arXiv subjects

Thilo Kopp

Publications and source records attributed to Thilo Kopp.

At least 37 records · Page 2Linked to original sources

arXiv2016

Artificial Atoms Based on Correlated Materials

Low-dimensional electron systems fabricated from quantum matter have in recent years become available and are being explored with great intensity. This article gives an overview of the fundamental properties of such systems and summarizes the state of the field. We furthermore present and consider the concept of artificial atoms fabricated from quantum materials, anticipating remarkable scientific advances and possibly important applications of this new field of research. The surprising properties of these artificial atoms and of molecules or even of solids assembled from them are presented and discussed.

cond-mat.str-el↗

arXiv2015

Charge instabilities of the two-dimensional Hubbard model with attractive nearest neighbour interaction

Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility---ultimately signalling charge instability and phase separation---and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter $F_0^s$ are presented, whereby the positivity of $F_0^s-1$ constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter $t'$ shifts their positions and produces a tendency towards charge instability even for low filling whereas the $t'$-controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction $V$ is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction $U$, at densities far from half filling.

cond-mat.str-el↗

arXiv2015

Spin-orbit controlled quantum capacitance of a polar heterostructure

Oxide heterostructures with polar films display special electronic properties, such as the electronic reconstruction at their internal interfaces with the formation of two-dimensional metallic states. Moreover, the electrical field from the polar layers is inversion-symmetry breaking and generates a Rashba spin-orbit coupling (RSOC) in the interfacial electronic system. We investigate the quantum capacitance of a heterostructure in which a sizeable RSOC at a metallic interface is controlled by the electric field of a surface electrode. Such a structure is, for example, given by a LaAlO_3 film on a SrTiO_3 substrate which is gated by a top electrode. Such heterostructures can exhibit a strong enhancement of their capacitance [Li et al., Science 332, 825 (2011)]. The capacitance is related to the electronic compressibility of the heterostructure, but the two quantities are not equivalent. In fact, the transfer of charge to the interface controls the relation between capacitance and compressibility. We find that due to a strong RSOC, the quantum capacitance can be larger than the classical geometric value. However, in contrast to the results of recent investigations [Caprara et al., Phys. Rev. Lett. 109, 196401 (2012); Bucheli et al., Phys. Rev. B 89, 195448 (2014); Seibold et al., Europhys. Lett. 109, 17006 (2015)] the compressibility does not become negative for realistic parameter values for LaAlO_3/SrTiO_3 and, therefore, we find that no phase-separated state is induced by the strong RSOC at these interfaces.

cond-mat.mes-hall↗

arXiv2014

Route to Topological Superconductivity via Magnetic Field Rotation

The verification of topological superconductivity has become a major experimental challenge. Apart from the very few spin-triplet superconductors with p-wave pairing symmetry, another candidate system is a conventional, two-dimensional (2D) s-wave superconductor in a magnetic field with a sufficiently strong Rashba spin-orbit coupling. Typically, the required magnetic field to convert the superconductor into a topologically non-trivial state is however by far larger than the upper critical field H_c2, which excludes its realization. In this article, we argue that this problem can be overcome by rotating the magnetic field into the superconducting plane. We explore the character of the superconducting state upon changing the strength and the orientation of the magnetic field and show that a topological state, established for a sufficiently strong out-of-plane magnetic field, indeed extends to an in-plane field orientation. We present a three-band model applicable to the superconducting interface between LaAlO_3 and SrTiO_3, which should fulfil the necessary conditions to realize a topological superconductor.

cond-mat.supr-con↗

arXiv2014

Formation of magnetic moments and resistance upturn at grain boundaries of two-dimensional electron systems

