# A dark state of Chern bands: Designing flat bands with higher Chern number

### Submission summary

 As Contributors: Nathan Goldman Arxiv Link: https://arxiv.org/abs/2002.05089v3 (pdf) Date submitted: 2020-09-23 15:41 Submitted by: Goldman, Nathan Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

We introduce a scheme by which flat bands with higher Chern number $| C|>1$ can be designed in ultracold gases through a coherent manipulation of Bloch bands. Inspired by quantum-optics methods, our approach consists in creating a "dark Bloch band", by coupling a set of source bands through resonant processes. The Chern number of the dark band is found to follow a simple sum rule in terms of the Chern numbers of the source bands. We illustrate our method based on a $\Lambda$ system, formed of the bands of the Harper-Hofstadter model, which leads to a very flat Chern band with $C\!=\!2$. We explore a realistic sequence to load atoms into the dark Chern band, as well as a probing scheme based on Hall drift measurements. Dark Chern bands offer a platform where exotic fractional quantum Hall states could be realized in ultracold gases.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2002.05089v3 on 23 September 2020

## Reports on this Submission

### Strengths

1) The article proposes a way of producing novel topological band structures that have a flat band characterised by a non-zero integer Chern number. The authors present a particular realisation of a flat band with a Chern number equal to 2, and describe how one could generalise this to arbitrary integers.
2) This proposal is feasible and sensible with an experimental realisation with ultra-cold atoms in optical lattices.
3) The authors provide proof-of-principle simulations for detecting the topological Chern number in current cold atom experiments.
4) This work is novel and interesting and provides a way of preparing and detecting novel topological features directly in an experimental setting. This has the potential to have a high impact in the field.

### Weaknesses

1) When the authors discuss experimental preparation and detection, specifically the timescales that are required experimentally, they do not discuss the experimental limitations. For example, some of the timescales that they quote in section 5 – for typical experimental parameters – would correspond to many seconds or even minutes, which are out with the capabilities of current experiments due to decoherence effects. It is a little unclear how their conclusions would change if more realistic values were used in their simulations.

### Report

This is an interesting and well written article. The results are presented clearly, the experimental proposals are for the most part sensible and the authors conclusions are backed up by numerical simulations.
The ability to experimentally prepare novel topological band structures opens up new avenues for exploring the behaviour of topological systems. In particular, being able to realise these systems in experiments with ultra-cold atoms offers a feasible way of including interactions between atoms allowing for investigations into interacting topological systems such as fractional quantum hall phases.

In this case I would recommend publication in this journal. However, I suggest that the authors address the below points, as I believe that this will increase the impact of their article.

### Requested changes

1) In the figure 3 caption, the authors state that for (a) they use a value of $Fa=5\times 10^{-4} J$ and a timescale of $t=15 \hbar/J$. In typical cold atom experiments, $J$ usually takes values around $J/h \approx 100 \rightarrow 1000 ~{\rm Hz}$. If the larger values are used then this will then correspond to a timescale of $t\approx 5~{\rm s}$.
These values for the timescales seem large compared to typical experimental coherence times of $< 1 {\rm s}$. Can the authors discuss how important these timescales are for detecting the Chern number in the way that they are proposing.
For (b) they use a value of $Fa=5\times 10^{-3} J$, which then corresponds to $t\approx 0.5~{\rm s}$ - which seems more experimentally feasible. But if smaller tunnelling amplitudes are realised (see Ref.[9] in the article for example) then even the timescales here may be too large.

2) Similarly, on page 9, when discussing preparing atoms in the flat band, they quote timescales for their linear adiabatic ramp of $T=10^6 \hbar/J = 160~{\rm s}$. The authors do state that this can be improved for different ramping procedures, but they do not present specific simulations or estimates. Can the authors discuss the errors in this preparation scheme for more experimentally realistic timescales, such as $T<1~{\rm s}$.

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