My research activity may be subdivided in two general parts: (classical) electronic properties of metals and high-temperature superconductivity. The latter involves a large variety of properties which I have been attempting to investigate: the normal state transport properties (the thermal conductivity, thermoelectric power (the Seebeck coefficient), in-plane and out-of-plane resistivities), magnetic properties in the superconducting state (mainly - the non-equilibrium magnetization), and the out-of-plane transport properties of high-T_c materials both in the normal and superconducting states. The out-of-plane (or c-axis) transport measurements turned to be very rich in physics and new effects, like intrinsic Josephson effect. I consider these to represent my main achievements in the field and likely be the subject of my near future studies, see p.4).

In the chronological order:

1) In 1982-87 I worked at Kapitza Institute, Moscow, first as a trainee, and then – as a PhD-student on a problem of detecting the van Hove singularities in the electronic spectra of common metals through measurements of their thermoelectric power S under the action of pressure P (or doping), which may change the Fermi-level E_F of electronic liquid in metals, thus pushing it towards the possible singularity in the electronic spectra. For instance, when the Fermi-level "touches" the bottom of the some otherwise empty zone from below, a new electronic-like part (void) of the Fermi-surface (FS) appears, see the picture. The elastic scattering of electrons by impurities can kick an electron from the main (large) part of the Fermi surface over to that small (new) one, where electrons have a negligibly small group velocity v(E).

This leads to a singularity in the energy-dependent mean free path l(E,P) = l₀(E) + d l(E,P) of electrons; dl = 0 for P<P_c, and dl ¹0 for P>P_c, P_c is the "critical" value of the pressure, at which FS acquires a new part. Since the size of the new part is very small, the probability of scattering on to it is also very small. This means that dl(E)<< l₀(E), and therefore there is no chances to detect it by measuring the electrical resistivity. However, the Seebeck coefficient of metals is proportional to l’(E),

which makes it to be sensitive to topological changes of FS. It has been theoretically shown¹, that the Seebeck coefficient as a function of pressure (or doping) should have a singularity ~ ±Re(P-P_c)^-1/2, see the picture above. The particular sign depends on whether the electron- or hole- like parts of FS appear or disappear. The measurements of S may thus provide a valuable information on the details of the electronic structure of some metals.

Experimentally, however, such measurements are not simple to perform due to smallness of S at low temperatures (for pure metals S~10^-8 V K^-1). This dictates the use of SQUID-based voltmeters with extremely high sensitivity of about 10^-12-10^-14 V, which moreover should be combined with the use of a special high-pressure cell, where the quasi hydrostatic pressure of up to 12-25 kbar at low temperatures can be achieved.

After scrambling through all the experimental difficulties, I finally managed to unambiguously demonstrate the existence of the effect in a number of common metals (In, Tl) and alloys (Mo-Re, Tl-Cd, Tl-In).^2-4,7 (See also a review paper by A. Varlamov, Adv. Phys. 38(5), 469 (1989))  Moreover, I have discovered that the sign of the effect for high purity indium changes with temperature. This was totally unexpected and therefore stimulated further theoretical investigations. It turned out that the inelastic processes (scattering on phonons) have, in fact, an opposite contribution to the effect.⁷

All this was summarized in my thesis "Thermo emf and electronic topological transitions in pure metals and alloys", which was successfully defended in 1987.
 

[1] See a recent review paper by Ya.M. Blanter, M.I. Kaganov, A.V. Pantsulaya, and A.A.Varlamov The theory of electronic topological transitions,  Physics Reports245(4), 159 (1994)

Among the most significant, there was a study of thermal conductivity of Y-123 and its dependence on the oxygen content.^6,7 For one and the same specimen, the thermal conductivity first decreased with decreasing of the oxygen content, and then increased again for nearly insulating state (maximum oxygen depletion). The changes in the thermal conductivity were completely reversible, i.e. after introducing oxygen back into the material by high-temperature annealing in the oxygen atmosphere, the thermal conductivity returned to its initial value.

This observation clearly indicated that quasi particles are predominantly scattered by the oxygen atoms or oxygen-atom vacancies. In the optimally doped specimen there is not many vacancies present, which means that the thermal conductivity should have (relatively) large value. When some of the oxygen atoms are removed, their vacancies play role of the scattering centers, and the thermal conductivity decreases. On the other hand, if one removes all the available oxygen atoms, one gets again the perfect crystal structure (although insulating) without scattering centers, and the thermal conductivity should increase again, in perfect correspondence with experiment.^6,8 See also a review paper by C. Uher, in Physical properties of high temperature superconductors III, ed. by D. M. Ginsberg, World Sci. Publ. Co., Singapore 1992.