Electronic correlations control the normal state of bulk high-Tc cuprates. Strong correlations also suppress the charge transport through cuprate grain boundaries (GBs). The question then arises if these correlations can produce magnetic states at cuprate GBs. We analyze the formation of local magnetic moments at the GB of a correlated two-dimensional electron systems which is represented by an inhomogeneous Hubbard model. The model Hamiltonian is diagonalized after the implementation of a mean-field decoupling. The formation of local magnetic moments is supported by a sufficiently strong variance in the bond kinetic energies at the GB. Local scattering potentials can assist or suppress the formation of a magnetic GB state, depending on the details of their spacial distribution. Grain boundary induced stripes are formed in the vicinity the GB and decay into the bulk. Moreover, we observe the build-up of conducting channels which are confined by magnetic clusters. The grain boundary resistance increases at decreasing temperatures. This low-temperature behavior is caused by the suppression of current correlations in the state with local magnetic GB moments. The resistance upturn at low temperatures is in qualitative agreement with experiments.

cond-mat.mes-hall↗

arXiv2013

Superconductivity with Rashba Spin-Orbit Coupling and Magnetic Field

Two dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin- orbit coupling (SOC), which is tunable by a transverse electric field. Ferromagnetism at the interface can simultaneously induce strong local magnetic fields. This combination of SOC and magnetism leads to asymmetric two-sheeted Fermi surfaces, on which either intra- or inter-band pairing is favored. The superconducting order parameters are derived within a microscopic pairing model realizing both, the Bardeen-Cooper-Schrieffer superconductor with inter-band pairing in the regime of dominating magnetic field, and a mixed-parity intra-band pairing state with finite-momentum pairing in the regime of dominating SOC. We present a phase diagram for the superconducting groundstates and analyze the density of states of the different phases. The results are discussed in the context of superconductivity and ferromagnetism at LaAlO3-SrTiO3 interfaces.

cond-mat.supr-con↗

arXiv2012

Fractional Flux Quantization in Loops of Unconventional Superconductors

The magnetic flux threading a conventional superconducting ring is typically quantized in units of $Φ_0=hc/2e$. The factor 2 in the denominator of $Φ_0$ originates from the existence of two different types of pairing states with minima of the free energy at even and odd multiples of $Φ_0$. Here we show that spatially modulated pairing states exist with energy minima at fractional flux values, in particular at multiples of $Φ_0/2$. In such states condensates with different center-of-mass momenta of the Cooper pairs coexist. The proposed mechanism for fractional flux quantization is discussed in the context of cuprate superconductors, where $hc/4e$ flux periodicities as well as uniaxially modulated superconducting states were observed.

cond-mat.supr-con↗

arXiv2012

Disorder Induced Stripes in d-Wave Superconductors

Stripe phases are observed experimentally in several copper-based high-Tc superconductors near 1/8 hole doping. However, the specific characteristics may vary depending on the degree of dopant disorder and the presence or absence of a low- temperature tetragonal phase. On the basis of a Hartree-Fock decoupling scheme for the t-J model we discuss the diverse behavior of stripe phases. In particular the effect of inhomogeneities is investigated in two distinctly different parameter regimes which are characterized by the strength of the interaction. We observe that small concen- trations of impurities or vortices pin the unidirectional density waves, and dopant disorder is capable to stabilize a stripe phase in parameter regimes where homogeneous phases are typically favored in clean systems. The momentum-space results exhibit universal features for all coexisting density-wave solutions, nearly unchanged even in strongly disordered systems. These coexisting solutions feature generically a full energy gap and a particle-hole asymmetry in the density of states.

cond-mat.supr-con↗

arXiv2012

Flux-Periodicity Crossover from hc/e in Normal Metallic to hc/2e in Superconducting Loops

