inter-Landau Level Transitions Research Articles

Graphene\u2019s 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-optical Kerr effect and signature of the chiral anomaly in a Weyl semimetal in magnetic field

One striking property of the Landau level spectrum of a Weyl semimetal (WSM) is the existence of a chiral Landau level, in which the electrons propagate unidirectionally along the magnetic field. This linearly dispersive level influences the optical properties of WSMs. For example, it was recently shown that a complete optical valley polarization is achievable in a time-reversal symmetric Weyl semimetal placed in a magnetic field\cite% {Bertrand2019}. This effect originates from inter-Landau level transitions involving the chiral Landau level and requires a tilt of the Weyl cones. In this paper, we show how the magneto-optical Kerr effect (MOKE) is modified in a WSM\ with tilted Weyl cones in comparison with its behavior in a normal metal and how a valley polarization can be detected using MOKE. We study both the Faraday (longitudinal) and Voigt (transverse) configurations for light incident on a semi-infinite WSM surface with no Fermi arcs. We use a minimal model of a WSM with four tilted Weyl nodes related by mirror and time-reversal symmetry. In the Voigt configuration, a large peak of the Kerr angle occurs at the plasmon frequency. We show that the blueshift in frequency of this peak with increasing magnetic field is a signature of the chiral anomaly in the MOKE.

Origin of layer decoupling in ordered multilayer graphene grown by high-temperature sublimation on C-face 4H-SiC

We study the origin of layer decoupling in ordered multilayer graphene grown by high temperature sublimation on C-face 4H-SiC. The mid-infrared optical Hall effect technique is used to determine the magnetic field dependence of the inter-Landau level transition energies and their optical polarization selection rules, which unambiguously show that the multilayer graphene consists of electronically decoupled layers. Transmission electron microscopy reveals no out-of-plane rotational disorder between layers in the stack, which is in contrast to what is typically observed for C-face graphene grown by low temperature sublimation. It is found that the multilayer graphene maintains AB-stacking order with increased interlayer spacing by 2.4%–8.4% as compared to highly oriented pyrolytic graphite. Electron energy loss spectroscopy mapping reveals Si atoms trapped in between layers, which are proposed to be the cause for the observed increased interlayer spacing leading to layer decoupling. Based on our results, we propose a defect-driven growth evolution mechanism for multilayer graphene on C-face SiC via high temperature sublimation.

Integer quantum Hall conductivity and longitudinal conductivity in silicene under the electric field and magnetic field

We investigate the integer Hall conductivity and longitudinal conductivity of silicene under the magnetic field, electric field, and exchange field in this paper. We focus not only on the case of low-temperature and δ-function impurities (i.e., independent of the scattering momentum), which only exist the intra-Landau level transition, but also on the case of inter-Landau level transition which also with the non-elastic scattering. The resulting longitudinal conductivity is very different from the intra-Landau level one at low-temperature. The expressions of the Hall conductivity, longitudinal conductivity, valley contributed Hall conductivity, and the spin or valley Hall conductivity are deduced in this paper. We also compute the dynamical polarization under the magnetic field which is an important quantity related to many exciting and novel properties of the two-dimension materials, including the screened Coulomb scattering due to the charged impurities. The polarization function here is also related to the Landau level index under the magnetic field, and shows a step-like feature rather than the logarithmically divergent as which appears in the zero-magnetic field case, and it is also naturally related to the conductivity in silicene. The generalized Laguerre polynomial is used in both the longitudinal conductivity and dynamical polarization function under magnetic field. Our results are also valid for the silicene-like materials like the genmanene, MoS2.

Ultrafast Terahertz Nonlinear Optics of Landau Level Transitions in a Monolayer Graphene.

We investigated the ultrafast terahertz (THz) nonlinearity in a monolayer graphene under the strong magnetic field using THz pump-THz probe spectroscopy. An ultrafast suppression of the Faraday rotation associated with inter-Landau level (LL) transitions is observed, reflecting the Dirac electron character of nonequidistant LLs with large transition dipole moments. A drastic modulation of electron distribution in LLs is induced by far off-resonant THz pulse excitation in the transparent region. Numerical simulation based on the density matrix formalism without rotating-wave approximation reproduces the experimental results. Our results indicate that the strong light-matter coupling regime is realized in graphene, with the Rabi frequency exceeding the carrier wave frequency and even the relevant energy scale of the inter-LL transition.

