A high-temperature superconductor sample with numerous internal Josephson junctions formed by atomic layers is a nonlinear system with unique dynamic properties. An external magnetic field penetrates in the sample in the form of moving Josephson vortices, which generate radiation. It has been shown that this radiation in a Bi2 + xSr2 – xCuO6 + δ (Bi2201) single crystal can be detected by means of a Josephson junction on a microbreak (break junction) directly inside the single crystal.

It has been more than 30 years since the discovery of high-temperature superconductors (HTSCs). The number of articles published on the subject is huge, but the cause of the high superconducting transition temperature T c is still an open question. The so-called ‘pseudogap’ HTSC phase — an anomalous ‘normal’ state — turned out to be as complicated a problem as high-temperature superconductivity itself. Its role remains unexplained. We discuss here only key experimental results with the aim to demonstrate the complexity and intricacy arising in the explanation of problems related to the nature of this unique phenomenon.

The dynamics of a Josephson vortex lattice in a superconducting single crystal of a one-layered high-temperature Bi2201 superconductor in parallel high magnetic fields is studied. Periodic oscillations in wide temperature and magnetic field ranges are detected in the magnetic field dependence of the flux flow resistance of Josephson vortices measured in the direction perpendicular to the layers, which is induced by the motion of the voltage vortices. The results assume that the observed oscillations are associated with the motion of a rectangular vortex lattice between the layers and matching with the transverse size of the single crystal.

Despite a large number of publications proving that a number of different materials can be classified as topological insulators, unambiguous proofs of the existence of promising topological superconductors have not been obtained as yet. The implementation of such systems is important not only for solid state physics, but also for applications, because topological superconductors can be used in quantum computers. We have made an attempt to confirm experimentally the assumption put forth in a number of theoretical publications that FeSe x Te 1 – x with the s -wave pairing, which is the simplest iron-containing superconductors, can become, under certain conditions, a topological superconductor with the π-wave pairing, which must have a superconducting gap in the bulk and the Majorana gapless surface states.

The basic concepts behind topological insulators are briefly reviewed. After discussing what makes some insulators topological and giving a brief history of this rapidly growing field, recent successes in experiments with these exotic materials are discussed.

It is demonstrated that the copper-doped high-quality Bi Se single crystals with a high density of bulk charge carriers are certainly 3D topological insulators. The analysis of quantum Shubnikov−de Haas (SdH) oscillations reveals that these materials simultaneously exhibit two types of such oscillations determined by the Landau levels related to both the 3D and 2D Fermi surfaces.

Two-dimensional (2D) Shubnikov–de Haas oscillations and 2D Hall oscillations are observed in 3D copper-doped Bi2Se3 single crystals in magnetic fields up to 19.5 T at temperatures down to 0.3 K. Three samples with a high bulk carrier concentration (n ≈ 1019–1020 cm–3) are studied. The rotation of the samples in a magnetic field shows that these oscillations are related to numerous parallel 2D conducting channels 1–5 nm thick. Their basic kinetic parameters are found. Quantized Hall resistance R xy is detected in 1-nm-thick 2D conducting channels at high fields. The distance Δ(1/R xy ) between the steps in the field dependence of 1/R xy is found to be constant for different Landau levels, 1.3e 2/h per 1-nm-thick layer. The constructed fan diagrams of 2D Landau levels for various angles of sample inclination with respect to the magnetic field direction allowed us to conclude that the Berry phase in the 2D conducting channels is γ ≈ π and independent of the magnetic field direction. When studying the angular dependence of upper resistive critical magnetic field H c2 in one of the superconducting samples, we showed that it can be considered as a bulk superconductor consisting of superconducting layers with an effective thickness of about 50 nm.

We present a careful study of the resistive superconducting transition in FeSe single crystals down to T = 40mK in continuous magnetic fields up to 30 T applied perpendicular and parallel to the ab plane. In the H parallel to c geometry the temperature dependence of the resistive upper critical field H-c2*, determined as the field at which the in-plane resistivity in the transition region is 90% of the normal state resistivity is down to temperatures T/T-c < 0.006, is in close agreement with the Werthamer-Helfand-Hohenberg (WHH) theoretical curve which describes the behavior of the upper critical field in conventional type-II superconductors. In contrast, for the H parallel to ab geometry, the data depart from the WHH model with increasing applied magnetic field according to the paramagnetic limitation of superconductivity. An anisotropy parameter gamma in our FeSe crystals decreases with decreasing temperature and FeSe becomes nearly isotropic when the temperature T -> 0. DOI: 10.1103/PhysRevB.87.134512

Plate-like β-FeSe0.90 crystals have been gro-wn. The composition, structure, and some superconducting characteristics of these crystals are studied. The critical magnetic field H c2(0) and the coherence length ξ are estimated; the energy gap is measured.

The observation of Shubnikov-de Haas and Hall oscillations in high-quality Bi 2 − x Cu x Se 3 single crystals is reported. Measurements carried out upon rotating the samples with respect to the magnetic field demonstrate that the oscillations originate from two-dimensional surface states in three-dimensional single crystals and are determined only by the perpendicular component of the magnetic field.

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The magnetic field and temperature dependence of the in-plane tunneling conductance dI/dV(V) in high-quality nonsuperconducting (down to 10 mK) layered oxycarbonate Bi2+xSr4-xCu2CO3O8+δ single crystals has been investigated using break junctions. Combining measurements of the in-plane magnetoresistivity ρab(T,H) and the magnetotunnelling, we present evidence for the existence of a small "pseudogap" in a nonsuperconducting cuprate, without local incoherent pairs or any correlation phenomena associated with superconductivity. We are unable to distinguish if such a "pseudogap" is totally unrelated to superconductivity or if its existence is a necessary condition for the subsequent occurrence of superconductivity with increasing carrier density in the sample.