The periodic response of a metallic or a superconducting ring to an external magnetic flux is one of the most evident manifestations of quantum mechanics. It is generally understood that the oscillation period hc/2e in the superconducting state is half the period hc/e in the metallic state, because the supercurrent is carried by Cooper pairs with a charge 2e. On the basis of the Bardeen-Cooper-Schrieffer theory we discuss, in which cases this simple interpretation is valid and when a more careful analysis is needed. In fact, the knowledge of the oscillation period of the current in the ring provides information on the electron interactions. In particular, we analyze the crossover from the hc/e periodic normal current to the hc/2e periodic supercurrent upon turning on a pairing interaction in a metal ring. Further, we elaborate on the periodicity crossover when cooling a metallic loop through the superconducting transition temperature Tc.

cond-mat.supr-con↗

arXiv2012

Magnetic transitions in strong coupling expansions for nearly degenerate states

We consider a strong coupling expansion for a two-band Hubbard model on two sites with nearly degenerate states. A comparative analysis is performed for different schemes of perturbation theory which are applicable to systems with nearly degenerate states. A fourth order approach which builds on a four-dimensional low-energy subspace with nearly degenerate states captures accurately the transition from an antiferromagnetic to a ferromagnetic ground state at large on-site Coulomb interaction.

cond-mat.str-el↗

arXiv2012

Magnetically ordered state at correlated oxide interfaces: the role of random oxygen defects

Using an effective one-band Hubbard model with disorder, we consider magnetic states of the correlated oxide interfaces, where effective hole self-doping and a magnetially ordered state emerge due to electronic and ionic reconstructions. By employing the coherent potential approximation, we analyze the effect of random oxygen vacancies on the two-dimensional magnetism. We find that the random vacancies enhance the ferromagnetically ordered state and stabilize a robust magnetization above a critical vacancy concentration of about c=0.1. In the strong-correlated regime, we also obtain a nonmonotonic increase of the magnetization upon an increase of vacancy concentration and a substantial increase of the magnetic moments, which can be realized at oxygen reduced high-Tc cuprate interfaces.

cond-mat.str-el↗

arXiv2012

Exact results with the Kotliar-Ruckenstein slave-boson representation

Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The expectation values of the radial (real) fields are in fact to be interpreted as the density of empty or singly occupied sites. Whereas the radial representation of the Barnes slave bosons has been investigated before, a setup for the functional integral of radial bosonic fields in the more physical Kotliar-Ruckenstein representation has not been accomplished to date. We implement a path integral procedure with suitable renormalization factors for a strongly correlated two-site model which allows to control the formal steps in the intricate evaluation, as the results for the partition function and the expectation values are known from exact diagonalization for such a minimal single impurity Anderson model. The partition function is shown to be a trace over a product of matrices local in time and therefore can be calculated analytically. Eventually, we establish the scheme for the evaluation of correlation functions and thermodynamic properties.

cond-mat.str-el↗

arXiv2011

Modeling of Superconducting Stripe Phases in High-Tc Cuprates

Even before the experimental discovery of spin- and charge-stripe order in La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_x$CuO$_4$ at x = 1/8, stripe formation was predicted from theoretical considerations. Nevertheless, a consistent description of the complex coexistence of stripe order with superconductivity has remained a challenge. Here we introduce a Hartree-Fock decoupling scheme which unifies previous approaches and allows for a detailed analysis of the competition between antiferromagnetism and superconductivity in real and momentum space. We identify two distinct parameter regimes, where spin-stripe order coexists with either one- or two-dimensional superconductivity; experiments on different striped cuprates are either compatible with the former or the latter regime. We argue that the cuprates at x = 1/8 fall into an intermediate coupling regime with a crossover to long-range phase coherence between individual superconducting stripes.

cond-mat.supr-con↗

arXiv2011

Pairing Theory of Striped Superconductivity

Striped high-$T_{\rm c}$ superconductors such as La$_{2-y-x}$Nd$_{y}$Sr$_x$CuO$_4$ and La$_{2-x}$Ba$_{x}$CuO$_4$ near $x=1/8$ show a fascinating competition between spin and charge order and superconductivity. A theory for these systems therefore has to capture both the spin correlations of an antiferromagnet and the pair correlations of a superconductor. For this purpose we present here an effective Hartree-Fock theory incorporating both electron pairing with finite center-of-mass momentum and antiferromagnetism. We show that this theory reproduces the key experimental features such as the formation of the antiferromagnetic stripe patterns at 7/8 band filling or the quasi one-dimensional electronic structure observed by photoemission spectroscopy.

