FG Computational Physics
We investigate order parameter fluctuations in the Hubbard model within a time-dependent Gutzwiller approach. While in the weak coupling limit we find that the amplitude fluctuations are short-lived due to a degeneracy with the energy of the edge of the quasiparticle continua (and in agreement with Hartree-Fock+RPA theory), these are shifted below the edge upon increasing the interaction. Our calculations therefore predict undamped amplitude (Higgs) oscillations of the order parameter in strongly coupled superconductors, cold atomic fermion condensates, and strongly interacting charge- and spin-density wave systems. We propose an experimental realization for the detection of the spin-type Higgs mode in undoped cuprates and related materials where, due to the Dzyaloshinsky-Moriya interaction, it can couple to an out-of-plane ferromagnetic excitation that is visible via the Faraday effect.
The Shrinking Fermi Liquid Scenario for Strange-Metal Behavior from Overdamped Optical Phonons
(2024)
We discuss how the interaction of electrons with an overdamped optical phonon can give rise to a strange-metal behavior over extended temperature and frequency ranges. Although the mode has a finite frequency, an increasing damping shifts spectral weight to progressively lower energies so that despite the ultimate Fermi liquid character of the system at the lowest temperatures and frequencies, the transport and optical properties of the electron system mimic a marginal Fermi liquid behavior. Within this shrinking Fermi liquid scenario, we extensively investigate the electron self-energy in all frequency and temperature ranges, emphasizing similarities and differences with respect to the marginal Fermi liquid scenario.
Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broadband THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy 2Δ. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency Ω and exhibited a resonant enhancement at temperature when Ω=2Δ. General theoretical considerations show that such a resonance can arise only from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that, even for a small amount of disorder, the Ω=2Δ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies.
Anisotropic transport properties have been assessed in a number of cuprate superconductors, providing evidence for a nematic state. We have recently shown that in ultra-thin YBa2Cu3O7−δ films, where nematicity is induced via strain engineering, there is a suppression of charge density wave scattering along the orthorhombic a-axis and a concomitant enhancement of strange metal behavior along the b-axis. Here we develop a microscopic model, that is based on the strong interaction between the substrate facets and the thin film, to account for the unconventional phenomenology. Based on the atomic force microscopy imaging of the substrates’ surface, the model is able to predict the absence (presence) of nematicity and the resulting transport properties in films grown on SrTiO3 (MgO) substrates. Our result paves the way to new tuning capabilities of the ground state of high-temperature superconductors by substrate engineering.
Electronic inhomogeneities are nowadays a well established feature of high-temperature superconductors, most prominently exemplified by the observation of charge-ordered states in a large number of cuprate materials. In this contribution we review the particular contribution of the Stuttgart-Tartu-Cottbus group to this field, which has been largely stimulated by intense discussion with K. Alex Müller. The original scenario, which was based on the formation of a percolative electronic network, is substantiated by a microscopic analysis of the clustering of magnetic polarons within the one-band Hubbard model.
We present a detailed theoretical investigation of the linear and nonlinear optical response in a model system for a disordered d-wave superconductor. By evaluating the quasiparticle contribution (BCS response) we show that for both quantities the gap symmetry considerably changes the paradigm of the optical response as compared to the conventional s-wave case. For what concerns the linear response our findings agree with previous work showing that in strongly disordered d-wave superconductors a large fraction of uncondensed spectral weight survives below Tc, making the optical absorption around the gap-frequency scale almost unchanged with respect to the normal state. Our numerical results are in excellent quantitative agreement with experiments in overdoped cuprates. In the nonlinear regime we focus on the third-harmonic generation (THG), finding that, as already established for the s-wave case, in general a large THG is triggered by disorder-activated paramagnetic processes. However, in the d-wave case the BCS response is monotonously increasing in frequency, losing any signature of THG enhancement when the THz pump frequency ω matches the gap maximum Δ, a hallmark of previous experiments in conventional s-wave superconductors. Our findings, along with the mild polarization dependence of the response, provide an explanation for recent THG measurements in cuprates, setting the framework for the theoretical understanding of nonlinear effects in unconventional cuprates.
The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.
We discuss a formalism that allows for the calculation of a higher-harmonic-current response to a strong applied electric field for disordered superconducting systems described on the basis of tight-binding models with on- and/or intersite interactions. The theory is based on an expansion of the density matrix in powers of the field amplitudes, where we solve the equation of motion for the individual components. This allows the evaluation of higher-order response functions on significantly larger lattices than one can achieve with a previously used approach, which is based on a direct temporal integration of the equation of motion for the complete density matrix. In the case of small lattices, where both methods can be applied by including also the contribution of collective modes, we demonstrate the agreement of the corresponding results.
