Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFinite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems
60
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In a quantum Hall system, the finite-wavevector Hall conductivity displays an intriguing dependence on the Hall viscosity, a coefficient that describes the non-dissipative response of the fluid to a velocity gradient. In this paper, we pursue this connection in detail for quantum Hall systems on a lattice, noting that the neat continuum relation breaks down and develops corrections due to the broken rotational symmetry. In the process, we introduce a new, quantum mechanical derivation of the finite-wavevector Hall conductivity for the integer quantum Hall effect, which allows terms to arbitrary order in the wavevector expansion to be calculated straightforwardly. We also develop a universal formalism for studying quantum Hall physics on a lattice, and find that at weak applied magnetic fields, generic lattice wavefunctions connect smoothly to the Landau levels of the continuum. At moderate field strengths, the lattice corrections can be significant and perturb the wavefunctions, energy levels, and transport properties from their continuum values. Our approach allows the finite-field behaviour of a system to be inferred directly from the zero-field band structure.
rate research
Read More
Two-dimensional semiconductor quantum dots are studied in the the filling-factor range 2<v<3. We find both theoretical and experimental evidence of a collective many-body phenomenon, where a fraction of the trapped electrons form an incompressible spin-droplet on the highest occupied Landau level. The phenomenon occurs only when the number of electrons in the quantum dot is larger than ~30. We find the onset of the spin-droplet regime at v=5/2. This proposes a finite-geometry alternative to the Moore-Read-type Pfaffian state of the bulk two-dimensional electron gas. Hence, the spin-droplet formation may be related to the observed fragility of the v=5/2 quantum Hall state in narrow quantum point contacts.
Parafermions are non-Abelian anyons which generalize Majorana fermions and hold great promise for topological quantum computation. We study the braiding of $mathbb{Z}_{2n}$ parafermions which have been predicted to emerge as bound states in fractional quantum Hall systems at filling factor $ u = 1/n$ ($n$ odd). Using a combination of bosonization and refermionization, we calculate the energy splitting as a function of distance and chemical potential for a pair of parafermions separated by a gapped region. Braiding of parafermions in quantum Hall edge states can be implemented by repeated fusion and nucleation of parafermion pairs. We simulate the conventional braiding protocol of parafermions numerically, taking into account the finite separation and finite chemical potential. We show that a nonzero chemical potential poses challenges for the adiabaticity of the braiding process because it leads to accidental crossings in the spectrum. To remedy this, we propose an improved braiding protocol which avoids those degeneracies.
We study the bilayer quantum Hall system at total filling factor u_T = 1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation firstly assuming that only one momentum Q0 is macroscopically occupied and later we consider the same situation for two modes pm Q0. We find strong evidences that a first-order quantum phase transition at small interlayer separation takes place from a zero-momentum condensate phase, which corresponds to Halperin 111 state, to a finite-momentum condensate of magnetic excitons.
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.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