cond-mat.supr-con↗

arXiv2010

Flux periodicities in loops and junctions with d-wave superconductors

The magnetic flux periodicity in superconducting loops is reviewed. Whereas quantization of the magnetic flux with hc/2e prevails in sufficiently thick loops with current free interior, the supercurrent in narrow loops is either hc/2e or hc/e periodic with the external magnetic flux. The periodicity depends on the properties of the condensate state, in particular on the Doppler shift of the energy spectrum. For an s-wave superconductor in a loop with diameter larger than the coherence length, the Doppler shift is small with respect to the energy gap, and the hc/2e periodic behavior of its flux dependent thermodynamic properties is maintained. However, for smaller s-wave loops and, more prominently, narrow d-wave loops of any diameter R, the Doppler shift has a strong effect on the supercurrent carrying state; as a consequence, the fundamental flux periodicity is in fact hc/e. It is shown analytically and numerically that the hc/e periodic component in the supercurrent decays only algebraically as 1/R for large d-wave loops. For nodal superconductors the discrete nature of the eigenergies close to the Fermi energy has to be respected in the evaluation of the Doppler shift. Furthermore, we investigate, whether the Doppler shift modifies the supercurrent through Josephson junctions with d-wave superconductors. For transparent junctions, the Josephson current behaves similar to the persistent supercurrent in a loop. These distinct physical phenomena can be compared, if the magnetic flux in units of hc/e is identified with the phase variation of the order parameter divided by 4 pi.

cond-mat.supr-con↗

arXiv2010

Structural relaxation and metal-insulator transition at the interface between SrTiO3 and LaAlO3

The electronic structure of interfaces between LaAlO$_3$ and SrTiO$_3$ is studied using local spin density approximation (LSDA) with intra-atomic Coulomb repulsion (LSDA+U). We find that the nature of the interface metallic states is strongly affected by the type of the structure (sandwich or bilayer) and by the termination surface of LaAlO$_3$. In all structures the atomic relaxation plays a crucial role in the electronic properties of the system. While in sandwiches the structural relaxation produces a significant polarization in SrTiO$_3$ and Jahn-Teller like splitting of Ti $3d_{xy}$ orbitals, in AlO$_2$-terminated bilayers the relaxation occurs primarily in LaAlO$_3$ and results in an insulator-metal transition which has been observed experimentally with increasing thickness of the LaAlO$_3$ layer.

cond-mat.str-el↗

arXiv2009

Superconductivity with Finite-Momentum Pairing in Zero Magnetic Field

In the BCS theory of superconductivity, one assumes that all Cooper pairs have the same center of mass momentum. This is indeed enforced by self consistency, if the pairing interaction is momentum independent. Here, we show that for an attractive nearest neighbor interaction, this is different. In this case, stable solutions with pairs with momenta q and -q coexist and, for a sufficiently strong interaction, one of these states becomes the groundstate of the superconductor. This finite-momentum pairing state is accompanied by a charge order with wave vector 2q. For a weak pairing interaction, the groundstate is a d-wave superconductor.

cond-mat.supr-con↗

arXiv2009

Calculation of the Capacitances of Conductors -- Perspectives for the Optimization of Electronic Devices

The equation describing the capacitance of capacitors is determined. It is shown that by optimizing the material of the conducting electrodes, the capacitance of capacitors reaching the quantum regime can be substantially enhanced or reduced. Dielectric capacitors with negative total capacitances are suggested and their properties analyzed. Resulting perspectives to enhance the performance of electronic devices are discussed.

cond-mat.mtrl-sci↗