We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. We show that, depending on the order of the thermodynamic limit and large times, a situation can arise in which the Fermi liquid keeps a memory of the parent BCS state. Furthermore, a time inversion of the interaction, supplemented by a manipulation analogous to a spin-/photon-echo experiment, allows us to recover the parent BCS state. Moreover, we study the evolution of the order parameter phase ϕ in transforming the BCS superconductor to a conventional metal. Since the global phase is the conjugate variable of the density, we explicitly show how to use the dynamics of ϕ together with gauge invariance to build up the noninteracting chemical potential away from particle-hole symmetry. We further analyze the role of ϕ in restoring the gauge-invariant current response when the noninteracting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field.
THz non-linear optical response in cuprates: predominance of the BCS response over the Higgs mode
(2022)
Recent experiments with strong THz fields in unconventional cuprate superconductors have clearly evidenced an increase of the non-linear optical response below the superconducting critical temperature Tc. As in the case of conventional superconductors, a theoretical estimate of the various effects contributing to the non-linear response is needed in order to interpret the experimental findings. Here, we report a detailed quantitative analysis of the non-linear THz optical kernel in cuprates within a realistic model, accounting for the band structure and disorder level appropriate for these systems. We show that the BCS quasiparticle response is the dominant contribution for cuprates, and its polarization dependence accounts very well for the third-harmonic generation measurements. On the other hand, the polarization dependence of the THz Kerr effect is only partly captured by our calculations, suggesting the presence of additional effects when the system is probed using light pulses with different central frequencies.
We use the time-dependent Gutzwiller approximation for the single-band Hubbard model to analyze the non-equilibrium dynamics for stripe ground states. In particular, we are interested in the interplay between spin and charge dynamics which is analyzed by quenching the system either in the charge or spin sector. This allows us to investigate the coupled relaxation dynamics as a function of the supplied energy. Further insight is provided by mapping the Gutzwiller dynamics onto a time-dependent Landau approach which lacks the double occupancy contribution to the time-evolution but allows to tune the coupling between spin- and charge degrees of freedom.
Recent resonant X-ray scattering experiments on cuprates allowed to identify a new kind of collective excitations, known as charge density fluctuations, which have finite characteristic wave vector, short correlation length and small characteristic energy. It was then shown that these fluctuations provide a microscopic scattering mechanism that accounts for the anomalous transport properties of cuprates in the so-called strange-metal phase and are a source of anomalies in the specific heat. In this work, we retrace the main steps that led us to attributing a central role to charge density fluctuations in the strange-metal phase of cuprates, discuss the state of the art on the issue and provide an in-depth analysis of the contribution of charge density fluctuations to the specific heat.
Anomalous metallic properties are often observed in the proximity of quantum critical points, with violation of the Fermi Liquid paradigm. We propose a scenario where, near the quantum critical point, dynamical fluctuations of the order parameter with finite correlation length mediate a nearly isotropic scattering among the quasiparticles over the entire Fermi surface. This scattering produces a strange metallic behavior, which is extended to the lowest temperatures by an increase of the damping of the fluctuations. We phenomenologically identify one single parameter ruling this increasing damping when the temperature decreases, accounting for both the linear-in-temperature resistivity and the seemingly divergent specific heat observed, e.g., in high-temperature superconducting cuprates and some heavy-fermion metals.
Recent experiments with strong THz fields in both conventional and unconventional superconductors have clearly evidenced a marked third-harmonic generation below the superconducting temperature Tc. Its interpretation challenged substantial theoretical work aimed at establishing the relative efficiency of quasiparticle excitations and collective modes in triggering such a resonant response. Here we compute the nonlinear current by implementing a time-dependent Bogoljubov–de Gennes approach, with the twofold aim to account nonperturbatively for the effect of local disorder, and to include the contribution of all collective modes, i.e., superconducting amplitude (Higgs) and phase fluctuations, and charge fluctuations. We show that, in agreement with previous work, already at small disorder the quasiparticle response is dominated by paramagnetic effects. We further demonstrate that paramagnetic processes mediate also the response of all collective modes, with a substantial contribution of charge/phase fluctuations. These processes, which have been overlooked so far, turn out to dominate the third-order current at strong disorder. In addition, we show that disorder strongly influences the polarization dependence of the nonlinear response, with a marked difference between the clean and the disordered case. Our results are particularly relevant for recent experiments in cuprates, whose band structure is in a first approximation reproduced by our lattice model.