From analysis of our experiments it became clear that the excited by light quasiparticles in Bi-2212 may have a prolonged lifetime due to inhomogeneities of the superconductor, which may effectively trap quasiparticles thus impeding the recombination. The diffusion length of the quasiparticles (during the time of their recombination) was estimated to be 10^-5-10^-3 cm, which is comparable with thickness of commonly used single crystals of Bi-2212.

First, the height of mesas may be controlled by changing, for instance, the etching time. The smaller the height - the smaller the number of IJJ participating in the measurements. This greatly facilitates analysis of the data obtained and allows one to see the properties of an individual IJJ more easily, without great deal of heat evolvement. Later, I introduced a more sophisticated technology involving in situ control of the mesa height which allowed us to make mesas of a specified height (a specified number of IJJ).²² Even properties of only one IJJ in the mesa have been thoroughly investigated.²⁰

Second, since the mesa volume is about 6 orders of magnitude smaller than that of the whole crystal, the probability of having defects in the former is by the same order of magnitude smaller. We consider this advantage as significant, because very often in practice far going conclusions are inadvertently made based on measurements on simply defect samples. Monitoring properties of the limited number of IJJ allows us to easily detect the defect mesas and reject such a sample.

Using the mesas we started to perform different kinds of measurements on them. These include:

a) Vortex matter. Abrikosov vortices (pancakes).

The pancakes interact with each other magnetically and via interlayer Josephson coupling. These interactions encourage pancakes to align in perpendicular to planes direction.
However, when the interlayer interactions are weak, thermal fluctuations and local pinning centers cause misalignment (see picture). This leads to a loss in phase coherence between adjacent pairs of superconducting planes and hence - a reduction in the critical current.^24,30 If the c-axis critical current is totally suppressed by the magnetic field, the measured c-axis resistance is nothing else but the sum of the sub-gap resistances of all the IJJ in series.²⁴ Although this directly follows from the Lawrence-Doniach model of highly anisotropic high-T_c compounds, it has never been shown experimentally.

We have demonstrated that indeed, the measured c-axis resistance in the magnetic field corresponds to the sub-gap resistance of an individual IJJ times the number of layers in a given stack of IJJ.²⁴ Moreover, the magnitude of the magnetoresistance peak effect may be predicted from the zero-field current-voltage characteristics measured in the whole temperature range.²⁴

In Ref. 30 our measurements of the field-dependent c-axis tunneling characteristics across the intrinsic inter-planar Josephson junctions in 2212-BSCCO mesa structures probe the inter-planar pancake correlation on an atomic interlayer length scale, complementing earlier measurements of vortex correlation on the much longer length scales involved in low angle neutron diffraction, mSR, magnetic, and bulk transport measurements. We have interpreted our measurements in terms of the interplane alignment of pancake vortices, which provided information on the rich magnetic phase diagram of Bi-2212.³⁰

One of the ideas for decreasing the creep of pancakes and helping them to align in the c-axis direction, was heavy-ion irradiation of the single crystals and thin films. High-energy heavy ions produce straight columns of damage tracks across the whole thickness of the crystal. It is then energy favorable for pancakes to sit at the columnar defects. However, for randomly distributed columns, the number of pancakes being aligned along the columns does not monotonically depend on the applied magnetic field. Numerical simulations showed that there is a maximum at approximately 1/3 of the matching field B_F(the field at which number of vortices equals number of columnar defects). In our measurements we have shown experimentally that indeed the c-axis critical current has a pronounced maximum at 1/3 of the matching field and no feature at B=B_F .^*

The highly anisotropic layered high-T_c compounds exhibit intrinsic Josephson effects. In the simplified picture, layered compounds may be viewed as stacks of Josephson tunnel junctions. To employ possible advantages of high- quality Josephson junctions made by the Nature inside the single-cristalline material, one has to study the main features of such junctions. One of the basic properties is the response to the external magnetic field, which in the case of ordinary low-temperature junctions causes the critical current of the junction to oscillate.