The magnetic-field-dependent in-plane tunneling conductance $dI/dV(V)$ on the ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ single crystals has been investigated using break junctions. In contrast to previous tunneling measurements of Bi2212, where the position of the gap peak in $dI/dV(V)$ remained almost unchanged in the applied magnetic fields, our data present evidence that the magnetic field suppresses the superconducting gap in Bi2212. The behavior of a dip-hump structure in tunnel spectra indicates that the magnetic field acts differently on the gap and pseudogap and suggests that the pseudogap does not correlate with the existence of a superconducting gap.

The magnetic-field-dependent in-plane tunneling conductance dI/dV(V) on the Bi2Sr2CaCu2O8+delta single crystals has been investigated using break junctions. In contrast to previous tunneling measurements of Bi2212, where the position of the gap peak in dI/dV(V) remained almost unchanged in the applied magnetic fields, our data present evidence that the magnetic field suppresses the superconducting gap in Bi2212. The behavior of a dip-hump structure in tunnel spectra indicates that the magnetic field acts differently on the gap and pseudogap and suggests that the pseudogap does not correlate with the existence of a superconducting gap.

Superconductor-insulator-superconductor (SIS) tunnel junctions have been used to investigate the enhancement of superconductivity in a single-crystal Bi2212 high-T-c superconductor in the presence of gigahertz-microwave radiation. When the microwave power is increased at constant temperature, the break-junction tunneling spectra show that the energy gap increases several times.

Superconductor-insulator-superconductor (SIS) tunnel junctions have been used to investigate the enhancement of superconductivity in a single-crystal Bi2212 high-${T}_{c}$ superconductor in the presence of gigahertz-microwave radiation. When the microwave power is increased at constant temperature, the break-junction tunneling spectra show that the energy gap increases several times.

We have investigated the in-plane I-V characteristics and the Josephson-vortex flow resistance in high-quality La-free Bi2+xSr2-xCuO6+delta (Bi-2201) single crystals in parallel and tilted magnetic fields at temperatures down to 40 mK. For parallel magnetic fields below the resistive upper critical field H-c2*, the I-V characteristics obey a power law with a smooth change with increasing magnetic field of the exponent from above 5 down to 1. In contrast to the double-layer cuprate Bi-2212, the observed smooth change suggests that there is no change in the mechanism of dissipation (no Kosterlitz-Thouless transition) over the range of temperatures investigated. At small angles between the applied field and the ab plane, prominent current steps in the I-V characteristics and periodic oscillations of Josephson-vortex flow resistance are observed. While the current steps are periodic in the voltage at constant fields, the voltage position of the steps, together with the flux-flow voltage, increases nonlinearly with magnetic field. The ab-flow resistance oscillates as a function of field with a constant period over a wide range of magnetic fields and temperatures. The current steps in the I-V characteristics and the flow resistance oscillations can be linked to the motion of Josephson vortices across layers.

We have investigated the in-plane $I(V)$ characteristics and the Josephson vortex flow resistance in high-quality La-free Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$ (Bi2201) single crystals in parallel and tilted magnetic fields at temperatures down to 40 mK. For parallel magnetic fields below the resistive upper critical field $H^{*}_{c2}$, the $I(V)$ characteristic obey a power-law with a smooth change with increasing magnetic-field of the exponent from above 5 down to 1. In contrast to the double-layer cuprate Bi2212, the observed smooth change suggests that there is no change in the mechanism of dissipation (no Kosterlitz-Thouless transition) over the range of temperatures investigated. At small angles between the applied field and the $ab$-plane, prominent current steps in the $I(V)$ characteristics and periodic oscillations of Josephson-vortex flow resistance are observed. While the current steps are periodic in the voltage at constant fields, the voltage position of the steps, together with the flux-flow voltage, increases nonlinearly with magnetic field. The $ab$-flow resistance oscillates as a function of field with a constant period over a wide range of magnetic fields and temperatures. The current steps in the $I(V)$ characteristics and the flow resistance oscillations can be linked to the motion of Josephson vortices across layers.

We have investigated the out-of-plane magnetotransport [rho(c)(H,T)] in a series of high-quality La-free Bi2+xSr2-xCuO6+delta (Bi2201) single crystals with a wide range of doping and over a wide range of temperatures down to 25 mK. For the measurements we have used pulsed magnetic fields up to 55 T and a resistive magnet up to 28 T with various field orientations relative to the ab plane of the crystal. Combining measurements of rho(c)(H) and the interlayer magnetotunneling, we present evidence that in high-T-c superconductors, the maximum in rho(c)(H) at the peak field H-c(p) is associated with the loss of phase coherence along the c axis, with a crossover from Josephson to quasiparticle tunneling. We find that H-c(p) is much less than the upper critical field H-c2. We show that the c-axis conductivity above the maximum in rho(c)(H) can be described by the functional form sigma(c)=sigma(0) exp(-Delta(0)/g mu H-B) and the slope in the ln sigma(c) versus 1/H plot allows us to determine a gap Delta(0). The doping dependence of Delta(0) and that of T-c have their maximum at the same doping. Unexpectedly, Delta(0) is similar in size to the superconducting energy gap. An interpretation of these observation based on the singlet formation as the origin of the pseudogap is proposed.