Resonant tunnelling between the chiral Landau states of twisted graphene lattices

A new class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An exemplar of such a structure is a transistor device in which relativistic Dirac Fermions can resonantly tunnel through a boron nitride barrier, a few atomic layers thick, sandwiched between two graphene electrodes. An applied magnetic field quantises graphene's gapless conduction and valence band states into discrete Landau levels, allowing us to resolve individual inter-Landau level transitions and thereby demonstrate that the energy, momentum and chiral properties of the electrons are conserved in the tunnelling process. We also demonstrate that the change in the semiclassical cyclotron trajectories, following a tunnelling event, is a form of Klein tunnelling for inter-layer transitions.

Electric field-induced valley degeneracy lifting in uniaxial strained graphene: Evidence from magnetophonon resonance

A double peak structure in the magneto-phonon resonance (MPR) spectrum of uniaxial strained graphene, under crossed electric and magnetic fields, is predicted. We focus on the $\Gamma$ point optical phonon modes coupled to the inter-Landau level transitions $0 \leftrightarrows \pm 1$ where MPR is expected to be more pronounced at high magnetic field. We derive the frequency shifts and the broadenings of the longitudinal (LO) and transverse (TO) optical phonon modes taking into account the effect of the strain modified electronic spectrum on the electron-phonon coupling. We show that the MPR lines acquire a double resonance structure originating from the two-fold valley degeneracy lifting. The latter is due to the different Landau level spacings in the two Dirac valleys resulting form the simultaneous action of the inplane electric field and the strain induced Dirac cone tilt. We discuss the role of some key parameters such as disorder, strain, doping and electric field amplitude on the emergence of the double resonance structure.

Ultrastrong light-matter coupling at terahertz frequencies with split ring resonators and inter-Landau level transitions

We study strong light-matter coupling at terahertz frequencies employing a system based on an array of deeply subwavelength split ring resonators deposited on top of an ensemble of modulation-doped quantum wells. By applying a magnetic field parallel to the epitaxial growth axis, at low temperatures, Landau Levels are formed. We probe the interaction of the inter-Landau level transitions with the resonators modes, measuring a normalized coupling ratio Ωωc=0.58 between the inter-Landau level frequency ωc and the Rabi frequency Ω of the system. The physics of the system is studied as a function of the metasurface composition and of the number of quantum wells. We demonstrate that the light-matter coupling strength is basically independent from the metamaterial lattice spacing.

Polarization of graphene in a strong magnetic field beyond the Dirac cone approximation

In this paper we study the excitation spectrum of graphene in a strong magnetic field, beyond the Dirac cone approximation. The dynamical polarizability is obtained using a full π-band tight-binding model where the effect of the magnetic field is accounted for by means of the Peierls substitution. The effect of electron–electron interaction is considered within the random phase approximation, from which we obtain the dressed polarization function and the dielectric function. The range of validity of the Landau level quantization within the continuum approximation is studied, as well as the non-trivial quantization of the spectrum around the Van Hove singularity. We further discuss the effect of disorder, which leads to a smearing of the absorption peaks and temperature, which activates additional inter-Landau level transitions induced by the Fermi distribution function.

Quantum Hall effect in exfoliated graphene affected by charged impurities: Metrological measurements

