Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDirect observation of composite fermions and their fully spin-polarized Fermi sea near $ u=5/2$
82
0
0.0
(
0
)
Added by
Md Shafayat Hossain
Publication date
2018
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The enigmatic even-denominator fractional quantum Hall state at Landau level filling factor $ u=5/2$ is arguably the most promising candidate for harboring Majorana quasi-particles with non-Abelian statistics and thus of potential use for topological quantum computing. The theoretical description of the $ u=5/2$ state is generally believed to involve a topological p-wave pairing of fully spin-polarized composite fermions through their condensation into a non-Abelian Moore-Read Pfaffian state. There is, however, no direct and conclusive experimental evidence for the existence of composite fermions near $ u=5/2$ or for an underlying fully spin-polarized Fermi sea. Here, we report the observation of composite fermions very near $ u=5/2$ through geometric resonance measurements, and find that the measured Fermi wavevector provides direct demonstration of a Fermi sea with full spin polarization. This lends crucial credence to the model of $5/2$ fractional quantum Hall effect as a topological p-wave paired state of composite fermions.
rate research
Read More
We have studied temperature dependence of both diagonal and Hall resistivity in the vicinity of $ u=1/2$. Magnetoresistance was found to be positive and almost independent of temperature: temperature enters resistivity as a logarithmic correction. At the same time, no measurable corrections to the Hall resistivity has been found. Neither of these results can be explained within the mean-field theory of composite fermions by an analogy with conventional low-field interaction theory. There is an indication that interactions of composite fermions with fluctuations of the gauge field may reconcile the theory and experiment.
There is increasing experimental evidence for fractional quantum Hall effect at filling factor $ u=2+3/8$. Modeling it as a system of composite fermions, we study the problem of interacting composite fermions by a number of methods. In our variational study, we consider the Fermi sea, the Pfaffian paired state, and bubble and stripe phases of composite fermions, and find that the Fermi sea state is favored for a wide range of transverse thickness. However, when we incorporate interactions between composite fermions through composite-fermion diagonalization on systems with up to 25 composite fermions, we find that a gap opens at the Fermi level, suggesting that inter-composite fermion interaction can induce fractional quantum Hall effect at $ u=2+3/8$. The resulting state is seen to be distinct from the Pfaffian wave function.
We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $ u=5/2$. Our studies are performed using both exact diagonalization and Density Matrix Renormalization Group (DMRG) on the sphere. We find that for the Coulomb interaction the exact finite-system ground state is fully polarized, for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction. The low-energy excitation spectrum is consistent with spin-wave excitations of a fully-magnetized ferromagnet.
There has been a surge of recent interest in the role of anisotropy in interaction-induced phenomena in two-dimensional (2D) charged carrier systems. A fundamental question is how an anisotropy in the energy-band structure of the carriers at zero magnetic field affects the properties of the interacting particles at high fields, in particular of the composite fermions (CFs) and the fractional quantum Hall states (FQHSs). We demonstrate here tunable anisotropy for holes and hole-flux CFs confined to GaAs quantum wells, via applying textit{in situ} in-plane strain and measuring their Fermi wavevector anisotropy through commensurability oscillations. For strains on the order of $10^{-4}$ we observe significant deformations of the shapes of the Fermi contours for both holes and CFs. The measured Fermi contour anisotropy for CFs at high magnetic field ($alpha_mathrm{CF}$) is less than the anisotropy of their low-field hole (fermion) counterparts ($alpha_mathrm{F}$), and closely follows the relation: $alpha_mathrm{CF} = sqrt{alpha_mathrm{F}}$. The energy gap measured for the $ u = 2/3$ FQHS, on the other hand, is nearly unaffected by the Fermi contour anisotropy up to $alpha_mathrm{F} sim 3.3$, the highest anisotropy achieved in our experiments.
The pairing of composite fermions (CFs), electron-flux quasi-particles, is commonly proposed to explain the even-denominator fractional quantum Hall state observed at $ u=5/2$ in the first excited ($N=1$) Landau level (LL) of a two-dimensional electron system (2DES). While well-established to exist in the lowest ($N=0$) LL, much is unknown about CFs in the $N=1$ LL. Here we carry out geometric resonance measurements to detect CFs at $ u=5/2$ by subjecting the 2DES to a one-dimensional density modulation. Our data, taken at a temperature of 0.3 K, reveal no geometric resonances for CFs in the $N=1$ LL. In stark contrast, we observe clear signatures of such resonances when $ u=5/2$ is placed in the $N=0$ LL of the anti-symmetric subband by varying the 2DES width. This finding implies that the CFs mean-free-path is significantly smaller in the $N=1$ LL compared to the $N=0$ LL. Our additional data as a function of in-plane magnetic field highlight the role of subband index and establish that CFs at $ u=5/2$ in the $N=0$ LL are more anisotropic in the symmetric subband than in the anti-symmetric subband.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