Besides the mechanism responsible for high critical temperature superconductivity, the grand unresolved issue of the cuprates is the occurrence of a strange metallic state above the so-called pseudogap temperature T*. Even though such state has been successfully described within a phenomenological scheme, the so-called Marginal Fermi-Liquid theory, a microscopic explanation is still missing. However, recent resonant X-ray scattering experiments identified a new class of charge density fluctuations characterized by low characteristic energies and short correlation lengths, which are related to the well-known charge density waves. These fluctuations are present over a wide region of the temperature-vs-doping phase diagram and extend well above T*. Here we investigate the consequences of charge density fluctuations on the electron and transport properties and find that they can explain the strange metal phenomenology. Therefore, charge density fluctuations are likely the long-sought microscopic mechanism underlying the peculiarities of the metallic state of cuprates.
Restored strange metal phase through suppression of charge density waves in underdoped YBa2Cu3O7–δ
(2021)
The normal state of optimally doped cuprates is dominated by the “strange metal” phase that shows a linear temperature (T) dependence of the resistivity persisting down to the lowest T. For underdoped cuprates, this behavior is lost below the pseudogap temperature T*, where charge density waves (CDWs), together with other intertwined local orders, characterize the ground state. We found that the T-linear resistivity of highly strained, ultrathin, underdoped YBa2Cu3O7–δ films is restored when the CDW amplitude, detected by resonant inelastic x-ray scattering, is suppressed. This observation suggests an intimate connection between the onset of CDWs and the departure from T-linear resistivity in underdoped cuprates. Our results illustrate the potential of using strain control to manipulate the ground state of quantum materials.
We investigate an inhomogeneous Ising model in the context of tax evasion dynamics where different types of agents are parametrised via local temperatures and magnetic fields. Our work focuses on the dynamic behavioural change of agents after an audit which either corresponds to a temporal reduction or enhancement of compliance and is also known under the terms 'bomb crater' and 'target effect', respectively. We analyse this effect for different types of agents: endogenously non-compliant types, agents that have the tendency to copy (non-)compliant behaviour from their social environment, ethical agents with strong endogenous morale attitudes and random types that show large uctuations between compliant and non-compliant behaviour. Each type in uences the overall tax evasion differently, and interestingly, our model predicts that increasing the audit probability can have the counterintuitive effect of increasing tax evasion under certain circumstances. We analyse audit strategies that can suppress this effect and thus contribute to the burgeoning literature on the actual impact of tax audits.
Defects play an important role for surface reconstructions and therefore also influence the substrate growth. In this work we present a first principle calculation for the Ge(001) surface without and with tin impurities incorporated into the top surface layer. By mapping the system onto an Ising-type model, with interaction constants taken from density functional theory, the stability of the surface reconstructions under the influence of different concentrations of tin impurities is explored. This approach allows us to simulate the possible phase transitions for the different surface reconstructions including the local structure around the tin impurity atoms. In addition, we compare our theoretical results with experimental STM images on clean and Sn-doped Ge(100) surfaces.
An experimental device previously developed for studying rotating baroclinic flows has been used to investigate undular bores formation, propagation and collision. Up to our knowledge this is the first experimental study of undular bores in a circular channel. For a setup without barriers, this geometry accomplishes in a natural way the periodic lateral boundary conditions, very often used in numerical simulations. An excellent agreement between the experiment and simulation has been achieved. The spatio-temporal structure of bores is well reproduced for the first few reflections or collisions.
The microscopic mechanism of charge instabilities and the formation of inhomogeneous states in systems with strong electron correlations is investigated. We demonstrate that within a strong coupling expansion the single-band Hubbard model shows an instability towards phase separation and extend the approach also for an analysis of phase separation in the Hubbard-Kanamori hamiltonian as a prototypical multiband model. We study the pairing fluctuations on top of an inhomogeneous stripe state where superconducting correlations in the extended s-wave and d-wave channels correspond to (anti)bound states in the two-particle spectra. Whereas extended s-wave fluctuations are relevant on the scale of the local interaction parameter U, we find that d-wave fluctuations are pronounced in the energy range of the active subband which crosses the Fermi level. As a result, low energy spin and charge fluctuations can transfer the d-wave correlations from the bound states to the low energy quasiparticle bands. Our investigations therefore help to understand the coexistence of stripe correlations and d-wave superconductivity in cuprates.