Metrological investigations of the quantum Hall effect (QHE) completed by transport measurements at low magnetic field are carried out in a-few-$\mu\mathrm{m}$-wide Hall bars made of monolayer (ML) or bilayer (BL) exfoliated graphene transferred on $\textrm{Si/SiO}_{2}$ substrate. From the charge carrier density dependence of the conductivity and from the measurement of the quantum corrections at low magnetic field, we deduce that transport properties in these devices are mainly governed by the Coulomb interaction of carriers with a large concentration of charged impurities. In the QHE regime, at high magnetic field and low temperature ($T<1.3 \textrm{K}$), the Hall resistance is measured by comparison with a GaAs based quantum resistance standard using a cryogenic current comparator. In the low dissipation limit, it is found quantized within 5 parts in $10^{7}$ (one standard deviation, $1 \sigma$) at the expected rational fractions of the von Klitzing constant, respectively $R_{\mathrm{K}}/2$ and $R_{\mathrm{K}}/4$ in the ML and BL devices. These results constitute the most accurate QHE quantization tests to date in monolayer and bilayer exfoliated graphene. It turns out that a main limitation to the quantization accuracy, which is found well above the $10^{-9}$ accuracy usually achieved in GaAs, is the low value of the QHE breakdown current being no more than $1 \mu\mathrm{A}$. The current dependence of the longitudinal conductivity investigated in the BL Hall bar shows that dissipation occurs through quasi-elastic inter-Landau level scattering, assisted by large local electric fields. We propose that charged impurities are responsible for an enhancement of such inter-Landau level transition rate and cause small breakdown currents.

THE MAGNETIC FIELD DEPENDENCE PROPERTIES OF ELECTRON-PIEZOELECTRIC PHONON INTERACTING MATERIALS IN SQUARE WELL CONFINEMENT POTENTIAL

ABSTRACT We consider the system is subject to the linearly polarized oscillatory external field. We study the optical quantum transition line shapes (QTLS) which show the absorption power and the quantum transition line widths (QTLW) of electron-piezoelectric phonon interacting system. We analyze the magnetic field dependence of the QTLS and the QTLW in various cases. In order to analyze the quantum transition, we compare the magnetic field dependence of the QTLW and QTLS of two transition process, the intra-Landau level transition process and the inter-Landau level transition process.

On spectral properties of bilayer graphene: the effect of an SiC substrate and infraredmagneto-spectroscopy

We investigate the effect of asymmetry in bilayer graphene induced by a diatomic substrate(such as SiC) and its influence on the bilayer spectrum in zero and strong magnetic fields. Wealso determine selection rules for inter-Landau level transitions, taking into account all fourπ bands.

LANDAU LEVEL SPECTROSCOPY OF DIRAC-LIKE FERMIONS IN MULTILAYER GRAPHENE

The results of spectroscopic (magneto-transmission and Raman scattering) studies1–8 of multilayers of carbon which are thermally decomposed from carbon-terminated surface of silicon carbide, and of thin layers of highly oriented pyrolytic and natural graphite were presented. Those carbon multilayers on silicon carbide which are not directly affected by the SiC / C interface and which in consequence are nearly charge neutral show the magneto-optical properties identical with the properties characteristic of a single graphite sheet, graphene. Inter Landau level transitions in this multilayer graphene have been studied in a wide spectral range from far-infrared to almost visible region. The dispersion relations of electronic states are found to reflect the form of the Dirac cone with almost perfect electron-hole symmetry and only weak deviations from linearity at high energies. Cyclotron resonance transition in multilayer graphene can be observed in magnetic fields down to 40 mT, and its width is practically independent on temperature up to 300 K. Such parameters as carrier mobility and minimal conductivity as well as the possibility to probe the immediate vicinity of the Dirac point were evaluated and discussed in detail. For comparison, the magneto-optical properties of thin layers of bulk graphite were also reported. The Dirac like electronic dispersion relations are also found in these systems, but only in the vicinity of the particular (H) point of the Brillouin zone. In general, the measured spectra are, however, more complex and reflect the three-dimensional character of graphene layers with Bernal stacking. Note from Publisher: This article contains the abstract only.

The influence of interlayer asymmetry on the magnetospectroscopy of bilayer graphene

We present a self-consistent calculation of the interlayer asymmetry in bilayer graphene caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally in [E.A. Henriksen, Z. Jiang, L.-C. Tung, M.E. Schwartz, M. Takita, Y.-J. Wang, P. Kim, and H.L. Stormer, Phys. Rev. Lett. 100 (2008), 087403]. We also analyse the magneto–optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers.

The magnetic field dependence of the deformation potential materials in the square well confinement potential

Abstract We study the optical Quantum Transition Line Shapes (QTLS) which show the absorption power and the Quantum Transition Line Widths (QTLW) of electron-deformation potential phonon interacting systems. In order to analyze the quantum transition, we compare the magnetic field dependencies of the QTLWand the QTLS on two transition processes, namely the intra-Landau level transition process and the inter-Landau level transition process. We apply the Quantum Transport theory (QTR) to the system in the confinement of electrons by square well confinement potential. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS).

