arXiv subjects

J. Fernández

Publications and source records attributed to J. Fernández.

8 recordsLinked to original sources

arXiv2024

A Brillouin torus decomposition for two-dimensional topological insulators

Two-band Chern insulators are topologically classified by the Chern number, $c$, which is given by the integral of the Berry curvature of the occupied band over the Brillouin torus. The curvature itself comes from the imaginary part of a more basic object, the quantum geometric tensor, $Q$. On the other hand, the integral over the Brillouin torus of the real part of $Q$ gives rise to another magnitude, the quantum volume, $v_{g}$, that like $c$, jumps when the system undergoes a topological phase transition and satisfies the inequality $v_{g}\ge 2\vert c \vert$. The information contained in $v_g$ about the topology of the system has been investigated recently. In this paper we present new results regarding the underlying geometric structure of two-dimensional two-band topological insulators. Since a generic model describing the system can be characterized by a map, the classifying map, from the Brillouin torus to the two-sphere, we study its properties at the geometric level. We present a procedure for splitting the Brillouin torus into different sectors in such a way that the classifying map when restricted to each of them is a local diffeomorphism. By doing so, in the topological phases we are able to isolate a region contained in the Brillouin torus whose volume is the minimal one, $v_{min}=2\vert c \vert$ and the integral of the Berry curvature on it is $c$. For cases in which $v_{g}> 2\vert c \vert$, the regions contributing to the excess of volume, $v_{ex}=v_{g}-2\vert c \vert$, are found and characterized. In addition, the present work makes contact with, and clarifies, some interpretations of the quantum volume in terms of the Euler characteristic number that were done in the recent literature. We illustrate our findings with a careful analysis of some selected models for Chern insulators corresponding to tight-binding Hamiltonians.

math-ph↗

arXiv2019

Kondo physics of magnetic adatoms on metallic surfaces when the onset of the surface conduction density of states crosses the Fermi level

We study the role of the onset of Shockley states, $D_s$, belonging to (111) surfaces of Cu, Ag and Au in the Kondo effect when a magnetic impurity is deposited on them. When $D_s$ approaches to the Fermi level, $E_F$, thing that can be done by compressing (stretching) the metallic sample, we found that most of the thermodynamic and dynamic properties of the impurity are affected in a non trivial way. We model the system by a generic Anderson impurity model and solve it by using the numerical renormalization group, NRG, technique. In particular, the impurity contribution to magnetic susceptibility and entropy as a function of temperature exhibit negative values and goes to zero slowly in a logarithmic shape. Furthermore, we found a suppression of the spectral density weight at the Fermi level when $D_s\sim E_F$ even in the Kondo regime. As a consequence, the conductance through the impurity is strongly reduced by near $25\%$ of the unitary value $2e^2/h$. Finally, we analyze these features in realistic systems like Co on Ag(111) reported in the literature.

cond-mat.str-el↗

arXiv2018

Quantifying the leading role of the surface state in the Kondo effect of Co/Ag(111)

Using a combination of scanning tunneling spectroscopy and atomic lateral manipulation, we obtained a systematic variation of the Kondo temperature ($T_\mathrm K$) of Co atoms on Ag(111) as a function of the surface state contribution to the total density of states at the atom adsorption site ($ρ_s$). By sampling the $T_\mathrm K$ of a Co atom on positions where $ρ_s$ was spatially resolved beforehand, we obtain a nearly linear relationship between both magnitudes. We interpret the data on the basis of an Anderson model including orbital and spin degrees of freedom (SU(4)) in good agreement with the experimental findings. The fact that the onset of the surface band is near the Fermi level is crucial to lead to the observed linear behavior. In the light of this model, the quantitative analysis of the experimental data evidences that at least a quarter of the coupling of Co impurities with extended states takes place through the hybridization to surface states. This result is of fundamental relevance in the understanding of Kondo screening of magnetic impurities on noble metal surfaces, where bulk and surface electronic states coexist.

cond-mat.str-el↗

arXiv2018

Two-stage three-channel Kondo physics for an FePc molecule on the Au(111) surface

