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Register a new userComposite fermion valley polarization energies: Evidence for particle-hole asymmetry
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In an ideal two-component two-dimensional electron system, particle-hole symmetry dictates that the fractional quantum Hall states around $ u = 1/2$ are equivalent to those around $ u = 3/2$. We demonstrate that composite fermions (CFs) around $ u = 1/2$ in AlAs possess a valley degree of freedom like their counterparts around $ u = 3/2$. However, focusing on $ u = 2/3$ and 4/3, we find that the energy needed to completely valley polarize the CFs around $ u = 1/2$ is considerably smaller than the corresponding value for CFs around $ u = 3/2$ thus betraying a particle-hole symmetry breaking.
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In two-dimensional electron systems confined to wide AlAs quantum wells, composite fermions around the filling factor $ u$ = 3/2 are fully spin polarized but possess a valley degree of freedom. Here we measure the energy needed to completely valley polarize these composite fermions as a function of electron density. Comparing our results to the existing theory, we find overall good quantitative agreement, but there is an unexpected trend: The measured composite fermion valley polarization energy, normalized to the Coulomb energy, decreases with decreasing density.
We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at $1/3$ and $2/3$. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.
We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $pi$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau level mixing. For this purpose, we consider a simple model wherein we determine the variational ground state as a function of Landau level mixing within the space spanned by two basis functions: the lowest-Landau-level projected and the unprojected composite-fermion Fermi sea wave functions. We evaluate Berry phase for a path around the Fermi circle within this model following a recent prescription, and find that it rotates rapidly as a function of Landau level mixing. We also consider the effect of a particle-hole symmetry breaking three-body interaction on the Berry phase while confining the Hilbert space to the lowest Landau level. Our study deepens the connection between the $pi$ Berry phase and the exact particle-hole symmetry in the lowest Landau level.
The Fibonacci topological order is the simplest platform for a universal topological quantum computer, consisting of a single type of non-Abelian anyon, $tau$, with fusion rule $tautimestau=1+tau$. While it has been proposed that the anyon spectrum of the $ u=12/5$ fractional quantum Hall state includes a Fibonacci sector, a dynamical picture of how a pure Fibonacci state may emerge in a quantum Hall system has been lacking. Here we use recently proposed non-Abelian dualities to construct a Fibonacci state of bosons at filling $ u=2$ starting from a trilayer of integer quantum Hall states. Our parent theory consists of bosonic composite vortices coupled to fluctuating $U(2)$ gauge fields, which is related to the standard theory of Laughlin quasiparticles by duality. The Fibonacci state is obtained by clustering the composite vortices between the layers, along with flux attachment, a procedure reminiscent of the clustering picture of the Read-Rezayi states. We further use this framework to motivate a wave function for the Fibonacci fractional quantum Hall state.
We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (`PH-Pfaffian) topological order, a phase consistent with the recently reported thermal Hall conductance [Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic $ u=5/2$ quantum-Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the $ u=5/2$ ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak $p$-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.
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