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Register a new userThermoelectric Hall conductivity of the fractional quantum Hall systems on a disk
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For the fractional quantum Hall states on a finite disc, we study the thermoelectric transport properties under the influence of an edge and its reconstruction. In a recent study on a torus [Phys. Rev. B 101, 241101 (2020)], Sheng and Fu found a universal non-Fermi liquid power-law scaling of the thermoelectric conductivity $alpha_{xy} propto T^{eta}$ for the gapless composite Fermi-liquid state. The exponent $eta sim 0.5$ appears an independence of the filling factors and the details of the interactions. In the presence of an edge, we find the properties of the edge spectrum dominants the low-temperature behaviors and breaks the universal scaling law of the thermoelectric conductivity. In order to consider individually the effects of the edge states, the entanglement spectrum in real space is employed and tuned by varying the area of subsystem. In non-Abelian Moore-Read state, the Majorana neutral edge mode is found to have more significant effect than that of the charge mode in the low temperature.
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The entanglement entropy of the $ u = 1/3$ and $ u = 5/2$ quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the fluctuation in the entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a clear signature of a transition as a function of the disorder strength for the $ u = 5/2$ state. Prospects for using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.
In a recent paper by Neupert, Santos, Chamon, and Mudry [Phys. Rev. B 86, 165133 (2012)] it is claimed that there is an elementary formula for the Hall conductivity of fractional Chern insulators. We show that the proposed formula cannot generally be correct, and we suggest one possible source of the error. Our reasoning can be generalized to show no quantity (such as Hall conductivity) expected to be constant throughout an entire phase of matter can possibly be given as the expectation of any time independent short ranged operator.
Measurements of the Hall and dissipative conductivity of a strained Ge quantum well on a SiGe/(001)Si substrate in the quantum Hall regime are reported. We find quantum Hall states in the Composite Fermion family and a precursor signal at filling fraction $ u=5/2$. We analyse the results in terms of thermally activated quantum tunneling of carriers from one internal edge state to another across saddle points in the long range impurity potential. This shows that the gaps for different filling fractions closely follow the dependence predicted by theory. We also find that the estimates of the separation of the edge states at the saddle are in line with the expectations of an electrostatic model in the lowest spin-polarised Landau level (LL), but not in the spin-reversed LL where the density of quasiparticle states is not high enough to accommodate the carriers required.
We study a model of a quantum dot coupled to a quantum Hall edge of the Laughlin state, taking into account short-range interactions between the dot and the edge. This system has been studied experimentally in electron quantum optics in the context of single particle sources. We consider driving the dot out of equilibrium by a time-dependent bias voltage. We calculate the resulting current on the edge by applying the Kubo formula to the bosonized Hamiltonian. The Hamiltonian of this system can also be mapped to the spin-boson model and in this picture, the current can be perturbatively calculated using the non-interacting blip approximation (NIBA). We show that both methods of solution are in fact equivalent. We present numerics demonstrating that the perturbative approaches capture the essential physics at early times, although they fail to capture the charge quantization (or lack thereof) in the current pulses integrated over long times.
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.
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