Spin of an electron is an alternative to its charge for designing logic circuits. Much lower intrinsic energy of the spins requires much less power for operations, allowing significantly cooler computing chips. The ability to preserve the spin information in an order state of a magnet provides naturally a good way for storing data, which is now widely utilised in magnetic disk drives by means of the giant magneto resistance (GMR) effect. However, implementing a robust generation, transmission, and detection of spin currents, needed for a complete spintronic circuit, presents still a technological problem.

Converting spin currents into a different signal that is easily detectable by the readily available techniques offers a promising way for generating and detecting them. One possibility is changing spin to change via the spin-Hall effect. Another is converting spin into heat current. Constructing a quantum transport theory of metals with magnetic nanoclusters, I showed that a strong magneto-thermopower (MTP) and a thermally generated spin current are intrinsically necessary attributes of GMR observed in these systems. This theory explained immediately the dependence of MTP on the size of the cobalt clusters in copper observed by the experimental group of Jean-Philippe Ansermet. A couple of years later, the prediction of thermo-spin (spin-Nernst) effect was confirmed experimentally in a similar system, thin nickel-iron films.

This work is published in Phys. Rev. B 74, 132403 (2006).

Non-Stationary Superconductivity

Superconductivity is a flow of electrons without any dissipations. It has not only found numerous applications (for example in transmitting  electricity over long distances without losses and in building the strongest magnets) but is a fascinating physical phenomenon that attracts researchers even now.  Development of the first microscopic theory, the Bardeen-Cooper-Schrieffer (BCS) model, had taken more than 40 year after the experimental discovery.  An attractive interaction (due to interplay with vibrations of the hosting crystal) forces electrons to condense into a strongly correlated state. The low energy excitations above it are new type of quasiparticles—Cooper pairs—that have a gap in the spectrum forbidding any scattering by impurities, unless the electric current becomes critically large.

Strong out-of-equilibirum dynamics of superconductors, when the state of the whole condensate changes rapidly, is another problem that could bring new applications of this intriguing phenomenon. This physics is already reachable in a lab, in niobium-titanium-nitrogen films by THz pump-probe spectroscopy, or could be implemented in quench experiments using cold atom in optical traps. The dynamical modes of the BCS model are elliptic instead of the usual harmonic, modified by the integrability of the model. My contribution was the spectral theory of these elliptic modes that identifies the number of the collective excitations in the dynamics corresponding to different initial states, see an example in the figure. This result  showed that there is a number of persistent oscillations in the non-stationary BCS theory, in addition to the already known relaxation of the time-dependent Ginzburg-Landau theory.

This work is published in Phys. Rev. Lett. 96, 097005 (2006) and Phys. Rev. B 79, 132504 (2009).

Quantum technology promises to a  revolution in computing by exploiting the massive parallelism inherited from quantum mechanics and in security of communications owning the property of entanglement that is destroyed by any physical witness. The commercially available lithography for semiconductors is a good candidate for implementing such a technology, e.g. an the spins of electrons localised inside the already manufactured quantum dots can serve as qubits—basic building blocks of  a quantum computer.  However, the quantum noise in a semiconductor crystal, caused by tiny magnets—nuclear spins—that the atoms of the lattice host, destroys the quantum coherence too quickly preventing currently a functional device from being manufactured.

Efficient control of the quantum noise, which would remove this roadblock, is still limited by poor understating of the many-body interaction between the electron and the nuclear spins. Diagonalising the corresponding central-spin model at finite magnetic fields, by means of the Gaudin's equations, I showed that the level spacing is exponentially small at the resonance with the electron spin but increases super exponentially away from it. This suggests the wings of the spectrum for applying the projective measurement technique in order to reduce the unwanted quantum noise efficiently. Studying the dipole-dipole interaction between the nuclear spins on a lattice, I showed that the shape of their Zeeman lines, measured by the the nuclear magnetic resonance technique, depends strongly on the nuclear polarisation. This result provides a precise tool for in situ measurements of the achieved polarisation in development of a  robust dynamical nuclear pumping technique that can fully eliminate the nuclear decoherence effect.

Strong Correlations in One Dimension

The challenge of understanding interacting electrons is a major open problem. Progress so far relied on the linear approximation to the relation between energy and momentum which restricts our understanding to low energies, where this assumption is valid. The well-established theories are Fermi liquid in two and three dimensions and Luttinger liquid in one dimension. The effective particles of Luttinger liquid are very different from the underlying electrons exemplifying a complete change of the electronic properties by the interactions between them.

The area away from the linear constraint and low energies remains mostly open. Studying this problem in one dimension by means of Bethe ansatz methods, I showed that the many-body solutions away from low energies can be characterised in a hierarchical fashion by their 'spectral weight'—a quantity determining how the solutions connect to physical observables. The levels of the hierarchy are separated by different powers of a tiny parameter, a ratio of the interaction radius to the system length.  At small energy this hierarchy crosses over to the already known hydrodynamic modes of Luttinger liquid, see sketch in the figure. This theory was confirmed experimentally by the group of Chris Ford in tunneling spectroscopy of quantum wires by measuring modes from the two strongest levels of the hierarchy and the crossover to Luttinger liquid. A weaker mode has been observed recently by the same group in short wires confirming further that the levels of the hierarchy are separated by the inverse length of the system.