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Title: Soft electronic matter in underdoped cuprates
Other Titles: PhD thesis
Authors: Capati, Matteo
Tutor: Lorenzana, José
Grilli, Marco
Keywords: Condensed matter theory superconductivity Monte Carlo numerical calculations
Issue Date: 29-Jan-2015
Abstract: Study of the underdoped region of the cuprates superconductors. Attempet to find a broken symmetry state close to superconductivity in anology with the other unconventional superconductors. We propose electronic phases in analogy with the soft matter phases. They explain very well the neutron scattering experiments.
Research interests: My field of research concerns the physics of strongly correlated electron systems, in par- ticular cuprates and pnictides High-Tc superconductors. Raman spectroscopy experiments During the laboratory course in the last year of my Master in Physics, I have performed the experimental characterization of the compound NiS_{2−x}Se_{x} by using Raman spec- troscopy. The measurements have been taken at room temperature for four different values of the doping concentration (x = 0, 0.5, 0.6, 1.2). The Raman peaks have been assigned to the stretching and librational modes of the S-S, S-Se and Se-Se pairs, by comparing our data with the results in literature. During my Master Thesis, I studied a frustrated Ising model with nearest-neighbor antiferromagnetic coupling J1 , next-nearest-neighbor coupling J2 , and a magneto-elastic coupling, using Monte Carlo simulations and analytical calculations [2]. The magnetic properties of the model, without magnetic coupling, have already been extensively investigated in literature. However, since our work is inspired to the physics of pnictide superconductors, the parameters are chosen such that the ground state is a striped spin state, as observed experimentally, but is close to the transition to the Neél ordered antiferromagnetic state. We find that in our finite clusters an orientational order (rotational symmetry breaking due to spin degrees of freedom) is found analogous to the liquid crystals nematic order. In our model, this nematic phase is characterized by finite values of the nematic order parameter, as a consequence of the breaking of the rotational C4 symmetry, but vanishing values of the staggered magnetization. The latter becomes different from zero at lower temperature, highlighting the presence of a long-range columnar magnetic state, analogous to the liquid crystal smectic phase. We found that the temperature window of the nematic state is larger for small systems. This can explain experiments in imperfect samples that find a more robust nematic state as the quality of the sample decreases, which we associate to finite size effects in real materials. Including the effect of a weak coupling with the lattice (magneto-elastic coupling), we find that a structural transition occurs associated with the nematic phase, with the magnetic transition occurring at a lower temperature. These two transitions merge into a single structural and magnetic transition with a stronger first-order char- acter for larger spin-lattice couplings. These two situations are in agreement with the different phenomenologies found in different families of pnictides. Indeed, 122 materials have larger critical temperature, first-order transitions, and a non-nematic state, as found for strong magneto-elastic coupling. On the other hand, 1111 systems have lower transition temperatures, second-order or weakly first-order transitions, and a nematic state as found for weak magneto-elastic coupling. It is sometimes argued that, since the structural transition occurs at a higher temperature than the magnetic transition, it is the structure that drives the magnetism. This argument is not justified, and our model is a counterexample showing that the structural transition can occur at a higher temperature than the magnetism although it is driven by the magnetism itself. This is because the structural transition is driven by the cohesive energy, which is determined by short-range spin correlations. Thus cooling the system, one can have a robust short-range spin correlation, which renders the lattice unstable, before the system has long-range magnetic order. The fact that the lattice tends to make the transition more first-order like, suggests that the nematic state observed is mainly driven by the electronic degrees of freedom and that the lattice acts as a spectator. My Ph.D project focused on the complex phases which characterize the cuprate supecon ductors in the underdoped regime. Our aim was to find an electronic long-range order from which unconventional superconductivity emerges. This scenario would put the cuprate phase diagram into the same class of phase diagrams of a wide class of materials, like heavy fermion, pnictide, organic, and other systems, where superconductivity arises in close proximity to some broken symmetry state. Despite the observation of charge ordering in La_{1.6−x}Nd_{0.4}Sr_{x} CuO_{4} and in La_{2−x}Ba_{x}CuO_{4} at doping concentration close to x = 1/8, incommensurate static charge order has never been reported in the heavily underdoped region of the cuprate phase diagram, in contrast to incommensurate spin order. Starting from the one-band Hubbard model with realistic parameters for cuprates, we have performed variational computations (unrestricted Gutzwiller-Hartree-Fock), which suggest that each pair of holes introduced by the chemical doping in the CuO2 planes, tend to occupy the core of a vortex and an antivortex of the spin background. These vortex and artivortex tend to form a bound state. With increasing doping these low-doping vortex-antivortex pairs tend to aggregate forming short stripe segments, i.e. “electronic polymers”. In order to enable simulations in large systems we did not consider explicitly the spin degrees of freedom but we have integrated them out to generate effective interactions among topological charges, obtaining a two-dimensional Coulomb gas, with effective interactions. Working at temperatures smaller than the binding energy of individual vortex-antivortex pairs (∼ 100 K), we have performed a classical Monte Carlo study based on the parallel tempering technique. We have found that in a system without disorder, by lowering the temperature the polymer melt condenses first in a smectic state (orientational order accompanied by charge modulation in one direction) and then in a Wigner crystal both with the addition of inversion symmetry breaking. Disorder given by the dopant ions laying between the CuO2 planes, blurs the positional order leaving a robust inversion symmetry breaking and nematic order accompanied by vector chiral spin order and with the persistence of a thermodynamic transition. Such electronic phases, produce incommensurate spin responses in good agreement with experiments. Unfortunately, with the present method we could not access quantitatively the crossover to collinear stripes. In this regime, the mapping to the Coulomb gas breaks down due to the increasing role of the fermionic degrees of freedom in the increasingly metallic state. However, one can anticipate that the average length of the electronic polymers will keep growing with doping, opening the possibility that they coalesce into stripes with long-range order. This topic could represent the natural continuation of our work. In my future research I would like to continue studying strongly correlated electron systems by using both numerical and theoretical many-body techniques. So far my work consisted of numerical mean-field Hartree-Fock and Gutzwiller calculations based on the Hubbard model, and mainly of classical Monte Carlo simulations, but I would like to acquire new competences mainly on computational methods, like quantum Monte Carlo and Density Functional Theory. For what concerns the specific topics I am interested in studying further the complex phases of the cuprate superconductors, and other topics like high-temperature superconductivity in iron based superconductors, disordered quantum systems, the glassy dynamics of correlated systems, frustrated magnetic systems, multiferroic materials, cold atomic gases.
Skills short description: Condensed matter physics; - Statistical mechanics and study of the phase transitions in disordered systems; - Strongly correlated electron systems (unconventional superconductors); - Soft matter like phenomena in electronic systems; - Numerical simulations of many-body systems (unrestricted Hartree-Fock, Gutzwiller, classical Monte Carlo). - Operating systems: Windows, Linux; - Software: Microsoft Office, Microcal Origin, Gnuplot, Latex, Wolfram Mathematica; - Programming languages: C (Development of software for scientific application); - Parallel programming with MPI (Message Passing Interface); - Monte Carlo method with parallel tempering technique for the numerical simulation of statistical mechanics models; - Raman spectroscopy (ARAMIS micro-Raman)
Personal skills keywords: Monte Carlo simulations with MPI
Unrestricted Hartee-Fock and Gutzwiller mean field calculations
C language, gnuplot, wolfram mathematica, Linux, Windows
Many body systems
Appears in PhD:FISICA

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