The time-dependent Gutzwiller approximation is rederived on the basis of a variational wave function which is a direct product of a Slater determinant and a coherent state. The latter can be related to the slave-boson formulation by Kotliar and Ruckenstein, and our approach offers a convenient way to generalize the theory towards the implementation of symmetry-broken states and the study of non-equilibrium phenomena. We discuss the concept with regard to applications in the linear response limit and for quenched antiferromagnetic order for which we evaluate the optical conductivity in non-equilibrium situations.
Within the time-dependent Gutzwiller approximation applied to the negative-U Hubbard model, we investigate the dynamics of a superconductor after an interaction quench for different values of the final interaction from weak to strong coupling. The equilibrium BCS-BEC crossover becomes a sharp transition in the out-of-equilibrium dynamics between weak- and strong-coupling dynamical phases. Two different frequencies (ΩJ<ΩU) dominate the order parameter dynamics. In the weak coupling phase, ΩJ follows twice the asymptotic average value of the gap (ΩJ≈2Δ∞) and ΩU is much larger but hardy visible in the anomalous density. At long times the BCS dynamics is recovered but surprisingly differences remain during the transient phase. In the strong coupling phase, the dynamics decouples from the asymptotic value of the order parameter except at exactly half filling and close to the dynamical transition where ΩU≈2Δ∞. The out-of-equilibrium transient spectral density and optical conductivity are presented and discussed in relation to pump probe experiments. Both ΩJ and ΩU give rise to a complex structure of self-driven slow Rabi oscillations which are visible in the nonequilibrium optical conductivity where also sidebands appear due to the modulation of the double occupancy by superconducting amplitude oscillations. Analogous results apply to CDW and SDW systems. Our results show that in systems with long coherence times, pump-probe experiments allow us to characterize the regime (BCS vs preformed pairs) through very specific out-of-equilibrium fingerprints.
Although charge density waves (CDWs) are omnipresent in cuprate high-temperature superconductors, they occur at significantly different wave vectors, confounding efforts to understand their formation mechanism. Here, we use resonant inelastic x-ray scattering to investigate the doping- and temperature-dependent CDW evolution in La₂₋ₓBaₓCuO₄ (x=0.115–0.155). We discover that the CDW develops in two stages with decreasing temperature. A precursor CDW with a quasicommensurate wave vector emerges first at high temperature. This doping-independent precursor CDW correlation originates from the CDW phase mode coupled with a phonon and “seeds” the low-temperature CDW with a strongly doping-dependent wave vector. Our observation reveals the precursor CDW and its phase mode as the building blocks of the highly intertwined electronic ground state in the cuprates.
Phase separation and proximity effects in itinerant ferromagnet/superconductor heterostructures
(2018)
Heterostructures made of itinerant ferromagnets and superconductors are studied. In contrast to most previous models, ferromagnetism is not enforced by an effective Zeeman field but induced in a correlated single-band model (CSBM) that displays itinerant ferromagnetism as a mean-field ground state. In this model superconductivity and magnetism are both calculated self-consistently. We calculate the magnitude of the magnetization, the superconducting correlations, and variations of the charge density self-consistently for a superconducting-magnetic bilayer by solving the Bogoliubov–de Gennes equations on a two-dimensional lattice. We determine all three quantities as a function of the Coulomb repulsion U and the ferromagnetic exchange interaction J. The CSBM displays a variety of features not present in the Zeeman exchange model—for example, the occurrence of electronic phase separation and the competition of magnetic and superconducting orders far away from the interface.
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We evaluate the non-equilibrium spin polarization induced by an applied electric field for a tight-binding model of electron states at oxides interfaces in LAO/STO heterostructures. By a combination of analytic and numerical approaches we investigate how the spin texture of the electron eigenstates due to the interplay of spin-orbit coupling and inversion asymmetry determines the sign of the induced spin polarization as a function of the chemical potential or band filling, both in the absence and presence of local disorder. With the latter, we find that the induced spin polarization evolves from a non monotonous behavior at zero temperature to a monotonous one at higher temperature. Our results may provide a sound framework for the interpretation of recent experiments.
