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G. Litak

Publications and source records attributed to G. Litak.

At least 19 recordsLinked to original sources
arXiv2012

Peculiarities of length scales in a two-orbital superconductor

We study the spatial behaviour of coherency and magnetic field in a two-orbital superconductor. The superconducting phase transition is caused here by the on-site intra-orbital attractions (negative-U Hubbard model) and inter-orbital pair-transfer interaction. We find the critical (diverging at $T_{c}$) and non-critical (remaining finite) coherence lengths and magnetic field penetration depth for various values of hopping integrals and the strengths of intra-orbital attractions. Numerical results have been obtained for a two-dimensional square lattice.

cond-mat.supr-con↗
arXiv2011

Coherence lengths for superconductivity in the two-orbital negative-U Hubbard model

We study the peculiarities of coherency in the superconductivity of two-orbital system. The superconducting phase transition is caused here by the on-site intra-orbital attractions (negative-U Hubbard model) and inter-orbital pair-transfer interaction. The dependencies of critical and noncritical correlation lengths on interaction channels and band fillings are analyzed.

cond-mat.supr-con↗
arXiv2008

Magnetic field induced rotation of the d-vector in the spin triplet superconductor Sr$_2$RuO$_4$

In zero magnetic field the superconductor Sr$_2$RuO$_4$ is believed to have a chiral spin triplet pairing state in which the gap function d-vector is aligned along the crystal c-axis. Using a phenomenological but orbital specific description of the spin dependent electron-electron attraction and a realistic quantitative account of the electronic structure in the normal state we analyze the orientation of the spin triplet Cooper pair d-vector in response to an external c-axis magnetic field. We show that for suitable values of the model parameters a c-axis field of only 20 mT is able to cause a reorientation phase transition of the d-vector from along $c$ to the $a-b$ plane, in agreement with recent experiments.

cond-mat.supr-con↗
arXiv2006

Combustion Process in a Spark Ignition Engine: Analysis of Cyclic Maximum Pressure and Peak Pressure Angle

In this paper we analyze the cycle-to-cycle variations of maximum pressure $p_{max}$ and peak pressure angle $α_{pmax}$ in a four-cylinder spark ignition engine. We examine the experimental time series of $p_{max}$ and $α_{pmax}$ for three different spark advance angles. Using standard statistical techniques such as return maps and histograms we show that depending on the spark advance angle, there are significant differences in the fluctuations of $p_{max}$ and $α_{pmax}$. We also calculate the multiscale entropy of the various time series to estimate the effect of randomness in these fluctuations. Finally, we explain how the information on both $p_{max}$ and $α_{pmax}$ can be used to develop optimal strategies for controlling the combustion process and improving engine performance.

nlin.CD↗
arXiv2006

Properties of the $π$ state induced by impurities in a d-wave superconductor

We study the properties of a quantum impurity embedded in a superconducting host of a d-wave symmetry. The superconductor is described by the extended negative $U$ Hubbard model while the impurity introduces a repulsive interaction to the system around the central site. We discuss the influence of this repulsion on the local properties (density of states, electron pairing and spontaneous current around the impurity) of the superconductor. We show the condition of $π$ - like behaviour, defined as two subsystems having a phase difference of $π$, in the system by using a proper combination of attractive pairing bond interaction and repulsive one between electrons located at the impurity and nearest neighbour sites.

cond-mat.supr-con↗
arXiv2006

Magnetic field induced rotation of the d-vector in Sr_2RuO_4

The superconductor Sr_2RuO_4 is widely believed to be a spin triplet system with a chiral order parameter analogous to the A phase of superfluid helium-3. The best evidence for this pairing state is that the Knight shift or spin susceptibility measured in neutron scattering is constant below T_c, unlike in a spin-singlet superconductor. The original Knight shift and neutron scattering measurements were performed for magnetic fields aligned in the ruthenate a-b plane. These would be consistent with a triplet d-vector d{k} aligned along the c-axis. However recently the Knight shift for fields along c was also found to be constant below T_c, which is not expected for this symmetry state. In this paper we show that while spin-orbit interaction stabilises the c-axis oriented d-vector, it is possible that only a very small external B field may be sufficient to rotate the d-vector into the a-b plane. In this case the triplet pairing model remains valid. We discuss characteristics of the transition and the prospects to detect it in thermodynamic quantities.

