Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

Hentschel, Martina; Ullmo, Denis; Baranger, Harold U.

doi:10.1103/physrevlett.93.176807

Cited by 14 publications

(27 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This analytic range-1 result is compared to the full overlap distribution P (|∆| 2 ) as well as the exact range-1 and range-2 approximations 34 (CUE case, see Ref. 8 for the corresponding COE figure). The agreement between the analytic approximation and the exact range-1 results is excellent.…”

Section: Analytic Results For the Overlap Distributionmentioning

confidence: 99%

“…The first one is the Anderson orthogonality catastrophe (AOC), which is a property of the overlap between many-body wavefunctions. However, in x-ray absorption and photoabsorption processes, besides AOC there is another many-body response of the conduction electrons to the impurity potential, 3,4,7,8 often referred to as Mahan's exciton, Mahan's enhancement, or the Mahan-Nozières-DeDominicis (MND) contribution. It counteracts the effect of AOC in situations where the dipole selections rules are fulfilled, and causes the photoabsorption cross section to diverge at the threshold.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fermi edge singularities in the mesoscopic regime: Anderson orthogonality catastrophe

2005

Self Cite

View full text Add to dashboard Cite

For generic mesoscopic systems like quantum dots or nanoparticles, we study the Anderson orthogonality catastrophe (AOC) and Fermi edge singularities in photoabsorption spectra in a series of two papers. In the present paper we focus on AOC for a finite number of particles in discrete energy levels where, in contrast to the bulk situation, AOC is not complete. Moreover, fluctuations characteristic for mesoscopic systems lead to a broad distribution of AOC ground state overlaps. The fluctuations originate dominantly in the levels around the Fermi energy, and we derive an analytic expression for the probability distribution of AOC overlaps in the limit of strong perturbations. We address the formation of a bound state and its importance for symmetries between the overlap distributions for attractive and repulsive potentials. Our results are based on a random matrix model for the chaotic conduction electrons that are subject to a rank one perturbation corresponding, e.g., to the localized core hole generated in the photoabsorption process.

show abstract

Section: Analytic Results For the Overlap Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fermi edge singularities in the mesoscopic regime: Anderson orthogonality catastrophe

2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…Furthermore, the zero bias anomaly in disordered metals [3] and anomalies in the tunneling density of states in quantum Hall systems [4] are related to the AOC The concept of fidelity can be generalised to any parametric perturbation of a system and be used to characterise quantum phase transitions [5]. The AOC has been explored in mesoscopic systems [6,7]. With the advent of engineered many-body systems in ensembles of ultracold atoms it is possible to study nonequilibrium quantum dynamics of such systems in a controlled way so that conseuqences of parameter changes become measurable directly [8].…”

mentioning

confidence: 99%

“…2 we plot the first moment of the Anderson Integral I A as function of Fermi energy E F in units of mobility Edge E M , Eqs. (6,7,8), for various system sizes L.…”

mentioning

confidence: 99%

Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition

Kettemann

2016

Phys. Rev. Lett.

View full text Add to dashboard Cite

We consider the orthogonality catastrophe at the Anderson Metal-Insulator transition (AMIT). The typical overlap F between the ground state of a Fermi liquid and the one of the same system with an added potential impurity is found to decay at the AMIT exponentially with system size L as F ∼ exp(− IA /2) = exp(−cL η ), where IA is the so called Anderson integral, η is the power of multifractal intensity correlations and ... denotes the ensemble average. Thus, strong disorder typically increases the sensitivity of a system to an additional impurity exponentially. We recover on the metallic side of the transition Anderson's result that fidelity F decays with a power law F ∼ L −q(E F ) with system size L. This power increases as Fermi energy EF approaches mobility edge EM as q(EF ) ∼ (where ν is the critical exponent of correlation length ξc. On the insulating side of the transition F is constant for system sizes exceeding localization length ξ. While these results are obtained from the mean value of IA, giving the typical fidelity F , we find that IA is widely, log normally, distributed with a width diverging at the AMIT. As a consequence, the mean value of fidelity F converges to one at the AMIT, in strong contrast to its typical value which converges to zero exponentially fast with system size L. This counterintuitive behavior is explained as a manifestation of multifractality at the AMIT.PACS numbers: 72.10. Fk,72.15.Rn,72.20.Ee,74.40.Kb,75.20.Hr, Anderson showed in Ref.1 that the addition of a static potential impurity to a system of N fermions changes its groundstate such that the overlap between the original ψ | and the new ground state ψ | has an upper bound,where the Anderson integral I A is for noninteracting electrons given in terms of the single particle eigenstates of the original system |n and the new system |m byIf the added impurity is short ranged and of strength λ, Anderson found for a clean metal I A = 2π 2 λ 2 ln N, diverging with the number of fermions N , so that F , also called fidelity, decays with a power law with N, leading to the so called orthogonality catastrophe (AOC). This implies that the local perturbation connects the system to a macroscpic number of excited states which has important consequences like the singularities in the X-Ray absorption and emission of metals [2]. Furthermore, the zero bias anomaly in disordered metals [3] and anomalies in the tunneling density of states in quantum Hall systems [4] are related to the AOC The concept of fidelity can be generalised to any parametric perturbation of a system and be used to characterise quantum phase transitions [5]. The AOC has been explored in mesoscopic systems [6,7]. With the advent of engineered many-body systems in ensembles of ultracold atoms it is possible to study nonequilibrium quantum dynamics of such systems in a controlled way so that conseuqences of parameter changes become measurable directly [8].An intriguing question is, if the system becomes less or more sensitive to the addition of another impurity if it alread...

show abstract

“…Photoabsorption cross section. Our calculation of the photoabsorption cross section is based on the Golden-rule approach to the X-ray edge problem [3,24,25]. We model the perturbation associated with the excitation of a core electron into the conduction band, causing the FES, as a localized, rank-one perturbation [3,29].…”

mentioning

confidence: 99%

Photoabsorption spectra and the X-ray edge problem in graphene

Röder

Tkachov²,

Hentschel³

2011

EPL

View full text Add to dashboard Cite

Abstract. -We study the photoabsorption cross section and Fermi-edge singularities (FES) in graphene. For fillings below one half, we find, besides the expected FES in form of a peaked edge at the threshold (Fermi) energy, a second singularity to arise at excitation energies that correspond to the Dirac point in the density of states. We can explain this behaviour by comparing our results with the photoabsorption cross section of a metal with a small central band gap where we find a very similar signature. The existence of the second singularity might prove useful for an experimental determination of the Dirac point. We also demonstrate that the photoabsorption signal is enhanced by the zigzag edge states due to their metallic-like character. Since the presence of the edge states indicates a topological defect at the boundary, our study gives an example for a Fermi-edge singularity in a system with a topologically nontrivial electronic spectrum.

show abstract

Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

Cited by 14 publications

References 20 publications

Fermi edge singularities in the mesoscopic regime: Anderson orthogonality catastrophe

Fermi edge singularities in the mesoscopic regime: Anderson orthogonality catastrophe

Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition

Photoabsorption spectra and the X-ray edge problem in graphene

Contact Info

Product

Resources

About