Strong magnetophonon oscillations in extra-large graphene

Electron wave and quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states,e.g., snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

Gate-tunable circular phonon dichroism effect in bilayer graphene

Circular phonon dichroism effect has been proposed in two-dimensional materials; however, the lack of tunability hinders the exploration of the effect. Here, we investigate the role of dual-gating-induced inversion symmetry breaking in the circular phonon dichroism effect in bilayer graphene. We find that the introduction of inversion symmetry breaking modifies the response in the layer-symmetric and layer-antisymmetric channels, and results in the occurrence of phonon dichroism in the cross-channel. In the layer representation, the inversion symmetry breaking breaks the equality of intralayer circular phonon dichroism and enhances the interlayer response. Our results suggest that layer degree of freedom provides possibilities to tune phonon dynamics, which paves a way toward different physics and applications of two-dimensional acoustoelectronics and layertronics.

Electrically driven amplification of terahertz acoustic waves in graphene

In graphene devices, the electronic drift velocity can easily exceed the speed of sound in the material at moderate current biases. Under these conditions, the electronic system can efficiently amplify acoustic phonons, leading to an exponential growth of sound waves in the direction of the carrier flow. Here, we show that such phonon amplification can significantly modify the electrical properties of graphene devices. We observe a superlinear growth of the resistivity in the direction of the carrier flow when the drift velocity exceeds the speed of sound - resulting in a sevenfold increase over a distance of 8 µm. The resistivity growth is observed at carrier densities away from the Dirac point and is enhanced at cryogenic temperatures. We develop a theoretical model for the resistivity growth due to the electrical amplification of acoustic phonons - reaching frequencies up to 2.2 THz - where the wavelength is controlled by gate-tunable transitions across the Fermi surface. These findings provide a route to on-chip high-frequency sound generation and detection in the THz frequency range.

Quantum Oscillations of the Energy Loss Rate of Hot Electrons in Graphene at Strong Magnetic Fields

We present a theoretical model for the calculation of the energy loss rate (ELR) of hot electrons in a monolayer graphene due to their coupling with acoustic phonons at high perpendicular magnetic fields. Electrons interact with both transverse acoustic (TA) and longitudinal acoustic (LA) phonons. Numerical simulations of the ELR are performed as a function of the magnetic field, the electron temperature, the electron density, and the Landau level broadening. We find robust oscillations of the ELR as a function of the filling factor ν that originate from the oscillating density of states at the Fermi level. Screening effects on the deformation potential coupling are taken into account, and it is found that they lead to a significant reduction of ELR, especially, at low electron temperatures, Te, and high magnetic fields. At temperatures much lower than the Bloch-Grüneisen temperature, the ELR shows a Te4 dependence that is related to the unscreened electron interaction with TA acoustic phonons. Finally, our theoretical model is compared with existing experimental results and a very good quantitative agreement is found.

Phonon-mediated room-temperature quantum Hall transport in graphene

The quantum Hall (QH) effect in two-dimensional electron systems (2DESs) is conventionally observed at liquid-helium temperatures, where lattice vibrations are strongly suppressed and bulk carrier scattering is dominated by disorder. However, due to large Landau level (LL) separation (~2000 K at B = 30 T), graphene can support the QH effect up to room temperature (RT), concomitant with a non-negligible population of acoustic phonons with a wave-vector commensurate to the inverse electronic magnetic length. Here, we demonstrate that graphene encapsulated in hexagonal boron nitride (hBN) realizes a novel transport regime, where dissipation in the QH phase is governed predominantly by electron-phonon scattering. Investigating thermally-activated transport at filling factor 2 up to RT in an ensemble of back-gated devices, we show that the high B-field behaviour correlates with their zero B-field transport mobility. By this means, we extend the well-accepted notion of phonon-limited resistivity in ultra-clean graphene to a hitherto unexplored high-field realm.

Graphene FETs with high and low mobilities have universal temperature-dependent properties

We use phenomenological modelling and detailed experimental studies of charge carrier transport to investigate the dependence of the electrical resistivity,ρ, on gate voltage,V_g, for a series of monolayer graphene field effect transistors with mobilities,μ, ranging between 5000 and 250 000 cm²V^-1s^-1at low-temperature. Our measurements over a wide range of temperatures from 4 to 400 K can be fitted by the universal relationμ=4/eδnmaxfor all devices, whereρmaxis the resistivity maximum at the neutrality point andδnis an 'uncertainty' in the bipolar carrier density, given by the full width at half maximum of the resistivity peak expressed in terms of carrier density,n. This relation is consistent with thermal broadening of the carrier distribution and the presence of the disordered potential landscape consisting of so-called electron-hole puddles near the Dirac point. To demonstrate its utility, we combine this relation with temperature-dependent linearised Boltzmann transport calculations that include the effect of optical phonon scattering. This approach demonstrates the similarity in the temperature-dependent behaviour of carriers in different types of single layer graphene transistors with widely differing carrier mobilities. It can also account for the relative stability, over a wide temperature range, of the measured carrier mobility of each device.

Graphene's non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.

