# Measurement of the dynamic charge response of materials using low-energy, momentum-resolved electron energy-loss spectroscopy (M-EELS)

### Submission summary

 As Contributors: Peter Abbamonte · Ali Husain · Anshul Kogar · Matteo Mitrano · Mindy Rak Arxiv Link: http://arxiv.org/abs/1509.04230v4 (pdf) Date submitted: 2017-07-13 02:00 Submitted by: Abbamonte, Peter Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Experiment Condensed Matter Physics - Theory Approaches: Experimental, Theoretical

### Abstract

One of the most fundamental properties of an interacting electron system is its frequency- and wave-vector-dependent density response function, $\chi({\bf q},\omega)$. The imaginary part, $\chi''({\bf q},\omega)$, defines the fundamental bosonic charge excitations of the system, exhibiting peaks wherever collective modes are present. $\chi$ quantifies the electronic compressibility of a material, its response to external fields, its ability to screen charge, and its tendency to form charge density waves. Unfortunately, there has never been a means to measure $\chi({\bf q},\omega)$ at the meV energy scale relevant to modern electronic materials. Here, we demonstrate a way to measure $\chi$ by applying momentum-resolution methods from x-ray and neutron scattering to surface high-resolution electron energy-loss spectroscopy (HR-EELS). This approach, referred to here as "M-EELS," allows quantitative measurement of $\chi''({\bf q},\omega)$ with meV resolution at wave vectors spanning multiple Brillouin zones. We apply this technique to finite-q excitations in the optimally-doped high temperature superconductor, Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212), which exhibits several phonons potentially relevant to dispersion anomalies observed in ARPES and STM experiments. Our study defines a path to studying the long-sought collective charge modes in quantum materials at the meV scale.

### Ontology / Topics

See full Ontology or Topics database.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 1509.04230v5 on 15 September 2017

Submission 1509.04230v4 on 13 July 2017

## Reports on this Submission

### Anonymous Report 2 on 2017-8-25 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1509.04230v4, delivered 2017-08-25, doi: 10.21468/SciPost.Report.230

### Strengths

1- the paper is very well written provide a detailed and highly valuable theoretical background, much better than those I came across in the existing in the litterature.
2- Whereas the technique has been around for some time, it has only marginally been applied to correlated systems. The present works highlights this very well and a strong case for the method is made.

### Weaknesses

1- Some inaccuracies. I am surprised by the statement 'The problem with EELS is that meV energy resolution has not yet been demonstrated in an instrument that is also momentum-resolved.' Such devices have been developped in Germany a few years ago (see e.g. http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.104.137203 or this still recent review http://dx.doi.org/10.1016/j.physrep.2014.08.001, where high-resolution momentum resolved EELS has been used to study magnetic excitations in ultrathin films. Arguably these experimental set-ups were not developed to measure charge dynamics (in fact spin polarization seem to be an extra complication), I believe they represent concrete examples of momentum-resolved EELS with meV energy resolution. I am surprise not to see such examples mentioned in the current paper.

2- To the best of my knowledge the statement 'Despite steady improvements, however, RIXS techniques are still
limited to an energy resolution of ∆E ∼ 120 meV' is only valid for Cu L-edge RIXS. Edges of lighter atoms have higher resolutions.
Improved energy resolution has recently also been demonstrated (http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys4157.html). I agree however with the authors that the cross-section issue is a strong caveat of this method.

3- EELS is an highly surface sensitive technique. Here the authors use relatively small energies and work in transmission. I´d expect they have to work on extremely thin layers of material, yet I haven´t found anything regarding the actual sample thickness.

4- Not much is learnt about the studied material

### Report

Overall I believe this is a very useful paper that should motivate subsequent work.
Demonstration of a table-top high energy resolution and momentum resolved probe of the charge dynamics, and this opens new exciting perspectives. The theoretical background and the method are so well described that, despite maybe limited novelty regarding the physics of the cuprates, I am convinced that this paper will serve as a reference for further HR-EELS studies for correlated materials.

### Requested changes

see the remarks in the weaknesses section above.

• validity: top
• significance: high
• originality: top
• clarity: top
• formatting: perfect
• grammar: perfect

### Anonymous Report 1 on 2017-8-15 (Invited Report)

• Cite as: Anonymous, Report on arXiv:1509.04230v4, delivered 2017-08-15, doi: 10.21468/SciPost.Report.212

### Strengths

1) Compared to other recent papers on momentum resolved EELS, this work contains a far more substantial introduction and theoretical background relating the experimental data to the dynamic charge susceptibility.

2) The paper is exceptionally well written.

3) The authors deserve credit for relating EELS data to more widely used momentum resolved spectroscopies, in particular ARPES.

4) The paper is likely to stimulate progress in correlated electron physics.

### Weaknesses

1) The paper does not provide significant new insight into the material under investigation.

2) The paper oversells the experimental advances made by this group. From reading abstract and introduction alone, one gets the impression that the authors would have invented momentum resolved EELS. However, this is completely wrong. Momentum resolved EELS with spectrometers of the same type is used in the surface science community since 2 decades (see e.g. PRB 61, 16911 (2000) as an example). Moreover, other groups have recently implemented technically more advanced approaches to momentum resolved EELS (Refs. 38, 39). Later sections of the paper acknowledge this work more or less appropriately but from the way the first two pages are written now, many readers will get a completely wrong impression of the history and current status of EELS from this paper.

### Report

Vig et al. apply low-energy EELS to derive the dynamic charge response function of optimally doped Bi2212. This topic is of significant interest for many scientists working on "quantum materials". The experimental data is of good quality and its analysis is scientifically sound. On the other hand, the main results of the paper, namely the identification of different phonon modes and the observation of a plasmon near 1 eV, are not new and do not significantly advance our understanding of high-Tc cuprates.

In my opinion, the key contribution of this paper is the theoretical part relating EELS data to quantities of interest for correlated electron physics. This offers plenty of food for thoughts and makes the work interesting for a large community. At the same time, it provides arguably the most comprehensive guide to the interpretation of EELS data to date and will be an extremely valuable resource for newcomers trying to get into this field.

### Requested changes

1) I suggest to rephrase the sentence "Here, we demonstrate a may to measure chi by applying momentum-resolution methods from x-ray and neutron scattering to surface HR-EELS" in the abstract and a similar sentence in the introduction to avoid giving the impression that the present work introduces a new technique.

• validity: high
• significance: good
• originality: high
• clarity: high
• formatting: excellent
• grammar: perfect