On the Evaluation of the Spin Galvanic Effect in Lattice Models with Rashba Spin-Orbit Coupling
(2018)
The spin galvanic effect (SGE) describes the conversion of a non-equilibrium spin polarization into a charge current and has recently attracted renewed interest due to the large conversion efficiency observed in oxide interfaces. An important factor in the SGE theory is disorder which ensures the stationarity of the conversion. Through this paper, we propose a procedure for the evaluation of the SGE on disordered lattices which can also be readily implemented for multiband systems. We demonstrate the performance of the method for a single-band Rashba model and compare our results with those obtained within the self-consistent Born approximation for a continuum model.
One major concern of channel engineering in nanotransistors is the coupling of the conduction channel to the source/drain contacts. In a number of previous publications, we have developed a semiempirical quantum model in quantitative agreement with three series of experimental transistors. On the basis of this model, an overlap parameter 0≤C≤1 can be defined as a criterion for the quality of the contact-to-channel coupling: A high level of C means good matching between the wave functions in the source/drain and in the conduction channel associated with a low contact-to-channel reflection. We show that a high level of C leads to a high saturation current in the ON-state and a large slope of the transfer characteristic in the OFF-state. Furthermore, relevant for future device miniaturization, we analyze the contribution of the tunneling current to the total drain current. It is seen for a device with a gate length of 26 nm that for all gate voltages, the share of the tunneling current becomes small for small drain voltages. With increasing drain voltage, the contribution of the tunneling current grows considerably showing Fowler–Nordheim oscillations. In the ON-state, the classically allowed current remains dominant for large drain voltages. In the OFF-state, the tunneling current becomes dominant.
The low-energy optical conductivity of conventional superconductors is usually well described by Mattis-Bardeen (MB) theory, which predicts the onset of absorption above an energy corresponding to twice the superconducing (SC) gap parameter Δ. Recent experiments on strongly disordered superconductors have challenged the application of the MB formulas due to the occurrence of additional spectral weight at low energies below 2Δ. Here we identify three crucial items that have to be included in the analysis of optical-conductivity data for these systems: (a) the correct identification of the optical threshold in the Mattis-Bardeen theory and its relation with the gap value extracted from the measured density of states, (b) the gauge-invariant evaluation of the current-current response function needed to account for the optical absorption by SC collective modes, and (c) the inclusion into the MB formula of the energy dependence of the density of states present already above Tc. By computing the optical conductivity in the disordered attractive Hubbard model, we analyze the relevance of all these items, and we provide a compelling scheme for the analysis and interpretation of the optical data in real materials.
Pseudogap and (An)isotropic Scattering in the Fluctuating Charge-Density Wave Phase of Cuprates
(2017)
We present a general scenario for high-temperature superconducting cuprates, based on the presence of dynamical charge density waves (CDWs) and to the occurrence of a CDW quantum critical point, which occurs, e.g., at doping p ≈ 0.16 in YBa2Cu3O6 + δ (YBCO). In this framework, the pseudogap temperature T∗ is interpreted in terms of a reduction of the density of states due to incipient CDW and, at lower temperature to the possible formation of incoherent superconducting pairs. The dynamically fluctuating character of CDW accounts for the different temperatures at which the CDW onset revealed by X-ray scattering (Tons(p)), and the static three-dimensional CDW ordering appear. We also investigate the anisotropic character of the CDW-mediated scattering. We find that this is strongly anisotropic only close to the CDW quantum critical point (QCP) at low temperature and very low energy. It rapidly becomes nearly isotropic and marginal-Fermi-liquid-like away from the CDW QCP and at finite (even rather small) energies. This may reconcile the interpretation of Hall measurements in terms of anisotropic CDW scattering with recent photoemission experiments Bok, J.M., et al. Sci. Adv. 2, e1501329 (2016).
Nanoscale electronic inhomogeneities are nowadays a well established feature of high-temperature superconductors, most prominently exemplified by the observation of charge-ordered states in a large number of cuprate materials. These inhomogeneities have profound consequences for the electron–phonon coupling since they allow for long-range pairing interactions due to the reduced screening supplemented by the enhancement of the electron–phonon vertex due to strong correlations. In this chapter we review the particular contribution of the Stuttgart-Tartu-Cottbus group to this field and discuss how the current status of experimental results provides affirmation to their ideas.
High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin–charge locking
(2017)
Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La1.875Ba0.125CuO4 across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.
