Beats of the Magnetocapacitance Oscillations in Lateral Semiconductor Superlattices

We present calculations on the magnetocapacitance of the two-dimensional electron gas in a lateral semiconductor superlattice under two-dimensional weak periodic potential modulation in the presence of a perpendicular magnetic field. Adopting a Gaussian broadening of magnetic-field-dependent width in the density of states, we present explicit and simple expressions for the magnetocapacitance, valid for the relevant weak magnetic fields and modulation strengths. As the modulation strength in both directions increase, beats of the magnetocapacitance oscillations are observed, in the low magnetic field range (Weiss-oscillations regime), which are absent in the one-dimensional weak modulation case.Comment: 11 pages, 7 figures, accepted by Mod. Phys. Lett. B (March 2007

Fractional Chern insulator on a triangular lattice of strongly correlated t2gt_{2g} electrons

We discuss the low-energy limit of three-orbital Kondo-lattice and Hubbard models describing $t_{2g}$ orbitals on a triangular lattice near half-filling. We analyze how very flat bands with non-trivial topological character, a Chern number C=1, arise both in the limit of infinite on-site interactions as well as in more realistic regimes. Exact diagonalization is then used to investigate fractional filling of an effective one-band spinless-fermion model including nearest-neighbor interaction $V$; it reveals signatures of fractional Chern insulators (FCIs) for several filling fractions. In addition to indications based on energies, e.g. flux insertion and fractional statistics of quasiholes, Chern numbers are obtained. It is shown that FCIs are robust against disorder in the underlying magnetic texture that defines the topological character of the band. We also investigate competition between FCI states and a charge density wave (CDW) and discuss particle-hole asymmetry as well as Fermi-surface nesting. FCI states turn out to be rather robust and do not require very flat bands, but can also arise when filling or an absence of Fermi-surface nesting disfavor the competing CDW. Nevertheless, very flat bands allow FCI states to be induced by weaker interactions than those needed for more dispersive bands.Comment: 14 pages, 13 figure

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.Comment: 19 pages, 5 figures. accepted to Int. J. Mod. Phys. B (April 2006

Integrated impedance bridge for absolute capacitance measurements at cryogenic temperatures and finite magnetic fields

We developed an impedance bridge that operates at cryogenic temperatures (down to 60 mK) and in perpendicular magnetic fields up to at least 12 T. This is achieved by mounting a GaAs HEMT amplifier perpendicular to a printed circuit board containing the device under test and thereby parallel to the magnetic field. The measured amplitude and phase of the output signal allows for the separation of the total impedance into an absolute capacitance and a resistance. Through a detailed noise characterization, we find that the best resolution is obtained when operating the HEMT amplifier at the highest gain. We obtained a resolution in the absolute capacitance of 6.4~aF$/\sqrt{\textrm{Hz}}$ at 77 K on a comb-drive actuator, while maintaining a small excitation amplitude of 15~$k_\text{B} T/e$. We show the magnetic field functionality of our impedance bridge by measuring the quantum Hall plateaus of a top-gated hBN/graphene/hBN heterostructure at 60~mK with a probe signal of 12.8~$k_\text{B} T/e$.Comment: 7 pages, 5 figure