The isolation of the first two-dimensional material, graphene – a monolayer of carbon atoms arranged in a hexagonal lattice - opened new exciting opportunities in the field of condensed matter physics and materials. Its isolation and subsequent studies demonstrated that it was possible to obtain sheets of atomically thin crystals and that these were stable, and they also began to show its outstanding properties, thus opening the door to a whole new family of materials, known as two-dimensional materials or 2D materials. The great interest in different 2D materials is motivated by the variety of properties they show, being candidates for numerous applications. Additionally, the combination of 2D crystals allows the assembly of composite, on-demand materials, known as van der Waals heterostructures, which take advantage of the properties of those materials to create functionalities that otherwise would not be accessible. For example, the combination of 2D materials, which can be done with high precision, is opening up opportunities for the study of new challenges in fundamental physics and novel applications. Here we review the latest fundamental discoveries in the area of 2D materials and offer a perspective on the future of the field.

Recent advances in graphene and other 2D materials

Synthesis of graphene nanoplatelets/polythiophene nanocomposites With Enhanced Photocatalytic Degradation of Bromophenol Blue and Antibacterial Properties

Summary Twisted graphene-based homo- and heterostructures, consisting of two-dimensional (2D) layered materials with a twist angle (θ), have attracted growing interest due to their unique twist-angle-dependent electronic properties. This novel twist-angle degree of freedom enables the in-depth exploration of quantum phases of matter, and intense observation of strongly correlated phenomena, including superconductivity, Mott insulators, correlated Chern bands, and ferromagnetism, emerging in succession, profits from the steady improvement of fabrication techniques. This timely review summarizes the latest breakthroughs in graphene-based twistronics and technical advances in precisely manifesting the twist angle. The perspectives and challenges of designing and improving 2D twistronic devices are also provided, attempting to offer some useful understanding and guidelines for experimentalists and theorists to explore desired exotic properties and boost practical twistronic applications.

Twist the doorknob to open the electronic properties of graphene-based van der Waals structure

Electrons exposed to a two-dimensional (2D) periodic potential and a uniform, perpendicular magnetic field exhibit a fractal, self-similar energy spectrum known as the Hofstadter butterfly. Recently, related high-temperature quantum oscillations (Brown-Zak oscillations) were discovered in graphene moiré systems, whose origin lies in the repetitive occurrence of extended minibands/magnetic Bloch states at rational fractions of magnetic flux per unit cell giving rise to an increase in band conductivity. In this work, we report on the experimental observation of band conductivity oscillations in an electrostatically defined and gate-tunable graphene superlattice, which are governed both by the internal structure of the Hofstadter butterfly (Brown-Zak oscillations) and by a commensurability relation between the cyclotron radius of electrons and the superlattice period (Weiss oscillations). We obtain a complete, unified description of band conductivity oscillations in two-dimensional superlattices, yielding a detailed match between theory and experiment. 

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Band conductivity oscillations in a gate-tunable graphene superlattice

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional filling of topologically non-trivial "Chern" bands. Here, we report the observation of gapped states at fractional filling of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene/hexagonal boron nitride heterostructure. We observe new phases at fractional filling of bands with Chern indices $\mathcal{C} = -1, \pm 2,$ and $\pm 3$. Some of these, in $\mathcal{C}=-1$ and $\mathcal{C}=2$ bands, are characterized by fractional Hall conductance---they are `fractional Chern insulators' and constitute a new example of topological order beyond Landau levels.

Observation of fractional Chern insulators in a van der Waals heterostructure

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational ($p/q$) fractions of the magnetic flux quantum per superlattice unit cell Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 10$^6$ cm$^2$V$^{-1}$s$^{-1}$ and the mean free path exceeding several micrometers The exceptional quality of our devices allows us to show that Brown-Zak minibands are $4q$ times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1K We also found negative bend resistance at $1/q$ fractions for electrical probes placed as far as several micrometers apart The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field

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Roshan Krishna-Kumar

Papers

Long-range ballistic transport of Brown-Zak fermions in graphene superlattices.