Magnetospectroscopy of epitaxial few-layer graphene

The inter-Landau level transitions observed in far-infrared transmission experiments on few-layer graphene samples show a behaviour characteristic of the linear dispersion expected in graphene. This behaviour persists in relatively thick samples, and is qualitatively different from that of thin samples of bulk graphite.

INTER-LANDAU-LEVEL TRANSITIONS AND ULTRAFAST DYNAMICS OF 2D MAGNETOEXCITONS

We study the role of many-body correlations in the ultrafast dynamics of quantum well magnetoexcitons. In linear response, inter-Landau level transitions are suppressed if magnetic field is stronger than magnetoexciton binding energy. However, in nonlinear response, two-electron Auger processes remain unsuppressed even at very strong field. We show that Auger scattering plays a dominant role in the coherent exciton dynamics in strong magnetic field. We perform numerical calculations of four-wave-mixing (FWM) polarization which incorporate Auger processes nonperturbatively, and find a strong amplitude enhancement of the FWM signal accompanied with polarization oscillations at negative time delays. We identify these oscillations as quantum beats between dark two-exciton states related to each other via Auger processes.

Observation of the magneto-phonon effect due to acoustic phonons in the planar Hall effect of bismuth

The magneto-phonon effect due to acoustic phonons in bismuth, first observed in the thermal variation of the longitudinal Shubnikov–de Haas oscillations, has been investigated by the measurement of the oscillatory planar Hall coefficient. The oscillatory planar Hall coefficient R was obtained from the measurements of magneto-resistivity component ρ yx ( y) of bismuth in magnetic fields up to 5 T at several fixed temperatures. The obtained R became largest in amplitude at temperatures around 6.5 or 5.4 K, and became less and less intense as the temperature decreased. This temperature dependence was understood by considering the magneto-phonon effect, in which the number of phonons responsible for the inter-Landau level transition of electrons decreased with lowering temperature.

Anomalous influence of a small amount of impurities on the longitudinal Shubnikov–de Haas oscillation amplitude in bismuth

Longitudinal magnetoresistivity components ρ yy ( y) of pure and tin-doped (0.2, 1 and 10 ppm tin) bismuth single crystals were measured in magnetic fields up to 5 T at several fixed temperatures between 1.2 and 25 K. In each of the samples, except 10-ppm tin-doped one, the longitudinal Shubnikov–de Haas (SdH) oscillation became largest in amplitude at temperatures around 15, 12 and 8 K, respectively. Then, the amplitude became smaller as the temperature decreased. In the case of 10-ppm tin-doped bismuth, on the other hand, the SdH oscillation increased in amplitude markedly as the temperature was decreased. To understand this anomalous temperature dependence of the SdH oscillation amplitude, we carried out simple numerical simulations. We positively demonstrated that the three-phonon processes of phonon–phonon collisions caused the inter-Landau level transition of carriers. We also found the reason why the longitudinal SdH oscillation amplitude of 10-ppm tin-doped sample became larger with decreasing temperature in spite of the collision broadening of Landau levels.

Multiband electron resonant Raman scattering in quantum wells in a magnetic field

A theoretical model has been developed for the electronic resonant Raman scattering processes in direct band zinc blende-type semiconductor quantum wells in a magnetic field. In order to take into account the spin-flip transitions, anomalous behavior of the Landau levels and the Landeg factor, an 8 38 Kane-Weiler Hamiltonian model has been considered for the evaluation of the Raman scattering amplitude. Elements concerning the selection rules of resonant inelastic light scattering in quantum well systems are reported. The multiband model predicts conditions for resonant spin-flip Raman processes in several light scattering con- figurations for crossed and parallel polarization. Special emphasis is given to the effects of the interlevel coupling and mixing within the conduction subband and their relation to spin-flip and inter-Landau level transitions. Symmetry and electronic properties of the level structure in the first conduction subband as well as anomalous Landefactors are discussed in terms of complementary Raman scattering configurations, Fermi energy, and multiband parameters.