Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThermopower as a Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall States
177
0
0.0
(
0
)
Authors
Kun Yang
Ask ChatGPT about the research
No Arabic abstract
This paper has been superseded by a new preprint: Kun Yang and Bertrand I. Halperin, arXiv:0901.1429.
rate research
Read More
Using the Onsager relation between electric and heat transport coefficients, and considering the very different roles played by the quantum Hall condensate and quasiparticles in transport, we argue that near the center of a quantum Hall plateau thermopower in a Corbino geometry measures {it entropy per quasiparticle per quasiparticle charge}. This relation indicates that thermopower measurement in a Corbino setup is a more direct measure of quasiparticle entropy than in a Hall bar. Treating disorder within the self-consistent Born approximation, we show through an explicit microscopic calculation that this relation holds on an integer quantum Hall plateau at low temperatures. Applying this to non-Abelian quantum Hall states, we argue that Corbino thermopower at sufficiently low temperature becomes temperature-independent, and measures the quantum dimension of non-Abelian quasiparticles that determines the topological entropy they carry.
We deduce a new set of symmetries and relations between the coefficients of the expansion of Abelian and Non-Abelian Fractional Quantum Hall (FQH) states in free (bosonic or fermionic) many-body states. Our rules allow to build an approximation of a FQH model state with an overlap increasing with growing system size (that may sometimes reach unity!) while using a fraction of the original Hilbert space. We prove these symmetries by deriving a previously unknown recursion formula for all the coefficients of the Slater expansion of the Laughlin, Read Rezayi and many other states (all Jacks multiplied by Vandermonde determinants), which completely removes the current need for diagonalization procedures.
Significant insights into non-Abelian quantum Hall states were obtained from studying special multi-particle interaction Hamiltonians, whose unique ground states are the Moore-Read and Read-Rezayi states for the case of spinless electrons. We generalize this approach to include the electronic spin-1/2 degree of freedom. We demonstrate that in the absence of Zeeman splitting the ground states of such Hamiltonians have large degeneracies and very rich spin structures. The spin structure of the ground states and low-energy excitations can be understood based on an emergent SU(3) symmetry for the case corresponding to the Moore-Read state. These states with different spin quantum numbers represent non-Abelian quantum Hall states with different magnetizations, whose quasi-hole properties are likely to be similar to those of their spin polarized counterparts.
We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced by an AFM tip) in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and edge confining potential. We find, in particular, at Laughlin filling fraction $ u = 1/3$, both quasihole and quasiparticle states can emerge as the ground state of the system in the presence of the trapping potential. As expected, we find the presence of an Abelian quasihole has no effect on the edge spectrum of the quantum liquid, unlike in the non-Abelian case [Phys. Rev. Lett. {bf 97}, 256804 (2006)]. Although quasiholes and quasiparticles can emerge generically in the system, their stability depends on the strength of the confining potential, the strength and the range of the trapping potential. We discuss the relevance of the calculation to the high-accuracy generation and control of individual anyons in potential experiments, in particular, in the context of topological quantum computing.
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 also 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).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
