Excitonic Condensation Reflecting Electronic States in Two-Band Penrose–Hubbard Model

Abstract

We study the excitonic insulating (EI) phase in the two-band Hubbard models on the Penrose tiling. Performing the real-space mean-field calculations systematically, we obtain the ground state phase diagrams for the vertex and center models. We find that, in some regimes, the stable EI phase is induced by small interband interactions. We argue that this originates from the electronhole pairing for the completely or nearly degenerate states, which are characteristic of the Penrose tiling. We also study spatial distribution of the order parameter, mapping it to the perpendicular space.

Antiferromagnetically Ordered State in the Half-Filled Hubbard Model on the Socolar Dodecagonal Tiling

“…This implies that electron correlations as well as quasiperiodic structures play an important role in understanding low temperature properties in the system [4][5][6][7][8][9]. Furthermore, the superconducting state has recently been observed in the quasicrystal Al-Zn-Mg [10], which stimulates further investigations on spontaneously symmetry breaking state in correlated electron systems on quasiperiodic lattices [11][12][13].…”

Hyperuniform electron distributions controlled by electron interactions in quasicrystal

“…Aside from the electron density, interesting spatial patterns have been reported in preceding theoretical studies for the magnetic moment [9][10][11][12][13][14][15][16][17][18][19][20] of antiferromagnets, superconducting order parameter [21][22][23][24][25][26][27][28], and the order parameter of the excitonic insulator [29]. The concept of hyperuniformity may also be useful to characterize these distributions.…”

“…Namely, sites in a similar ambient geometry in the physical space are assembled into the same area in the perpendicular space. Thereby, the perpendicular-space map has often been used to analyze the real-space patterns on quasiperiodic lattices [13,17,18,27,29,53,54].…”

“…Theoretical studies of the electron states on related quasiperiodic lattices have indeed revealed interesting spatially inhomogeneous but orderly distributions of the wave function amplitude [4][5][6][7] and electron density [8] in the normal phase, according to the underlying lattice structure. In symmetry broken phases, further interesting spatial patterns have been reported for the magnetic moment of quasiperiodic antiferromagnets [9][10][11][12][13][14][15][16][17][18][19][20] and the order parameters of superconductivity [21][22][23][24][25][26][27][28] and the excitonic insulator [29].…”

Doped Mott insulator on Penrose tiling

“…In this case, various electronic phases have been studied, based on the Heisenberg-type or Hubbard-type models. These include metallic [25][26][27][28][29][30][31] , magnetic [32][33][34][35][36][37][38][39][40][41][42][43][44][45] , superconducting [46][47][48][49][50][51][52][53][54] and excitonic insulating 55 phases, where relations between the local site geometry and the electron density or order parameters have been clarified. While these ordered states are basically captured by a static mean-field approach, the Mott insulating state, involving a singular electron self-energy, cannot be described by it: We need to take account of dynamical correlation effects in a nonperturbative way.…”