In stacks of Josephson junctions, the coupling between adjacent junctions via magnetic interaction gets important. If sufficiently strong, this coupling may provide synchronization of many junctions in the stack (phase locking), so that the collective behavior of all junctions is equivalent to a single one with a much higher I_cR_n. This is very important for possible practical applications.

It has been shown both experimentally and theoretically (Krasnov) that in stacks of IJJ the Josephson vortices may have a number of modes with almost equal Gibbs free energy. This cause the measured critical current to have mutiple most probable values at a given temperature. The probability may change with temperature due to change of the magnetic coupling in between adjacent layers. This, in turn, may lead to a sudden change of the critical current in perfect correspondence with experiemnt.^27,28

Usual experimental methods of the energy gap spectroscopy in high- Tc materials are essentially surface probes, like STM or ARPES (angle resolved photo emission spectroscopy). The intrinsic tunneling effects allow one to get information on superconducting properties far away from the possibly deteriorated surface (moisture, loss of oxygen, etc.). In contrast to other techniques, we argue that tunnel junctions formed inside the single crystal provide genuine information of the properties of bismuth compounds.

From the c-axis current-voltage characteristics we can obtain the value of the c-axis energy gap parameter, which turned out to be about 10 –15 meV, about one half of the expected value (from earlier STM and similar measurements). We argued that the reason for that may be a proximity induced superconductivity in the intermediate BiO layers. This assumption allowed us to explain both the reduced energy gap in the c-direction and its unusually strong temperature dependence.²²

The interlayer tunneling model (ILT), developed by Anderson with collaborators is one of the leading candidates for high-temperature superconductivity (P. W. Anderson et al., The theory of Superconductivity in the High-T_c Cuprate Superconductors (Princeton Univ. Press, Princeton, 1997). In this model the energy gain that drives the formation of the pairs is associated with the decrease of the kinetic energy due to the easy motion of the pairs accompanied by the impeded single-particle tunneling along the c-axis. The model  predicts an increase of the condensation energy E_c proportionally to the interlayer Josephson coupling, or to the inverse square of the c-axis penetration depth l_c. A conclusive experimental check of this prediction for different single-layer high-T_c materials would provide a critical test of ILT model.

Having been working quite a lot with high-pressure techniques (see p.1) I came to an idea of checking the theory by using the hydrostatic pressure as a tool to change the interlayer coupling in the layered compounds. The c-axis critical current (which we can nicely measure) directly reflects the interlayer coupling, while the superconducting critical temperature may serve as a measure of the condensation energy.

Quickly after the emergence of the idea we made the corresponding experiements on Bi- based single layer compound Bi-2201, and its double-layer ally, Bi-2212. We have observed that while the interlayer coupling I_c increases dramatically with pressure (up to 270 % GPa^-1), the critical temperature only slightly increases at a rate of 2-6 %GPa^-1. See these Figures. These incommensurate effects of pressure suggest that the CuO-interlayer coupling has a little effect on T_c of the Bi-compounds, in contrast to the ILT model.

The existence of a pseudo-gap in electronic excitation spectra of high-T_csuperconductors, which appears below certain temperature T^*> T_c is considered to be amongst the most important features of high-T_c cuprates.²⁹ Many experiments have provided evidence for a gap-like structure in electronic excitation spectra, like NMR, ARPES, specific heat, electron-tunneling spectroscopy, and STM. The latter two methods have the additional advantage as being able to measure the density of states locally. However, they also have a drawback of being essentially surface probes. Surface is often poorly characterized and is subject of chemical influence from moisture etc.

Intrinsic Josephson effect allows one to monitor the intrinsically inherent tunneling properties inside the single crystal far away from the surface. This is the main advantage of using IJJ for electronic spectroscopy. However, it has its drawbacks, too. Due to relatively high value of the c-axis superconducting energy gap parameter D_c (12-15 meV), and relatively high critical current density J_c (200-1000 A cm^-2), the heating and non-equilibrium effects become important. They may obscure results. This means that one has to work very close to T_c (where both J_c and D_c get much smaller).

Another approach, which we tried to use, was decreasing the interlayer coupling via intercalation of big molecules of (chemically inert) HgBr₂ in between BiO layers in Bi-2212. Experiments show that doing this does not change T_c much, but allow one to decrease the c-axis critical current more than two orders of magnitude, thus allowing us to avoid heating and non-equilibrium problems and to widen the temperature range where the pseudo-gap features in tunneling spectra could be observed.