A UNIFIED QUANTUM HALL CLOSE-PACKED COMPOSITE BOSON (CPCB) MODEL

Abstract

Single-wavelength Landau cyclotron orbitals (SWOs) have been used as quantum Hall basis states to reproduce integer quantum Hall plateaus in a two-dimensional (2D) close-packing representation. But at the high magnetic fields B that correspond to fractional Hall plateaus, these SWOs are too small to give close packing. It is conventionally assumed that the fractional quantum Hall states are formed from collective electron excitations (CEEs). However, by invoking the use of multiple-wavelength Landau orbitals (MWOs), we can close-pack the fractional Hall plateaus in the same manner as the integer plateaus. Quantum Hall plateaus are characterized by the filling fractions ν≡ne/nφ=k/m, where k=1, 2,... (all integers) and m=1, 3,... (all odd integers), and where ne and nφ are the 2D electron e and magnetic flux φ=h/e densities, respectively. A composite particle (CP) is a bound state of an electron and m flux quanta φ. If m is even or odd, the CP is a composite fermion (CF) or composite boson (CB). In the CEE models, both CF and CB formalisms have been used. In the alternative MWO approach introduced here, the close-packed MWOs on a ν=k/m plateau each contain m de Broglie wavelengths λ. Each MWO traps mφ external flux quanta, produces mφ diamagnetic induced flux quanta, and carries the filling fraction ν, which accounts for the extreme accuracy (one part in 108) of the Hall plateau conductance, σH=νe2/h. Since m is odd, these MWOs are CB states, and they form a boson condensate of close-packed composite boson (CPCB) states. The m=1 (m<1) CPCBs tile the integer (fractional) Hall plateaus. The filling fraction index k corresponds to k layers of CPCB orbitals. Plateau formation itself is due to the linear B dependence of the density of CPCB states. The CPCBs are decoupled from the semiconductor substrate, and hence may have large m* effective mass values. THE MWOs near the ν=1/2 non-plateau region are m=2 CF states.