Stability of the Dirac cone in artificial graphene formed in quantum wells: a computational many-electron study

Abstract

We carry out a comprehensive computational study on the stability of the Dirac cone in artificial graphene realized in nanopatterned quantum wells. Our real-space approach allows us to vary the size, shape, and positioning of the quantum dots in the hexagonal lattice. We compare the (noninteracting) single-particle calculations to density-functional studies within both local-density approximation and meta-generalized-gradient approximation. Furthermore, the density-functional results are compared against numerically precise path-integral quantum Monte Carlo calculations. As a whole, our results indicate high stability of the Dirac bands against external parameters, which is reassuring for further experimental investigations.

Density-functional approach to the band gaps of finite and periodic two-dimensional systems

“…In order to compute the band structure, we sample 100 equally spaced k points along the path Γ-M -K-Γ. Here, we will show energies in meV and lengths in nm in accordance with the previous works [3,5,92].…”

“…In particular, we focus on AG realized in nanopatterned 2D electron gas in GaAs heterostructures [2][3][4][5]91] that can be modeled in real space with a hegagonal array of QDs [5,92]. This system shows Dirac cones similar to conventional graphene, and the band structure can be tuned at will through, e.g., Kekulé distortion.…”

Quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry: magnetism, correlations, and phase transitions

“…Much progress in quantum simulators has been achieved with cold atoms and trapped ions [1][2][3][4][5][6][7][8][9][10][11]. Progress in solid state and photonic based simulators [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] is enabled by progress in new materials, including quasi-two-dimensional electronic systems (2DES) in semiconductor heterojunctions [29][30][31][32] and graphene. The isolation of a single carbon layer, graphene, introduced a new 2DES with unusual electronic properties, including the zero energy band gap, relativistic nature of quasiparticles, sublattice pseudospin and two non-equivalent valleys [32][33][34][35][36][37][38][39].…”

“…Artificial graphene structures have been realized already using photonic lattices, nano-patterning, modulation doping, and scanning probe methods for atomic manipulation on metal surfaces. [2,18,[20][21][22][23][24][25][26][27][50][51][52][53]. Here we propose a quantum simulator of graphene inspired bipartite extended Hubbard model with broken sublattice symmetry.…”

“…These advantages include tunable distance between the dots and depth of confining potential, programmable lattice symmetry and termination (i.e. edge type), tunable electron-electron interactions and interdot tunneling [18,25,27]. Further advantages of artificial graphene include the ability to control values of U/t in a bipartite Hubbard model, which is not possible with graphene [61,62].…”