arXiv subjects

Dung Xuan Nguyen

Publications and source records attributed to Dung Xuan Nguyen.

30 records · Page 2Linked to original sources

arXiv2021

Dirac Composite Fermion Theory of General Jain's Sequences

We reconsider the composite fermion theory of general Jain's sequences with filling factor $ν=N/(4N\pm1)$. We show that Goldman and Fradkin's proposal of a Dirac composite fermion leads to a violation of the Haldane bound on the coefficient of the static structure factor. To resolve this apparent contradiction, we add to the effective theory a gapped chiral mode (or modes) which already exists in the Fermi liquid state at $ν=1/4$. We interpret the additional mode as an internal degree of freedom of the composite fermion, related to area-preserving deformations of the elementary droplet built up from electrons and correlation holes. In addition to providing a suitable static structure factor, our model also gives the expected Wen-Zee shift and a Hall conductivity that manifests Galilean invariance. We show that the charge density in the model satisfies the long-wavelength version of the Girvin-MacDonald-Platzman algebra.

cond-mat.str-el↗

arXiv2021

Magic configurations in Moiré Superlattice of Bilayer Photonic crystal: Almost-Perfect Flatbands and Unconventional Localization

We investigate the physics of photonic band structures of the moiré patterns that emerged when overlapping two uni-dimensional (1D) photonic crystal slabs with mismatched periods. The band structure of our system is a result of the interplay between intra-layer and inter-layer coupling mechanisms, which can be fine-tuned via the distance separating the two layers. We derive an effective Hamiltonian that captures the essential physics of the system and reproduces all numerical simulations of electromagnetic solutions with high accuracy. Most interestingly, \textit{magic distances} corresponding to the emergence of photonic flatbands within the whole Brillouin zone of the moiré superlattice are observed. We demonstrate that these flatband modes are tightly localized within a moiré period. Moreover, we suggest a single-band tight-binding model that describes the moiré minibands, of which the tunnelling rate can be continuously tuned via the inter-layer strength. Our results show that the band structure of bilayer photonic moiré can be engineered in the same fashion as the electronic/excitonic counterparts. It would pave the way to study many-body physics at photonic moiré flatbands and novel optoelectronic devices.

physics.optics↗

arXiv2021

Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering

Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons $ω_0$ is close to the energy gap $E_G$, but $|ω_0-E_G|$ is much larger than the energy scales of the quantum Hall problem. In the literature, it is often assumed that Raman scattering measures the dynamic structure factor $S(ω,\mathbf{k})$ of the FQH. However, in this paper, we find that the light scattering spectrum measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit $k\to0$. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densities that enter the Raman scattering amplitudes. We propose that Raman scattering provides a way to probe the bulk of the $ν=5/2$ quantum Hall state to determine its nature.

cond-mat.mes-hall↗

arXiv2020

Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

cond-mat.quant-gas↗

arXiv2020

Electrodynamics of Thin Sheets of Twisted Material

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity", which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic waves with wavelength larger than the thickness of the sheet. We show that the low-frequency Faraday rotation angle has different behaviors in different phases. For an insulator, the Faraday angle behaves as $ω^2$ at low frequencies, with the coefficient being determined by the linear relationship between a component of the electric quadrupole moment and the external electric field. For superconductors, the Faraday rotation angle is constant when the frequency of the incoming EM waves is below the superconducting gap and is determined by the coefficient of the Lifshitz invariant in the Ginzburg-Landau functional describing the superconducting state. In the metallic state, we show that the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. The theory is general and is applicable to strongly correlated phases.

cond-mat.mes-hall↗

arXiv2018

Algebraic Approach to Fractional Quantum Hall Effect

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $ν=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure factor at large $N$ and fixed $z=(2N+1) q\ell_B\sim 1$. When $z<3.8$, the result does not depend on the particular form of the Hamiltonian.

cond-mat.str-el↗

arXiv2017

Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

cond-mat.str-el↗

arXiv2017

Particle-hole symmetry and composite fermions in fractional quantum Hall states

We study fractional quantum Hall states at filling fractions in the Jain sequences using the framework of composite Dirac fermions. Synthesizing previous work, we write down an effective field theory consistent with all symmetry requirements, including Galilean invariance and particle-hole symmetry. Employing a Fermi liquid description, we demonstrate the appearance of the Girvin--Macdonlald--Platzman algebra and compute the dispersion relation of neutral excitations and various response functions. Our results satisfy requirements of particle-hole symmetry. We show that while the dispersion relation obtained from the HLR theory is particle-hole symmetric, correlation functions obtained from HLR are not. The results of the Dirac theory are shown to be consistent with the Haldane bound on the projected structure factor, while those of the HLR theory violate it.

cond-mat.mes-hall↗

arXiv2016

Particle-Hole Duality in the Lowest Landau Level

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding properties of the original states. These relations establish a precise duality between chiral quantum Hall states and their PH-conjugates. The key ingredient in the proof of the relations is a generalization of Girvin's construction of PH-conjugate states to inhomogeneous magnetic field and curvature. Finally, we make several non-trivial checks of the relations, including for the Jain states and their PH-conjugates.

cond-mat.str-el↗

arXiv2016

Higher-Spin Theory of the Magnetorotons

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions $ν=N/(2N+1)$ at large $N$. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are $O(N)$ neutral excitations, each carrying a well-defined spin that runs integer values $2,3,\ldots$. The mixing of modes at nonzero momentum $q$ leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at $q\ell_B=z_i/(2N+1)$, where $\ell_B$ is the magnetic length and $z_i$ are the zeros of the Bessel function $J_1$, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.

cond-mat.mes-hall↗

arXiv2016

Exact Electromagnetic Response of Landau Level Electrons

We present a simple method that allows to calculate the electromagnetic response of non-interacting electrons in strong magnetic field to arbitrary order in the gradients of external electric and magnetic fields. We illustrate the method on both non-relativistic and massless Dirac electrons filling $N$ Landau levels. First, we derive an exact relation between the electromagnetic response of the non-relativistic and Dirac electrons in the lowest Landau level. Next, we obtain a closed form expression for the polarization operator in the large $N$ (or weak magnetic field) limit. We explicitly show that in the large $N$ limit the random phase approximation (RPA) computation of the polarization tensor agrees - in leading and sub-leading order in $N$ - with a Fermi liquid computation to {\it all} orders in the gradient expansion and for arbitrary value of the $\mathrm{g}$-factor. Finally, we show that in the large $N$ limit the non-relativistic polarization tensor agrees with Dirac's in the leading and sub-leading orders in $N$, provided that Berry phase of the Dirac cone is taken into account via replacement $N\longrightarrow N+\frac{1}{2}$.

cond-mat.str-el↗

arXiv2014

Lowest Landau Level Stress Tensor and Structure Factor of Trial Quantum Hall Wave Functions

We show that for a class of model Hamiltonians for which certain trial quantum Hall wavefunctions are exact ground states, there is a single spectral density function which controls all two-point correlation functions of density, current and stress tensor components. From this we show that the static structure factors of these wavefunctions behaves at long wavelengths as $s_4 k^4$ where the coefficient $s_4$ is directly related to the shift: $s_4=(\mathcal S-1)/8$.

cond-mat.str-el↗