It is shown that non-homogeneity in the spin-orbit coupling (SOC) arising from structure inversion asymmetry gives rise to a finite intrinsic spin Hall conductivity in contrast with the corresponding case of a homogeneous SOC in the disordered two-dimensional electron gas. In particular, we examine the inhomogeneity arising from a striped modulation of the Rashba type spin-orbit coupling. A corresponding structure could be realized at oxide interfaces with periodic top gating or in semiconductor heterostructures.
Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the “linear-response assumption” is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.
In the last few years, charge density waves (CDWs) have been ubiquitously observed in high-temperature superconducting cuprates and are now the most investigated among the competing orders in the still hot debate on these systems. A wealth of new experimental data raises several fundamental issues that challenge the various theoretical proposals. We here relate our mean-field instability line T0CDW of a strongly correlated Fermi liquid to the pseudogap T∗(p) line, marking in this way the onset of CDW-fluctuations. These fluctuations reduce strongly the mean-field critical line. Controlling this reduction via an infrared frequency cutoff related to the characteristic time of the probes, we account for the complex experimental temperature versus doping phase diagram. We provide a coherent scenario explaining why different CDW onset curves are observed by different experimental probes and seem to extrapolate at zero temperature into seemingly different quantum critical points (QCPs) in the intermediate and overdoped region. The nearly singular anisotropic scattering mediated by these fluctuations also accounts for the rapid changes of the Hall number seen in experiments and provides the first necessary step for a possible Fermi surface reconstruction fully establishing at lower doping. Finally, we show that phase fluctuations of the CDWs, which are enhanced in the presence of strong correlations near the Mott insulating phase, naturally account for the disappearance of the CDWs at low doping with yet another QCP as seen by the experiments.
There is steadily increasing evidence that the two-dimensional electron gas (2DEG) formed at the interface of some insulating oxides like LaAlO3/SrTiO3 and LaTiO3/SrTiO3 is strongly inhomogeneous. The inhomogeneous distribution of electron density is accompanied by an inhomogeneous distribution of the (self-consistent) electric field confining the electrons at the interface. In turn this inhomogeneous transverse electric field induces an inhomogeneous Rashba spin-orbit coupling (RSOC). After an introductory summary on two mechanisms possibly giving rise to an electronic phase separation accounting for the above inhomogeneity, we introduce a phenomenological model to describe the density-dependent RSOC and its consequences. Besides being itself a possible source of inhomogeneity or charge-density waves, the density-dependent RSOC gives rise to interesting physical effects like the occurrence of inhomogeneous spin-current distributions and inhomogeneous quantum-Hall states with chiral “edge” states taking place in the bulk of the 2DEG. The inhomogeneous RSOC can also be exploited for spintronic devices since it can be used to produce a disorder-robust spin Hall effect.
The spin galvanic effect (SGE) describes the conversion of a nonequilibrium spin polarization into a transverse charge current. Recent experiments have demonstrated a large conversion efficiency for the two-dimensional electron gas formed at the interface between two insulating oxides, LaAlO3 and SrTiO3. Here, we analyze the SGE for oxide interfaces within a three-band model for the Ti t2g orbitals which displays an interesting variety of effective spin-orbit couplings in the individual bands that contribute differently to the spin-charge conversion. Our analytical approach is supplemented by a numerical treatment where we also investigate the influence of disorder and temperature, which turns out to be crucial to providing an appropriate description of the experimental data.
In a series of recent papers we have established a semiempirical model for quantum transport in a nanotransistor. Here we apply this model to characterize four industrial transistors with gate lengths ranging between 22 nm and 30 nm finding excellent quantitative agreement between theory and experiment. Adjusting our semiempirical model to the experimental output traces, three calibration parameters are found: First, the height of the source–drain barrier, second, the device temperature, and, third, the overlap parameter. The overlap parameter describes the wave function overlap between the source/drain contact and the conduction channel. With the aid of the calibration parameters the considered devices can be classified in three groups: A first group (G1) with good contact-channel coupling and a high saturation current, a second group (G2) with intermediate values and a third group (G3) with poor contact-channel coupling and a small saturation current. We calculate the gate capacitance of the transistors: At threshold voltage a peak of the gate capacitance is observed which is associated with a jump in the overlap parameter. This finding is most pronounced in G1, weaker in G2 and absent in G3. We attribute it to favorable screening conditions in G1 leading to a smooth transition between the contacts and the conduction channel. Our results indicate that this screening effect is favored by an efficient release of the Ohmic heat.
