Double-layer systems at zero magnetic field

Abstract

We investigate theoretically the effects of intralayer and interlayer exchange in biased double-layer electron and hole systems, in the absence of a magnetic field. We use a variational Hartree-Fock-like approximation to analyze the effects of layer separation, layer density, tunneling, and applied gate voltages on the layer densities and on interlayer phase coherence. In agreement with earlier work, we find that for very low layer separations and layer densities, an interlayercorrelated ground state possessing spontaneous interlayer coherence (SILC) is obtained, even in the absence of interlayer tunneling. In contrast to earlier work, we find that as a function of total density, there exist four, rather than three, distinct noncrystalline phases for balanced double-layer systems without interlayer tunneling. The newly identified phase exists for a narrow range of densities and has three components and slightly unequal layer densities, with one layer being spin-polarized and the other unpolarized. An additional twocomponent phase is also possible in the presence of sufficiently strong bias or tunneling. The lowest-density SILC phase is the fully spin-and pseudospin-polarized "one-component" phase discussed by Zheng and co-workers [Phys. Rev. B 55, 4506 (1997)]. We argue that this phase will produce a finite interlayer Coulomb drag at zero temperature due to the SILC. We calculate the particle densities in each layer as a function of the gate voltage and total particle density, and find that interlayer exchange can reduce or prevent abrupt transfers of charge between the two layers. We also calculate the effect of interlayer exchange on the interlayer capacitance.

Calculation of the capacitances of conductors: Perspectives for the optimization of electronic devices

“…This ground state has been introduced and predicted for bilayer quantum Hall systems. 37,38 It is characterized by a spontaneous interlayer phase coherence (SILC) of two layers which are each entirely isolated except for their in- 35 A nite bias may support charge separated states.…”

Coulomb and tunneling-coupled trilayer systems at zero magnetic field

“…The straight line corresponds to the approximation given in Eq. (13) for the boundary between α and β configurations.…”

“…( 1) implies that no exact solution is available for the model, and forces us to attempt its approximate solution. For this, we will employ a Hartree-Fock variational approximation, widely used for the bilayer case, either at zero [13] or with magnetic field [16][17][18], and also used in the previous trilayer zero-tunneling and zero-site energy study [4]. But before that, we find convenient to perform an exact transformation of the Hamiltonian, by defining the following operators:…”

“…We provide in this work an exhaustive theoretical study of trilayer systems at zero-magnetic field, within the framework of a Hartree-Fock mean field approximation, already used for bilayer systems [13], and also for a simplified version of the trilayer system considered here [4]. The model, schematically illustrated in Fig.…”

Pseudospin anisotropy of trilayer semiconductor quantum Hall ferromagnets

“…In the case when the crossing is between LLs with equal orbital quantum numbers and different spins we obtain, through similar arguments as used in the case of the crossing between LLs in the same subband, that the only non-zero anisotropy term is U zz , with the same value as in Eq. (27). U zz is always non negative and the crossing belongs then to the easy-plane category for U zz > 0, with the x − y plane as the easy-plane.…”