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Register a new userMagnetoconductivity of Hubbard bands induced in Silicon MOSFETs
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Sodium impurities are diffused electrically to the oxide-semiconductor interface of a silicon MOSFET to create an impurity band. At low temperature and at low electron density, the band is split into an upper and a lower sections under the influence of Coulomb interactions. We used magnetoconductivity measurements to provide evidence for the existence of Hubbard bands and determine the nature of the states in each band.
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We report measurements of the temperature-dependent conductivity in a silicon metal-oxide-semiconductor field-effect transistor that contains sodium impurities in the oxide layer. We explain the variation of conductivity in terms of Coulomb interactions that are partially screened by the proximity of the metal gate. The study of the conductivity exponential prefactor and the localization length as a function of gate voltage have allowed us to determine the electronic density of states and has provided arguments for the presence of two distinct bands and a soft gap at low temperature.
For densities above $n=1.6 times 10^{11}$ cm$^{-2}$ in the strongly interacting system of electrons in two-dimensional silicon inversion layers, excellent agreement between experiment and the theory of Zala, Narozhny and Aleiner is obtained for the response of the conductivity to a magnetic field applied parallel to the plane of the electrons. However, the Fermi liquid parameter $F_0^sigma(n)$ and the valley splitting $Delta_V(n)$ obtained from fits to the magnetoconductivity, although providing qualitatively correct behavior (including sign), do not yield quantitative agreement with the temperature dependence of the conductivity in zero magnetic field. Our results suggest the existence of additional scattering processes not included in the theory in its present form.
We have studied the temperature dependence of the conductivity of a silicon MOSFET containing sodium ions in the oxide above 20 K. We find the impurity band resulting from the presence of charges at the silicon-oxide interface is split into a lower and an upper band. We have observed activation of electrons from the upper band to the conduction band edge as well as from the lower to the upper band. A possible explanation implying the presence of Hubbard bands is given.
We observe a complex change in the hopping exponent value from 1/2 to 1/3 as a function of disorder strength and electron density in a sodium-doped silicon MOSFET. The disorder was varied by applying a gate voltage and thermally drifting the ions to different positions in the oxide. The same gate was then used at low temperature to modify the carrier concentration. Magnetoconductivity measurements are compatible with a change in transport mechanisms when either the disorder or the electron density is modified suggesting a possible transition from a Mott insulator to an Anderson insulator in these systems.
In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Neverethless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher lying bands via perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian and that the compressibility is diverging as a consequence of an emergent $SU(2)$ symmetry. This symmetry is broken by second order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality $D geq mathcal{W}^2$ between the Drude weight $D$ and the winding number $mathcal{W}$, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.
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