Magneto-oscillations have revealed many interesting phenomena in graphene and quantum Hall systems, but they are typically measured at low currents and in equilibrium. Here, the authors report several non-equilibrium quantum effects observed in magneto-oscillations in graphene at high currents.

Strong Interminivalley Scattering in Twisted Bilayer Graphene Revealed by High-Temperature Magneto-Oscillations

Twisted bilayer graphene (TBG) provides an example of a system in which the interplay of interlayer interactions and superlattice structure impacts electron transport in a variety of nontrivial ways and gives rise to a plethora of interesting effects. Understanding the mechanisms of electron scattering in TBG has, however, proven challenging, raising many questions about the origins of resistivity in this system. Here we show that TBG exhibits high-temperature magneto-oscillations originating from the scattering of charge carriers between TBG minivalleys. The amplitude of these oscillations reveals that interminivalley scattering is strong, and its characteristic timescale is comparable to that of its intraminivalley counterpart. Furthermore, by exploring the temperature dependence of these oscillations, we estimate the electron-electron collision rate in TBG and find that it exceeds that of monolayer graphene. Our study demonstrates the consequences of the relatively small size of the superlattice Brillouin zone and Fermi velocity reduction on lateral transport in TBG.

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

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 10⁶ cm² 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 1 K. 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.

Here, the authors show that Brown-Zak fermions in graphene-on-boron-nitride superlattices exhibit mobilities above 10⁶ cm²/V s and micrometer scale ballistic transport.

Observation of Terahertz-Induced Magnetooscillations in Graphene

When high-frequency radiation is incident upon graphene subjected to a perpendicular magnetic field, graphene absorbs incident photons by allowing transitions between nearest Landau levels that follow strict selection rules dictated by angular momentum conservation. Here, we show a qualitative deviation from this behavior in high-quality graphene devices exposed to terahertz (THz) radiation. We demonstrate the emergence of a pronounced THz-driven photoresponse, which exhibits low-field magnetooscillations governed by the ratio of the frequency of the incoming radiation and the quasiclassical cyclotron frequency. We analyze the modifications of generated photovoltage with the radiation frequency and carrier density and demonstrate that the observed photoresponse shares a common origin with microwave-induced resistance oscillations discovered in GaAs-based heterostructures; however, in graphene it appears at much higher frequencies and persists above liquid nitrogen temperatures. Our observations expand the family of radiation-driven phenomena in graphene, paving the way for future studies of nonequilibrium electron transport.

Full consideration of acoustic phonon scatterings in two-dimensional Dirac materials

The in-plane acoustic phonon scattering in graphene is solved by considering fully inelastic acoustic phonon scatterings in two-dimensional (2D) Dirac materials for a large range of temperatures (T) and chemical potentials (μ). Rigorous analytical solutions and symmetry properties of Fermionic and Bosonic functions are obtained. We illustrate how doping alters the temperature dependence of acoustic phonon scattering rates. It is shown that the quasi-elastic and ansatz equations previously derived for acoustic phonon scatterings in graphene are limiting cases of the inelastic-scattering equations derived here. For heavily-doped graphene, we found that the high-T behavior of resistivity is better described by ρ(T,μ) ∝T(1 -ζ_aμ²/3(k_BT)²) rather than a linear T behavior, and in the low T regime we found τ^-1∝ (k_BT)⁴ but with a different prefactor (i.e.∼3 times smaller) in comparison with the existing quasi-elastic expressions. Furthermore, we found a simple analytic "semi-inelastic" expression of the form τ^-1∝ (k_BT)⁴/(1 + cT³) which matches nearly perfectly with the full inelastic results for any temperature up to 500 K and μ up to 1 eV. Our simple analytical results agree well with previous first-principles studies and available experimental data. Moreover, we obtain an analytical form for the acoustic gauge field . Our analyses pave a way for investigating scatterings between electrons and other fundamental excitations with linear dispersion relation in 2D Dirac material-based heterostructures such as bogolon-mediated electron scattering in graphene-based hybrid Bose-Fermi systems.

Hexagonal Boron Nitride Synthesized at Atmospheric Pressure Using Metal Alloy Solvents: Evaluation as a Substrate for 2D Materials

Hexagonal boron nitride (h-BN) synthesized under high pressure and high temperature (HPHT) has been used worldwide in two-dimensional (2D) materials research as an essential material for constructing van der Waals heterostructures. Here, we study h-BN synthesized with another method, i.e., via synthesis at atmospheric pressure and high temperature (APHT) using a metal alloy solvent. First, we examine the APHT h-BN in a bulk crystal form using cathodoluminescence and find that it does not have carbon-rich domains that inevitably exist in a core region of all the HPHT h-BN crystals. Next, we statistically compare the size of the crystal flakes exfoliated on a SiO₂/Si substrate from APHT and HPHT h-BN crystals by employing our automated 2D material searching system. Finally, we provide direct evidence that APHT h-BN can serve as a high-quality substrate for 2D materials by demonstrating high carrier mobility, ballistic transport, and Hofstadter butterfly in graphene and photoluminescence in WS₂.