Se p 20 00 Improved perturbation theory in the vortex liquids state of type II superconductors (original) (raw)
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Improved perturbation theory in the vortex liquids state of type II superconductors
Physical Review B, 2000
We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent. Radius of convergence on the lowest Landau level is aT=−3a_{T}=-3aT=−3 in 2D and aT=−5a_{T}=-5aT=−5 in 3D. It allows a systematic calculation of magnetization and specific heat contributions due to thermal fluctuations of vortices in strongly type II superconductors to a very high precision. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.
Optimized perturbation theory in the vortex liquid of type-II superconductors
Physical Review B, 2001
We develop an optimized perturbation theory for the Ginzburg -Landau description of thermal fluctuations effects in the vortex liquids. Unlike the high temperature expansion which is asymptotic, the optimized expansion is convergent. Radius of convergence on the lowest Landau level is a T = −3 in 2D and a T = −5 in 3D. It allows a systematic calculation of magnetization and specific heat contributions due to thermal fluctuations of vortices in strongly type II superconductors to a very high precision. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.
Physical Review Letters, 2001
A new systematic calculation of magnetization and specific heat contributions of vortex liquids and solids (not very close to the melting line) is presented. We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. The expansion is convergent in contrast to the conventional high temperature expansion which is asymptotic. In the solid phase we calculate first two orders which are already quite accurate. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.
2008
A systematic calculation of magnetization and specific heat contributions due to fluctuations of vortex lattice in strongly type II superconductors to precision of 1% is presented. We complete the calculation of the two loop low temperature perturbation theory by including the umklapp processes. Then the gaussian variational method is adapted to calculation of thermodynamic characteristics of the 2D and the 3D vortex solids in high magnetic field. Based on it as a starting point for a perturbation theory we calculate the leading correction providing simultaneously an estimate of precision. The results are compared to existing nonperturbative approaches. PACS numbers: 74.60.-w, 74.40.+k, 74.25.Ha, 74.25.Dw ∗e-mail: lidp@mono1.math.nctu.edu.tw †e-mail: baruch@vortex1.ep.nctu.edu.tw
2001
A systematic calculation of magnetization and specific heat contributions due to fluctuations of vortex lattice in strongly type II superconductors to precision of 1% is presented. We complete the calculation of the two loop low temperature perturbation theory by including the umklapp processes. Then the gaussian variational method is adapted to calculation of thermodynamic characteristics of the 2D and the 3D vortex solids in high magnetic field. Based on it as a starting point for a perturbation theory we calculate the leading correction providing simultaneously an estimate of precision. The results are compared to existing nonperturbative approaches.
Physical Review B, 2002
A systematic calculation of magnetization and specific heat contributions due to fluctuations of vortex lattice in strongly type II superconductors to precision of 1% is presented. We complete the calculation of the two loop low temperature perturbation theory by including the umklapp processes. Then the gaussian variational method is adapted to calculation of thermodynamic characteristics of the 2D and the 3D vortex solids in high magnetic field. Based on it as a starting point for a perturbation theory we calculate the leading correction providing simultaneously an estimate of precision. The results are compared to existing nonperturbative approaches.
Quantitative theory of stable and metastable phases in the vortex matter of type II superconductors
2004
Theory of melting of the vortex lattice in type II superconductors in the framework of Ginzburg-Landau approach is presented. Not very far from H c2 (T) the lowest Landau level approximation can be used. To obtain a very accurate description of both the vortex lattice and the vortex liquid, different methods are applied. In the solid state, the low temperature perturbation theory to the two loop order is used. In the liquid state, one utilizes high order high temperature series supplemented by interpolation to a T = 0 metastable "perfect liquid" state. The melting line location is determined, and magnetization and specific heat jumps along it are calculated. The magnetization of liquid is larger than that of solid by 1.8% irrespective of the melting temperature, while the specific heat jump is about 6% and decreases slowly with temperature. Moreover, our theory of solid predicting the location of spinodal line has been recently confirmed experimentally.
Physical Review B, 2004
A metastable homogeneous state exists down to zero temperature in systems of repelling objects. Zero ''fluctuation temperature'' liquid state therefore serves as a (pseudo) ''fixed point'' controlling the properties of vortex liquid below and even around melting point. There exists Madelung constant for the liquid in the limit of zero temperature which is higher than that of the solid by an amount approximately equal to the latent heat of melting. This picture is supported by an exactly solvable large NNN Ginzburg - Landau model in magnetic field. Based on this understanding we apply Borel - Pade resummation technique to develop a theory of the vortex liquid in type II superconductors. Applicability of the effective lowest Landau level model is discussed and corrections due to higher levels is calculated. Combined with previous quantitative description of the vortex solid the melting line is located. Magnetization, entropy and specific heat jumps along it are calculated. The magnetization of liquid is larger than that of solid by % 1.8% irrespective of the melting temperature. We compare the result with experiments on high TcT_{c}Tc cuprates YBa2Cu3O7YBa_{2}Cu_{3}O_{7}YBa2Cu3O7, DyBCODyBCODyBCO, low % T_{c} material (K,Ba)BiO3(K,Ba)BiO_{3}(K,Ba)BiO3 and with Monte Carlo simulations.
Quantitative theory of thermal fluctuations and disorder in the vortex matter
Pramana-journal of Physics, 2006
A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zerotemperature liquid state therefore serves as a (pseudo) 'fixed point' controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.
2019
Usually, the measurements of electronic and magnetic properties of superconducting samples are carried out under a constant temperature bath. On the other hand, thermal gradients induce local variation of the superconducting order parameter, and the vortex dynamics can present interesting behaviors. In this work, we solved the time-dependent Ginzburg-Landau equations simulating samples under two different thermal gradients, and considering two values of the Ginzburg-Landau parameter, \k{appa}. We find out that both parameters, i.e., \k{appa} and thermal gradients, play an important role on the vortex dynamics and on the magnetization behavior of the samples.