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Publication# Emergent transport in a many-body open system driven by interacting quantum baths

Résumé

We analyze an open many-body system that is strongly coupled at its boundaries to interacting quantum baths. We show that the two-body interactions inside the baths induce emergent phenomena in the spin transport. The system and baths are modeled as independent spin chains resulting in a global nonhomogeneous XXZ model. The evolution of the system-bath state is simulated using matrix-product-states methods. We present two phase transitions induced by bath interactions. For weak bath interactions we observe ballistic and insulating phases. However, for strong bath interactions a diffusive phase emerges with a distinct power-law decay of the time-dependent spin current Q alpha t(-alpha). Furthermore, we investigate long-lasting current oscillations arising from the non-Markovian dynamics in the homogeneous case and find a sharp change in their frequency scaling coinciding with the triple point of the phase diagram.

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In my thesis, transport measurements such as resistivity and, more importantly, thermopower S, were used to explore the phase diagram of bad metals. Bad metals are electronically correlated systems whose ground state lies close to a quantum phase transition. By tuning the control parameters, such as temperature (T ), magnetic field (B), hydrostatic pressure (p) or chemical substitution (x), we can induce phase transitions between the various electronic, magnetic and structural phases. Here, the thermopower is presented as a unique tool for probing quantum phase transition because it is a measure of the entropy of conducting electrons. The main part of the thesis is dedicated to the study of Fe-based superconductors (FeSC) discovered in 2008. Their parent compound has an antiferromagnetic (AF) ground state, where the itinerant electrons form a spin-density wave (SDW), a periodic modulation of spin density. This coincides or is preceded by a structural, tetragonal-to-orthorhombic transition. The nesting between the electron and hole Fermi surface is believed to be the driving mechanism for the SDW state. By changing the structural or chemical properties the AF ground state of FeSC is suppressed, giving way to superconductivity (SC). The remaining antiferromagnetic fluctuations above the transition can provide a glue for SC pairing. Here, the analysis of the thermopower S/T of BaFe1−xCoxAs2 (BFCA) in the x-T phase diagram shows the signatures of the spin fluctuation which have a dome-like dependence and follow the trend of superconducting Tc . The logarithmic increase of S/T upon decreasing T is ascribed to the proximity of the spin-density-wave quantum critical point. It can be understood as an increase of entropy due to the incommensurate AF spin fluctuations. We can ascribe the high values of thermopower in BFCA at intermediate- and room-temperatures to the influence of low-T quantum criticality. To probe the response of the electronic system in FeSC to structural changes, we performed measurements under pressure of the parent compound BaFe2As2 (BFA), the SC electron-doped BFCA, and hole-doped Ba1−xKxFe2As2 (BKFA). In the parent compound pressure suppresses the structural/SDW transition, similar to the effect of doping. For doped systems, in order to describe the behavior of thermopower in the high-T range (above 100K) we used a semi-metallic two-band model which was fitted to the data in order to extract the pressure dependence of the band parameters. In both doping cases the effect of pressure was similar, an increase of the band overlap and of the effective number of charge carriers. With this model we can explain the high-T , x and p dependence of thermopower in both electron- and hole-doped BFA. In a structurally simpler Fe-chalcogenide Fe1+yTe1−xSex compound, the excess of Fe has a Kondo-like influence on the charge carriers which dramatically changes the physics of the normal state. To probe the normal state, pressure, doping, magnetic Fe-excess concentration (y) and temperature were used as control parameters. At low-T a characteristic upturn of resistivity (ρmag ) is observed, followed by an increase of thermopower (Smag ), which we identify as the magnetic contribution caused by the spin-flip scattering events. Increasing the y resulted in an increase of ρmag , and a decrease of Smag , which is in agreement with the behavior of canonical Kondo-systems. Pressure suppresses the magnetic contribution to transport, thus increasing the itinerancy of the system. MnSi is another system in which the sensitivity of thermopower to entropy brings new information related to the complex magnetic structure. Pressure was used to drive the system from a helically ordered, canonical Fermi-liquid (FL) phase with T 2-resistivity to the intrinsically disordered, non-Fermi-liquid (NFL) phase above pc with T3/2-dependence. Our contour plot of S/T demonstrated how powerful the thermopower technique is, by reproducing the whole previously established T -p phase diagram. At the phase transition from the magnetically-ordered FL phase to the disordered NFL, the thermopower is dramatically enhanced. We bring useful information about the mysterious partial order (PO) phase inside the NFL phase, previously detected only by neutron scattering. The fluctuating helices scenario can describe the observed increase of entropy/thermopower in the PO phase. At ambient pressure, close to the helical transition of MnSi, a moderate magnetic field can stabilize the skyrmion lattice - the lattice of topological magnetic whirls, vortices. We observe a signature of the skyrmion lattice as a minute drop in thermopower. It is located exactly in the same region of the T − B phase diagram where an increase in magnetoresistance and Hall effect was reported previously. This feature originates from the additional scattering of conducting electrons on magnetic vortices, while the change in S is dominated by the decrease of entropy as the stable skyrmion lattice is formed. Overall, resistivity was used to confirm the established phase diagram, while thermopower, as an interesting and not sufficiently understood technique, was used to probe the sensitive changes of the charge carriers at the Fermi surface. We explored various phases showing how useful thermopower is to probe the entropy of electronic system on the verge of quantum phase transition.

