164 research outputs found
Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
While an ordinary Fermi sea is perturbatively robust to interactions, the
paradigmatic composite-fermion (CF) Fermi sea arises as a non-perturbative
consequence of emergent gauge fields in a system where there was no Fermi sea
to begin with. A mean-field picture suggests two Fermi seas, of composite
fermions made from electrons or holes in the lowest Landau level, which occupy
different areas away from half filling and thus appear to represent distinct
states. We show that in the microscopic theory of composite fermions, which
satisfies particle-hole symmetry in the lowest Landau level to an excellent
degree, the Fermi wave vectors at filling factors and are the
same, and are generally consistent with the experimental findings of Kamburov
{\em et al.} [Phys. Rev. Lett. {\bf 113}, 196801 (2014)]. Our calculations
suggest that the area of the CF Fermi sea may slightly violate the Luttinger
area rule.Comment: 21 pages, 17 figures including supplemental material, published
versio
Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
While the integer quantum Hall effect of composite fermions manifests as the
prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of
composite fermions produces further, more delicate states, arising from a weak
residual interaction between composite fermions. We study the spin phase
diagram of these states, motivated by the recent experimental observation by
Liu {\em et al.} \cite{Liu14a,Liu14b} of several spin-polarization transitions
at 4/5, 5/7, 6/5, 9/7, 7/9, 8/11 and 10/13 in GaAs systems. We show that the
FQHE of composite fermions is much more prevalent in multicomponent systems,
and consider the feasibility of such states for systems with
components for an SU() symmetric interaction. Our results apply to
GaAs quantum wells, wherein electrons have two components, to AlAs quantum
wells and graphene, wherein electrons have four components (two spins and two
valleys), and to an H-terminated Si(111) surface, which can have six
components. The aim of this article is to provide a fairly comprehensive list
of possible incompressible fractional quantum Hall states of composite
fermions, their SU() spin content, their energies, and their phase
diagram as a function of the generalized "Zeeman" energy. We obtain results at
three levels of approximation: from ground state wave functions of the
composite fermion theory, from composite fermion diagonalization, and, whenever
possible, from exact diagonalization. Effects of finite quantum well thickness
and Landau level mixing are neglected in this study. We compare our theoretical
results with the experiments of Liu {\em et al.} \cite{Liu14a,Liu14b} as well
as of Yeh {\em et al.} \cite{Yeh99} for a two component system.Comment: 29 pages, 6 figure
Prediction of a non-Abelian fractional quantum Hall state with -wave pairing of composite fermions in wide quantum wells
We theoretically investigate the nature of the state at quarter filled lowest
Landau level and predict that, as the quantum well width is increased, a
transition occurs from the composite fermion Fermi sea into a novel non-Abelian
fractional quantum Hall state that is topologically equivalent to -wave
pairing of composite fermions. This state is topologically distinct from the
familiar -wave paired Pfaffian state. We compare our calculated phase
diagram with experiments and make predictions for many observable quantities
Moving boundary and photoelastic coupling in GaAs optomechanical resonators
Chip-based cavity optomechanical systems are being considered for
applications in sensing, metrology, and quantum information science. Critical
to their development is an understanding of how the optical and mechanical
modes interact, quantified by the coupling rate . Here, we develop GaAs
optomechanical resonators and investigate the moving dielectric boundary and
photoelastic contributions to . First, we consider coupling between the
fundamental radial breathing mechanical mode and a 1550 nm band optical
whispering gallery mode in microdisks. For decreasing disk radius from
m to m, simulations and measurements show that changes
from being dominated by the moving boundary contribution to having an equal
photoelastic contribution. Next, we design and demonstrate nanobeam
optomechanical crystals in which a GHz mechanical breathing mode couples
to a 1550 nm optical mode predominantly through the photoelastic effect. We
show a significant (30 ) dependence of on the device's in-plane
orientation, resulting from the difference in GaAs photoelastic coefficients
along different crystalline axes, with fabricated devices exhibiting
as high as 1.1 MHz for orientation along the [110] axis.
GaAs nanobeam optomechanical crystals are a promising system which can combine
the demonstrated large optomechanical coupling strength with additional
functionality, such as piezoelectric actuation and incorporation of optical
gain media
- …