondence between the Euclidean and hyperbolic relations, which can be most clearly demonstrated if we take a set of horocycles tangent to one line of constant curvature on the Lobachevsky plane. In this case, if the length of the segment of the geodesic tangent to the horocycles is
, then the length of the “horocyclic” tangent to them is equal to
. Hence, if the geodesic tangents are connected by a “hyperbolic” relation, then the “horocyclic” tangents will be connected by the corresponding “Euclidean” relation.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based ...high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Z
of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Z
appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that Formula: see text, consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.
Full text
Available for:
IJS, KISLJ, NUK, SBMB, UL, UM, UPUK
The Dini helicoid is a surface obtained by a screw motion of the tractrix. In this paper, we consider various analogs of the Dini helicoid in the three-dimensional Minkowski space. As profiles, we ...take nontrivial pseudo-Euclidean analogs of the tractrix different from pseudo-Euclidean circles. We prove that on analogs of the Dini helicoid in a the pseudo-Euclidean space, one of the following metrics is induced: the metric of the Lobachevsky plane, the metric of the de Sitter plane, or a degenerate metric.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Within the framework of the theory of operator cosine functions and its application, a solution of the Dirichlet boundary value problem for the generalized Helmholtz equation in a strip is found and ...the correct solvability of this problem is established. The critical width of the strip is found depending on the boundary conditions. Applying this result to the problem of heat propagation in a dihedral angle allows us to determine the angle of correctness of this problem and specify the law of heat propagation in the considered region.
Using the operator functional relation Sh(
t
+
s
)+Sh(
t
−
s
) = 2
I
+2Sh
2
(
t
2
) Sh(
s
), Sh(0) = 0, we introduce and study the strongly continuous sine function Sh(
t
),
t
∈ (−∞, ∞), of linear ...bounded transformations acting in a complex Banach space
E
. Also, we study the cosine function Ch(
t
) given by the equation Ch(
t
) =
I
+ 2Sh
2
(
t
2
), where
I
is the identity operator in
E
.
The pair Ch(
t
) and Sh(
t
) is called an exponential trigonometric pair (ETP, in brief). For such pairs, we determine the generating operator (generator) by the equation Sh″ (0)
φ
= Ch″ (0)
φ
=
Aφ
and we give a criterion for
A
to be the generator of ETP. We find a connection between Sh(
t
) and the uniform well-posedness of the Cauchy problem with Krein’s condition for the equation
d
2
u
t
dt
2
=
Au
(
t
). This problem is uniformly well-posed if and only if
A
is the exponent generator of the sine function Sh(
t
). We introduce the concept of a bundle of several ETPs, which also forms an ETP, and we give a representation for bundle’s generator. The facts obtained significantly expand the applicability of operator methods to study the well-posedness of initial-boundary value problems.
Full text
Available for:
DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this work the possibility of using the IR intensity of the stretching vibration νs of proton donor group for estimation of hydrogen bond strength was investigated. For a set of complexes with ...FH···X (X = F, N, O) hydrogen bonds in the wide range of energies (0.1–49.2 kcal/mol) vibrational frequencies νs and their intensities A were calculated (CCSD at complete basis set limit). The validity of the previously proposed linear proportionality between the intensification of the stretching vibration νs in IR spectra and hydrogen bond enthalpy –ΔH = 12.2 ∆A (A. V. Iogansen, Spectrochimica Acta A 1999) was examined. It is shown that for a range of similar hydrogen bond types with complexation energies ∆E <15 kcal/mol the ∆E(∆A) function remains similar to that proposed in the Iogansen's work, while upon strengthening this dependency becomes significantly nonlinear. We examined two other parameters (∆Aνs and ∆A∙mR) related to IR intensity as descriptors of hydrogen bond strength which are proportional to transition dipole moment matrix element and mass‐independent dipole moment derivative. It was found that the dependency ∆E(∆Aνs) stays linear in the whole studied range of complexation energies and it can be used for evaluation of ∆E from infrared spectral data with the accuracy about 2 kcal/mol. The mass‐independent product ∆A∙mR is an appropriate descriptor for sets of complexes with various hydrogen bond types. Simple equations proposed in this work can be used for estimations of hydrogen bond strength in various systems, where experimental thermodynamic methods or direct calculations are difficult or even impossible.
Quantum‐chemical calculations of geometries and vibrational frequencies for a set of complexes with FH···X hydrogen bond (X = F, N, O) were performed. It is shown that the energy of a hydrogen bond is linearly proportional to the transition dipole moment matrix element, which, in turn, is proportional to the square root of the ratio of the absolute integrated intensity of proton donor group stretching and its frequency. Corresponding simple equations were proposed.
Full text
Available for:
BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
PDF