We study an impurity Anderson model to describe an iron phthalocyanine (FePc) molecule on Au(111), motivated by previous results of scanning tunneling spectroscopy (STS) and theoretical studies. The model hybridizes a spin doublet consisting in one hole at the $3d_{z^2}$ orbital of iron and two degenerate doublets corresponding to one hole either in the $3d_{xz}$ or in the $3d_{yz}$ orbital (called $π$ orbitals) with two degenerate Hund-rule triplets with one hole in the $3d_{z}$ orbital and another one in a $π$ orbital. We solve the model using a slave-boson mean-field approximation (SBMFA). For reasonable parameters we can describe very well the observed STS spectrum between sample bias -60 mV to 20 mV. For these parameters the Kondo stage takes place in two stages, with different energy scales $T_K^z > T_K^π$ corresponding to the Kondo temperatures related with the hopping of the $z^2$ and $π$ orbitals respectively. There is a strong interference between the different channels and the Kondo temperatures, particularly the lowest one is strongly reduced compared with the value in the absence of the competing channel.

cond-mat.str-el↗

arXiv2018

Numerical solution of stochastic master equations using stochastic interacting wave functions

We develop a new approach for solving stochastic quantum master equations with mixed initial states. First, we obtain that the solution of the jump-diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of Schrödinger type. Then, we design three exponential schemes for these coupled stochastic Schrödinger equations, which are driven by Brownian motions and jump processes. Hence, we have constructed efficient numerical methods for the stochastic master equations based on quantum trajectories. The good performance of the new numerical integrators is illustrated by simulations of two quantum measurement processes.

physics.comp-ph↗

arXiv2017

Width of the charge-transfer peak in the SU(N) impurity Anderson model and its relevance to non-equilibrium transport

We calculate the width $2Δ_{\text{CT}}$ and intensity of the charge-transfer peak (the one lying at the on-site energy $E_d$) in the impurity spectral density of states as a function of $E_d$ in the SU($N$) impurity Anderson model (IAM). We use the dynamical density-matrix renormalization group (DDMRG) and the noncrossing-approximation (NCA) for $N$=4, and a 1/$N$ variational approximation in the general case. In particular, while for $E_d \gg Δ$, where $Δ$ is the resonant level half-width, $Δ_{\text{CT}}=Δ$ as expected in the noninteracting case, for $-E_d \gg N Δ$ one has $Δ_{\text{CT}}=NΔ$. In the $N$=2 case, some effects of the variation of $% Δ_{\text{CT}}$ with $E_d$ were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. Könemann \textit{et al.}, Phys. Rev. B \textbf{73}, 033313 (2006)]. More dramatic effects are expected in similar experiments, that can be carried out in systems of two quantum dots, carbon nanotubes or other, realizing the SU(4) IAM.

cond-mat.str-el↗

arXiv2017

Kondo temperature when the Fermi level is near a step in the conduction density of states

The (111) surface of Cu, Ag and Au is characterized by a band of surface Shockley states, with constant density of states beginning slightly below the Fermi energy. These states as well as bulk states hybridize with magnetic impurities which can be placed above the surface. We calculate the characteristic low-temperature energy scale, the Kondo temperature $T_K$ of the impurity Anderson model, as the bottom of the conduction band $D_s$ crosses the Fermi energy $ε_F$. We find simple power laws $T_K \simeq |D_s-ε_F|^η$, where $η$ depends on the sign of $D_s-ε_F$, the ratio between surface and bulk hybridizations with the impurity $Δ_s/Δ_b$ and the ratio between on-site and Coulomb energy $E_d/U$ in the model.

cond-mat.str-el↗

arXiv2015

Valence fluctuations in a lattice of magnetic molecules: application to iron(II) phtalocyanine molecules on Au(111)

We study theoretically a square lattice of the organometallic Kondo adsorbate iron(II) phtalocyanine (FePc) deposited on top of Au(111), motivated by recent scanning tunneling microscopy experiments. We describe the system by means of an effective Hubbard-Anderson model, where each molecule has degenerate effective $d-$orbitals with $xz$ and $yz$ symmetry, which we solve for arbitrary occupation and arbitrary on-site repulsion $U$. To that end, we introduce a generalized slave-boson mean-field approximation (SBMFA) which correctly describes both the non-interacting limit (NIL) $U=0$ and the strongly-interacting limit $U \rightarrow \infty$, where our formalism reproduces the correct value of the Kondo temperature for an isolated FePc molecule. Our results indicate that while the isolated molecule can be described by an SU(4) Anderson model in the Kondo regime, the case of the square lattice corresponds to the intermediate-valence regime, with a total occupation of nearly 1.65 holes in the FePc molecular orbitals. Our results have important implications for the physical interpretation of the experiment.

cond-mat.str-el↗