اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Fractional Quantum Hall States at $ u=13/5$ and $12/5$ and their Non-Abelian Nature
131
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We investigate the nature of the fractional quantum Hall (FQH) state at filling factor $ u=13/5$, and its particle-hole conjugate state at $12/5$, with the Coulomb interaction, and address the issue of possible competing states. Based on a large-scale density-matrix renormalization group (DMRG) calculation in spherical geometry, we present evidence that the physics of the Coulomb ground state (GS) at $ u=13/5$ and $12/5$ is captured by the $k=3$ parafermion Read-Rezayi RR state, $text{RR}_3$. We first establish that the state at $ u=13/5$ is an incompressible FQH state, with a GS protected by a finite excitation gap, with the shift in accordance with the RR state. Then, by performing a finite-size scaling analysis of the GS energies for $ u=12/5$ with different shifts, we find that the $text{RR}_3$ state has the lowest energy among different competing states in the thermodynamic limit. We find the fingerprint of $text{RR}_3$ topological order in the FQH $13/5$ and $12/5$ states, based on their entanglement spectrum and topological entanglement entropy, both of which strongly support their identification with the $text{RR}_3$ state. Furthermore, by considering the shift-free infinite-cylinder geometry, we expose two topologically-distinct GS sectors, one identity sector and a second one matching the non-Abelian sector of the Fibonacci anyonic quasiparticle, which serves as additional evidence for the $text{RR}_3$ state at $13/5$ and $12/5$.
قيم البحث
اقرأ أيضاً
We investigate the finite frequency noise of a quantum point contact at filling factor { u} = 5/2 using a weakly coupled resonant LC circuit as a detector. We show how one could spectroscopically address the fractional charged excitations inspecting
separately their charge and scaling dimensions. We thus compare the behaviour of the Pfaffian and the anti-Pfaffian non-Abelian edge states models in order to give possible experimental signatures to identify the appropriate model for this fractional quantum Hall states. Finally we investigate how the temperature of the LC resonant circuit can be used in order to enhance the sensibility of the measurement scheme.
We study the nature of the u=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. We introduce a general method to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfa
ffian, under periodic boundary conditions in a quartered Brillouin zone scheme containing both even and odd numbers of electrons. We examine the rotational quantum numbers on the torus, and show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing the particle-hole symmetry is broken in such a way that the anti-Pfaffian is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.
We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $ u = 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We al
so mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. From the evolution of edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle (with charge $pm e/4$) when propagating at the edge; using numbers obtained from a specific set of parameters we estimate the decoherence length to be around four microns. This sets an upper bound for the separation of the two point contacts in a double point contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge) while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).
In this work we report the opening of an energy gap at the filling factor $ u=3+1/3$, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifical
ly, we find that the relative magnitudes of the energy gaps of the $ u=3+1/3$ and $3+1/5$ states from the upper spin branch are reversed when compared to the $ u=2+1/3$ and $2+1/5$ counterpart states in the lower spin branch. Our findings raise the possibility that the former states have a non-conventional origin.
We report a reliable method to estimate the disorder broadening parameter from the scaling of the gaps of the even and major odd denominator fractional quantum Hall states of the second Landau level. We apply this technique to several samples of vast
ly different densities and grown in different MBE chambers. Excellent agreement is found between the estimated intrinsic and numerically obtained energy gaps for the $ u=5/2$ fractional quantum Hall state. Futhermore, we quantify, for the first time, the dependence of the intrinsic gap at $ u=5/2$ on Landau level mixing.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