Im ersten Teil untersuchen wir den phononischen Wärmetransport in nanoskaligen, heterogenen
Strukturen. Mit Hilfe des Nichtgleichgewicht-Green-Funktionen-Formalismus
leiten wir eine Entwicklung der phononischen Stromtransmission für kleine Frequenzen
her. Diese besitzt Gültigkeit für eine beliebige Oszillatorkette, welche eine typische
Kontakt-Device-Kontakt-Struktur aufweist. Wir nutzen die gefundene Entwicklung in
der Landauer Darstellung der Wärmeleitfähigkeit, wodurch wir eine systematische Tieftemperaturentwicklung
bestimmen können. Betrachtet man diese Entwicklung bis zur
zweiten Ordnung, erscheint die quantisierte Wärmeleitfähigkeit als ein konstantes Plateau,
in der Darstellung der Wärmeleitfähigkeit geteilt durch die Temperatur. Dies gilt
für die von uns untersuchten Kontakt-Device-Kontakt-Systeme, welche vollständig heterogen
sein können, insofern das Produkt aus Kopplungskonstante und Oszillatormasse
in beiden Kontakten identisch ist. Dabei ist das Ergebnis vollkommen unabhängig vom
Streugebiet. Im Anschluss an das Plateau gewinnen die höheren Ordnungen der Tieftemperaturentwicklung
an Bedeutung und führen zu endlichen Temperaturkorrekturen,
die einem kubischen Potenzgesetz gehorchen. Dieses Verhalten hängt von den strukturellen
Details des Streugebiets ab und ist in Übereinstimmung mit dem Experiment und
numerischen Berechnungen. Als Anwendung unserer allgemeinen Ergebnisse betrachten
wir eine “Double Junction”-Kette und finden als erstes Phänomen nach unserer Tieftemperaturentwicklung
ein zweites Plateau. Dieses Plateau steht in Verbindung mit einer
phasengemittelten Phononentransmission, welche für steigende Temperaturen zu einer
Unabhängigkeit der Wärmeleitfähigkeit von der Device-Länge führt. Im weiteren Verlauf
dieser Arbeit werden diese Ergebnisse auf quasi-eindimensionale 3D-Systeme in der
Kontakt-Device-Kontakt-Struktur verallgemeinert. Dazu werden exemplarisch geeignete
Kristallstrukturen identifiziert und anschließend für langwellige Phononen mathematisch
analysiert. Für Temperaturen unterhalb eines kritischen Wertes TK sind die Ergebnisse
des eindimensionalen Falls auf jede der akustischen Moden übertragbar. Daraus resultiert
eine analoge Beschreibung und Diskussion des Tieftemperaturverhaltens der Wärmeleitung, wie wir sie im strikt eindimensionalen Fall vorfinden.
Im zweiten Teil betrachten wir ein thermisches Modell integrierter Schaltkreise, unter
Berücksichtigung der zugehörigen Chip-Umgebung. Als die einfachste Wahl, behandeln
wir die aktive Schicht (“Front End Of Line”) als ein Feld, bestehend aus identischen
Quantenbauelementen mit der gleichen, von der Zeit abhängigen mittleren Temperatur.
Um die Chip-Umgebung zu modellieren, setzen wir voraus, dass sich die aktive Schicht
zwischen zwei planparallelen Wärmereservoirs befindet. Das obere Reservoir stellt dabei
die Verdrahtungsschicht des Chips dar (“Back End Of Line”). Die Temperatur dieser
Schicht ist weitestgehend durch die in den Leitern dissipierte joulesche Wärme bestimmt
und ist typischerweise in der Größenordnung von hundert Grad Celsius. Das untere
Reservoir verkörpert die Kühleinheit, die sich ungefähr auf Raumtemperatur befindet.
Wir lösen die gekoppelten Gleichungen, die auf der einen Seite den Wärmetransport
zwischen der aktiven Schicht und den umgebendenWärmereservoirs und auf der anderen
Seite den elektrischen Transport im Quantenbauelement beschreiben. Daraus ergeben
sich die Arbeitstemperaturen der betrachteten Quantenbauelemente, welche Lösungen
eines Fixpunktproblems sind. Diese Temperaturen hängen von der Position der aktiven
Schicht zwischen den beiden Wärmereservoirs ab. Die Stabilität der Fixpunkte lässt
sich aus einer geeigneten Linearisierung der zeitabhängigen Gesamtlösung ableiten. Für
ausgewählte Parameter und eine aktive Schicht aus identischen Nanotransistoren werden
numerische Lösungen präsentiert.