cond-mat.supr-con↗
arXiv2004

Spin-Orbit Coupling and Symmetry of the Order Parameter in Strontium Ruthenate

Determination of the orbital symmetry of a state in spin triplet Sr$_2$RuO$_4$ superconductor is a challenge of considerable importance. Most of the experiments show that the chiral state of the $\hat{z} (k_x \pm ik_y)$ type is realized and remains stable on lowering the temperature. Here we have studied the stability of various superconducting states of Sr$_2$RuO$_4$ in the presence of spin-orbit coupling. Numerically we found that the chiral state is never the minimum energy. Alone among the five states studied it has $<{\bf \hat L}.{\bf \hat S} >=0$ and is therefore not affected to linear order in the coupling parameter $λ$. We found that stability of the chiral state requires spin dependent pairing interactions. This imposes strong constraint on the pairing mechanism.

cond-mat.supr-con↗
arXiv2004

A Numerical Study of a Simple Stochastic/Deterministic Model of Cycle-to-Cycle Combustion Fluctuations in Spark Ignition Engines

We examine a simple, fuel-air, model of combustion in a spark ignition (si) engine with indirect injection. In our two fluid model, variations of fuel mass burned in cycle sequences appear due to stochastic fluctuations of a fuel feed amount. We have shown that a small amplitude of these fluctuations affects considerably the stability of a combustion process strongly depending on the quality of air-fuel mixture. The largest influence was found in the limit of a lean combustion. The possible effect of nonlinearities in the combustion process has been also discussed.

nlin.CD↗
arXiv2003

Cycle-to-Cycle Fluctuations of Burned Fuel Mass in Spark Ignition Combustion Engines

We examine a simple, fuel-air, model of combustion in spark ignition (si) engine with indirect injection. In our two fluid model, variations of fuel mass burned in cycle sequences appear due to stochastic fluctuations of a fuel feed amount. We have shown that a small amplitude of these fluctuations affects considerably the stability of a combustion process strongly depending on the quality of air-fulel mixture. The largest influence was found in the limit of a lean combustion. The possible effect of nonlinearities in the combustion process were also discussed.

nlin.CD↗
arXiv2003

Horizontal line nodes in superconducting Sr2RuO4

We analyze the possibilities of triplet pairing in Sr2RuO4 based upon an idea of interlayer coupling. We have considered two models differing by the effective interactions. In one model the quasi-particle spectra have horizontal line nodes on all three Fermi surface sheets, while in the other the spectra have line or point nodes on the alpha and beta sheets and no nodes on the gamma sheet. Both models reproduce the experimental heat capacity and penetration depth results, but the calculated specific heat is sightly closer to experiment in the second solution with nodes only on the alpha and beta sheets.

cond-mat.supr-con↗
arXiv2003

Combustion Process in a Spark Ignition Engine: Dynamics and Noise Level Estimation

We analyse the experimental time series of internal pressure in a four cylinder spark ignition engine. In our experiment, performed for different spark advance angles, apart from usual cyclic changes of engine pressure we observed oscillations. These oscillations are with longer time scales ranging from one to several hundred engine cycles depending on engine working conditions. Basing on the pressure time dependence we have calculated the heat released per cycle. Using the time series of heat release to calculate the correlation coarse-grained entropy we estimated the noise level for internal combustion process. Our results show that for a smaller spark advance angle the system is more deterministic.