The first part of this thesis discusses technical details relating to measurements of magnetic properties at ultra low temperatures. The implementation of AC susceptibility at temperatures down to 30 mK is introduced and used as a platform to showcase selected quantum magnets measured during the thesis. Each presented system illustrates a particular strength of AC susceptibility. This is followed by in-depth analysis of the design and implementation of a new solution for a SQUID magnetometer capable of running below 100 mK. The system employs a piezomotor to move the sample inside a dilution fridge, rather than the existing designs, which involve moving the entire dilution fridge. Furthermore, the system is completely modular, allowing for rapid removal from the fridge, and opening the possibility to use it on virtually any commercial dilution refrigerator. The latter part of the thesis presents a comprehensive study of a new family of model magnets, LiHox Er1−x F4, which combines the Ising spins of ferromagnetic LiHoF4 with the XY ones of antiferromagnetic LiErF4. The temperature-doping (T − x) phase diagram has been studied using AC susceptibility, and three key regions investigated in detail using additional neutron scattering experiments and mean-field calculations. The first region, x ≳ 0.6, corresponds to an Ising ferromagnet, where Tc (x) decreases linearly and faster than what mean-field predicts. At T < TC a so-called embedded spin-glass state is observed. The second region, 0.6 ≳ x ≳ 0.3, undergoes a spin-glass transition, where needle-like spin clusters form along the Ising axis below Tg (x) ∼ 0.4 − 0.5 K. Applying a field along the Ising axis at T < 200 mK produces a thermal runaway in the x = 0.50 sample, when the field reaches a value of H = 0.029 ± 0.002 T. The final region, x ≲ 0.3, corresponds to an antiferromagnetically coupled spin-glass, which shows archetypal spin-glass behaviour.

This thesis presents a theoretical description of the phase transition, with formation of long-range spatial coherence, occurring in a gas of exciton-polaritons in a semiconductor microcavity structure. The results and predictions of the theories developed in this thesis suggest that this phase transition, recently observed in experiments, can be interpreted as the Bose-Einstein Condensation (BEC) of microcavity polaritons. Our theoretical framework is conceived as a generalization to the microcavity polariton system of the standard theories describing the BEC of a weakly interacting Bose gas. These latter are reviewed in Chapter 2, where an introduction to the physics of polaritons is also given. The polariton system is peculiar, basically due to three main features, i.e. the composite nature of polaritons, which are a linear superposition of photon and exciton states, their intrinsic 2-D nature, and the presence of two-body interactions, arising both from the mutual interaction between excitons and from the saturation of the exciton oscillator strength. Therefore it is not clear whether the observed phase transition can be properly described in terms of BEC of a trapped gas. To clarify this point, one has to describe self-consistently the linear exciton-photon coupling giving rise to polariton quasiparticles, and the exciton-nonlinearities. This is made in Chapter 3, where a bosonic theory is developed by generalizing the Hartree-Fock-Popov description of BEC to the case of two coupled Bose fields at thermal equilibrium. Hence, we derive the classical equations describing the condensate wave function and the Dyson-Beliaev equations for the field of collective excitations. In this way, for each value of the temperature and of the total polariton density, a self-consistent solution can be obtained, fixing the populations of the condensate and of the excited states. In particular, the theory allows to describe simultaneously the properties of the polariton, the exciton and the photon fields, this latter being directly investigated in the typical optical measurements. The predicted phase diagram, the energy shifts, the population energy distribution and the behavior of the resulting first order spatial correlation function agree with the recent experimental findings [Kasprzak 06, Balili 07]. These results thus support the idea that the observed experimental signatures are a clear evidence of polariton BEC. However, from a quantitative pint of view, the measured coherence amount in the condensed regime is significantly lower than the predicted one. This discrepancy could be due to deviations from the weakly interacting Bose gas picture and/or to deviations from the thermal equilibrium regime. In particular, these latter are expected to be strong in current experiments, because polaritons have a short radiative lifetime, while the rate of the energy-relaxation mechanisms is very slow. To investigate how the deviations from equilibrium could affect the condensate fraction and the formation of off-diagonal long-range correlations, in Chapter 4, we develop a kinetic theory of the polariton condensation, accounting for both the relaxation mechanisms and for the field dynamics of fluctuations. Within the Hartree-Fock-Bogoliubov limit, we derive a set of coupled equations of motion for the one-particle populations and for the two particle correlations describing quantum fluctuations. We account for the relaxation processes due both to the polariton-phonon coupling and to the exciton-exciton scattering. The actual spectrum of the system is evaluated within the Popov limit, during the relaxation kinetics. Within this model, we solve self-consistently the populations kinetics and the dynamics of the excitation field, for typical experimental conditions. In particular, we show that the role of quantum fluctuations is amplified by non-equilibrium, resulting in a significant condensate depletion. This behavior could explain the partial suppression of off-diagonal long-range coherence reported in experiments [Kasprzak 06, Balili 07]. We complete the analysis, by studying how the deviations from equilibrium depend on the system parameters. Our results show that the polariton lifetime plays a crucial role. In particular, we expect that the increase of the polariton lifetime above 10 ps would lead to thermal-equilibrium polariton BEC in realistic samples. In Chapter 5, devoted to the conclusions, we discuss which issues of BEC could be clarified, by achieving polariton BEC at thermal-equilibrium, and which extensions of the present work would be most promising in this respect.