The spin-Hall effect is the generation of a transverse spin-current induced by a longitudinal electric field. Among the various scattering mechanisms which can induce a finite spin-Hall effect we focus on the intrinsic contribution arising from a Rashba-type spin–orbit (RSO) coupling which for couplings linear in momentum usually vanishes. Here we show that non-homogeneity in the spin–orbit coupling arising from structure inversion asymmetry gives rise to a finite spin-Hall effect which we exemplify for a system with striped Rashba spin–orbit coupling.
Empirical evidence in heavy fermion, pnictide and other systems suggests that unconventional superconductivity appears associated to some form of real-space electronic order. For the cuprates, despite several proposals, the emergence of order in the phase diagram between the commensurate antiferromagnetic state and the superconducting state is not well understood. Here we show that in this regime doped holes assemble in ‘electronic polymers’. Within a Monte Carlo study, we find that in clean systems by lowering the temperature the polymer melt condenses first in a smectic state and then in a Wigner crystal both with the addition of inversion symmetry breaking. Disorder blurs the positional order leaving a robust inversion symmetry breaking and a nematic order, accompanied by vector chiral spin order and with the persistence of a thermodynamic transition. Such electronic phases, whose properties are reminiscent of soft-matter physics, produce charge and spin responses in good accord with experiments.
We investigate the disorder dependence of the static density, amplitude, and current correlations within the attractive Hubbard model supplemented with onsite disorder. It is found that strong disorder favors a decoupling of density and amplitude correlations due to the formation of superconducting (SC) islands. This emergent granularity also induces an enhancement of the density correlations on the SC islands whereas amplitude fluctuations are most pronounced in the “insulating” regions. While density and amplitude correlations are short ranged at strong disorder, we show that current correlations have a long-range tail due to the formation of percolative current paths in agreement with the constant behavior expected from the analysis of one-dimensional models.
Besides significant electronic correlations, high-temperature superconductors also show a strong coupling of electrons to a number of lattice modes. Combined with the experimental detection of electronic inhomogeneities and ordering phenomena in many high-Tc compounds, these features raise the question as to what extent phonons are involved in the associated instabilities. Here we address this problem based on the Hubbard model including a coupling to phonons in order to capture several salient features of the phase diagram of hole-doped cuprates. Charge degrees of freedom, which are suppressed by the large Hubbard U near half-filling, are found to become active at a fairly low doping level. We find that possible charge order is mainly driven by Fermi surface nesting, with competition between a near-$(\pi ,\pi )$ order at low doping and antinodal nesting at higher doping, very similar to the momentum structure of magnetic fluctuations. The resulting nesting vectors are generally consistent with photoemission and tunneling observations, evidence for charge density wave order in YBa2Cu3O$_{7-\delta }$ including Kohn anomalies, and suggestions of competition between one- and two-q-vector nesting.
We investigate a two-dimensional electron model with Rashba spin-orbit interaction where the coupling constant $g=g(n)$ depends on the electronic density. It is shown that this dependence may drive the system unstable towards a long-wavelength charge density wave (CDW) where the associated second-order instability occurs in close vicinity to global phase separation. For very low electron densities the CDW instability is nesting-induced and the modulation follows the Fermi momentum kF. At higher density the instability criterion becomes independent of kF and the system may become unstable in a broad momentum range. Finally, upon filling the upper spin-orbit split band, finite momentum instabilities disappear in favor of phase separation alone. We discuss our results with regard to the inhomogeneous phases observed at the LaAlO3/SrTiO3 or LaTiO3/SrTiO3 interfaces.
LaAlO 3/SrTiO 3 and LaTiO 3/SrTiO 3 (LXO / STO) interfaces are known to host a strongly inhomogeneous (nearly) two-dimensional electron gas (2DEG). In this work, we present three unconventional electronic mechanisms of electronic phase separation (EPS) in a 2DEG as a possible source of inhomogeneity in oxide interfaces. Common to all three mechanisms is the dependence of some (interaction) potential on the 2DEGs density. We first consider a mechanism resulting from a sizable density-dependent Rashba spin-orbit coupling. Next, we point out that an EPS may also occur in the case of a density-dependent superconducting pairing interaction. Finally, we show that the confinement of the 2DEG to the interface by a density-dependent, self-consistent electrostatic potential can by itself cause an EPS.