nlin.CD↗
arXiv2003

Gap Nodes and Time Reversal Symmetry Breaking in Strontium Ruthenate

We study the superconducting state of Sr$_2$RuO$_4$ on the bases of a phenomenological but orbital specific description of the electron-electron attraction and a realistic quantitative account of the electronic structure in the normal state. We found that a simple model which features both `in plane' and `out of plane' coupling with strengths $U_{\parallel}=40$meV and $U_{\perp}=48$meV respectively reproduced the experimentally observed power law behaviour of the low temperature specific heat $C_v(T)$, superfluid density $n_s(T)$ and thermal conductivity in quantitative detail. Moreover, it predicts that the quasi-particle spectrum on the $γ$ -sheet is fully gaped and the corresponding order parameter breaks the time reversal symmetry. We have also investigated the stability of this model to inclusion of further interaction constants in particular %those which describe `proximity coupling' between orbitals contributing to the $γ$ sheet of the Fermi surface and the $α$ and $β$ sheets. We found that the predictions of the model are robust under such changes. Finally, we have incorporated a description of weak disorder into the model and explored some of its consequences. For example we demonstrated that the disorder has a more significant effect on the $f$-wave component of the order parameter than on the p-wave one.

cond-mat.supr-con↗
arXiv2003

Nonperiodic Oscillations of Pressure in a Spark Ignition Engine

We report our results on non-periodic experimental time series of pressure in a spark ignition engine. The experiments were performed for a low rotational velocity of a crankshaft and a relatively large spark advance angle. We show that the combustion process has many chaotic features. Surprisingly, the reconstructed attractor has a characteristic butterfly shape similar to a chaotic attractor of Lorentz type. The suitable recurrence plot shows that the dynamics of the combustion is a nonlinear multidimensional process mediated by stochastic noise.

nlin.CD↗
arXiv2002

Chaotic Combustion in Spark Ignition Engines

We analyse the combustion process in a spark ignition engine using the experimental data of an internal pressure during the combustion process and show that the system can be driven to chaotic behaviour. Our conclusion is based on the observation of unperiodicity in the time series, suitable stroboscopic maps and a complex structure of a reconstructed strange attractor. This analysis can explain that in some circumstances the level of noise in spark ignition engines increases considerably due to nonlinear dynamics of a combustion process.

nlin.CD↗
arXiv2002

Spin triplet superconductivity in Sr2RuO4

Sr2RuO4 is at present the best candidate for being a superconducting analogue of the triplet superfluidity in ^3He. This material is a good (albeit correlated) Fermi liquid in the normal state and an exotic superconductor below Tc. The mechanism of superconductivity and symmetry of the order parameter are the main puzzling issues of on-going research. Here we present the results of our search for a viable description of the superconducting state realised in this material. Our calculations are based on a three-dimensional effective three-band model with a realistic band structure. We have found a state with non-zero order parameter on each of the three sheets of the Fermi surface. The corresponding gap in the quasi-particle spectrum has line or point nodes on the alpha and beta sheets and is complex with no nodes on the gamma sheet. This state describes remarkably well a number of existing experiments including power low temperature dependence of the specific heat, penetration depth, thermal conductivity etc. The stability of the state with respect to disorder and different interaction parameters are also analyzed briefly.

cond-mat.supr-con↗
arXiv2002

Superconductivity Induced by Negative Centers

We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative $U$ Hubbard model where the interaction $U_i$, defined on the two dimensional lattice, can be $-|U|$ and 0 with probability $c$ and $1-c$ depending on the lattice site $i$. Using the determinant quantum Monte Carlo approach, we find the critical concentration $c_0$ of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.

cond-mat.supr-con↗
arXiv2002

P-wave Pairing in superconducting Sr2RuO4

Two models for the superconducting state of Sr2RuO4 have been analyzed. In an "orbital model" the in-plane and out of-plane interactions between electrons on neighboring Ru atoms are assumed to be attractive. In spite of the single particle hybrisation of the orbitals the model shows two superconducting transitions and fine-tuning of parameters is necessary to get a single transition. Otherwise the model correctly describes a number of experimental data. The "orbital proximity model" introduced here assumes the existence of special kind of inter-orbital interaction, which mixes the symmetries of the order parameters. This model naturally shows single temperature transition, but as our calculations indicate, does not lead to correct dependence of the electronic specific heat.

cond-mat.supr-con↗