Exciton absorption spectra in narrow armchair graphene nanoribbons in an electric field

Abstract

We present an analytical investigation of the exciton optical absorption in a narrow armchair graphene nanoribbon (AGNR) in the presence of a longitudinal external electric field directed parallel to the ribbon axis. The two-body 2D Dirac equation for the massless electron and hole subject to the ribbon confinement, Coulomb interaction and electric field is employed. The ribbon confinement is assumed to be much stronger than the internal exciton electric field which in turn considerably exceeds the external electric field. This justifies an adiabatic approximation implying a slow longitudinal and fast transverse electron-hole relative motion governed by the exciton attraction and accompanied by the external electric field and ribbon confinement effects, respectively. In the single subband approximation of the isolated size-quantized subbands induced by the ribbon confinement the exciton electroabsorption coefficient is determined in an explicit form. The pronounced dependencies of the 1 arXiv:1812.06450v1 [cond-mat.mes-hall] 16 Dec 2018 exciton peak positions, widths and intensities on the ribbon width and electric field strength are traced. The electron-hole exciton attraction modifies remarkably the Franz-Keldysh electroabsorption in the frequency region both below and above the edges determined by the size-quantized energy levels. In the double-subband approximation of the interacting ground and first excited subbands the combined effect of the exciton electro-and autoionization caused by the electric field and intersubband coupling, respectively, are explored. Our analytical results are in agreement with those obtained by numerical methods. Estimates of the expected experimental values for the typically employed AGNR show that for a weak electric field the exciton quasi-discrete states remain sufficiently stable to be observed in optical experiments, while relatively strong fields free the captured carriers to further restore their contribution to the transport.

2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons

“…The optical properties of armchair GNRs (AGNRs) have been intensively studied theoretically 27–36 and more recently experimentally 37,38 , nevertheless the absorption peak dependence on the ribbon width is not yet complete. Hitherto, rather narrow energy or width ranges have been reported.…”

“…The and excitons were also reported for the similar width ranges 33–35 . Recently, an analytical width dependence has been proposed for exciton of semiconducting AGNRs 36 . Even so, none of these previous works have provided a proper comparison of the AGNR optical resonances with those of zigzag SWCNTs, whereas such comparative analysis is highly desirable for a reliable optical nanodevice and nanocircuit engineering.…”

Electric field induced injection and shift currents in zigzag graphene nanoribbons

“…( 23) and the shift conductivity in Eq. (25). During the numerical evaluation, the Brillouin zone is divided into a 3100 grid, the δ function is approximated by a Gaussian function…”

“…8,33 Because of the insufficient Coulomb screening, the excitonic effects are important for narrow ribbons. 24,25,45,46 In addition to linear optical responses, the nonlinear optical properties of GNR also attracted much attention. By tuning the doping level electrically, Cox et al studied the plasmon-assisted harmonic generation, sum and difference frequency generation, and fourwave mixing of graphene nanostructures, 10,12 and these calculated responses can be several order of magnitude larger than that of metal nanoparticles with similar sizes.…”

Developing Graphene‐Based Moiré Heterostructures for Twistronics

“…Excitons are the bound states of an electron and a hole in semiconductors, which are generated by exciting an electron from the full valence band to the empty conduction band to form a tightly bound electron−hole pair. The exciton effect has an important influence on physical processes, such as photoluminescence emission, [ 182 ] light absorption, [ 183 ] and optical nonlinear effects [ 184 ] in semiconductors; thus, the exciton effect plays a vital role in optical properties. Despite practical interest, it is difficult to observe excitons.…”