Landau-Level Mixing and the Emergence of Pfaffian Excitations for the5/2Fractional Quantum Hall Effect

Abstract

We report on exact diagonalization studies for fully spin polarized 5/2 fractional quantum Hall effect, incorporating Landau level mixing through the Bishara-Nayak effective interaction. We find that there is an experimentally accessible region in the phase diagram where the Pfaffian model accurately describes not only the ground state but also the neutral and charged excitations. These results are consistent with the observed persistence of the 5/2 Hall effect down to very low magnetic fields; they are also relevant to the experimental attempts to detect nonabelian braid statistics. The proposed route to nonabelian braid statistics in the 5/2 fractional quantum Hall effect (FQHE) [1][2][3], discovered more than two decades ago [4], proceeds through a sequence of remarkable emergences. To minimize the bulk of the repulsive interaction, electrons in the second Landau level (LL) dress themselves with two vortices to transform into composite fermions [5]; composite fermions (CFs) experience a vanishing magnetic field and form a Fermi sea [6]; the CF Fermi sea, however, is unstable due to a weak residual attractive interaction between composite fermions, which causes an equal spin p x ± ip y pairing, thereby opening a gap and producing an FQHE state [1,2,7]; the Abrikosov vortices of the paired CF state support zero mode solutions, namely majorana CFs, which are symmetric combinations of the CF creation and annihilation operators [3]; these obey nonabelian braid statistics [3] and are potential candidates for fault tolerant topological quantum computation [8].While the decisive verification of these ideas will eventually come from laboratory experiments, we have come to expect any successful theoretical postulate in the field of FQHE to pass the test against "computer experiments," that is, exact solutions of the full many body problem for finite systems typically containing up to 16-18 particles. A concrete realization of the above physics is through the Pfaffian (Pf) model of Moore and Read [1], which has been subjected to such tests. The Pf wave function for the ground state has a moderate overlap with the exact Coulomb ground state, which can be improved either by artificially strengthening the short range part of the interaction [9][10][11] or by considering the effect of finite thickness [12]. The sensitivity to such slight modifications in the interaction indicates that the physical 5/2 FQHE state lies close to an instability. An adiabatic connection has been shown in finite system studies between the Coulomb and the Pf ground states [11,13,14]. The situation is less clear for excitations, however. A test of the Pf quasiholes has not found them to be satisfactory approximations of the actual quasiholes of the unperturbed Coulomb interaction [15], and an adiabatic connection between the Pf and the Coulomb quasiparticles and quasiholes has not yet been demonstrated. Given that the nonabelian braid properties of the quasiparticles and quasiholes are of primary interest, it would appear important to ascertain the...

Influence of device geometry on tunneling in theν=52quantum Hall liquid

“…At the same time, several papers 56,68,76,77 lend support to a spin-polarized ground state. Another limitation comes from the incomplete understanding of the Landau-level mixing effects [78][79][80][81] . Disorder apparently plays a major role in the discrepancy of the theoretical and experimental results for the energy gap 73,82 and may affect the nature of the ground state.…”

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

“…Later in this work we add additional V α terms to V C in order to explore the neighboring phases. In experiment, such variations of the interaction may arise due to Landau level mixing [48,[87][88][89][90][91][92][93][94].…”

Competing Quantum Hall Phases in the Second Landau Level in Low Density Limit

“…In particular, the stripe phase prevails when there are two states close to the Fermi energy and when the filling of one or both states is very close to the half-filling. Furthermore, numerical calculations [21] showed that the overlap between a specific exact ground state and a Pfaffian state (which is expected to be also responsible for the 7/2 FQHE state in high-density samples) decreased when  > 2, suggesting an instability of the Pfaffian state at low densities. In sample A  = 3.3 at =7/2, much larger than  = 1.3 in the high-density samples of n=310 11 cm -2 , where an isotropic =7/2 FQHE state has been observed.…”

“…The authors in Ref. [21] did not calculate the overlap between the exact ground state and an anisotropic state. It remains interesting to observe whether under their numerical model the anisotropic state actually becomes more stable in the large  regime.…”

“…It has been shown that a large Landau level mixing effect strongly affects the electron physics in the second Landau level [20][21][22][23][24].…”