Comparison of Coulomb Impurity, Longitudinal Acoustic Phonons, and Surface Optical Phonons Affecting the <i>n</i> = 0 Landau Level in Monolayer Graphene

<div>Relations between splitting energy <svg height="8.68572pt" id="M143" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 14.7273 8.68572" width="14.7273pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"></path></g></svg> and magnetic field B with different <svg height="9.4347pt" id="M144" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.14359 11.2181 9.4347" width="11.2181pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg> for SiO<sub>2</sub> (a) and h-BN (b) as substrates, respectively.</div>

Advances in Condensed Matter Physics

fig4

Figure 4

Figure 4: Comparison of Coulomb Impurity, Longitudinal Acoustic Phonons, and Surface Optical Phonons Affecting the <i>n</i> = 0 Landau Level in Monolayer Graphene 

Figure 4 | Comparison of Coulomb Impurity, Longitudinal Acoustic Phonons, and Surface Optical Phonons Affecting the n = 0 Landau Level in Monolayer Graphene 