Resonances in a periodically driven bosonic system

Periodically driven systems are a common topic in modern physics. In optical lattices specifically, driving is at the origin of many interesting phenomena. However, energy is not conserved in driven systems, and under periodic driving, heating of a system is a real concern. In an effort to better understand this phenomenon, the heating of single-band systems has been studied, with a focus on disorder- and interaction-induced effects, such as many-body localisation. Nevertheless, driven systems occur in a much wider context than this, leaving room for further research. Here, we fill this gap by studying a non-interacting model, characterised by discrete, periodically spaced energy levels that are unbounded from above. We couple these energy levels resonantly through a periodic drive, and discuss the heating dynamics of this system as a function of the driving protocol. In this way, we show that a combination of stimulated emission and absorption causes the presence of resonant stable states. This will serve to elucidate the conditions under which resonant driving causes heating in quantum systems

Rashba and intrinsic spin-orbit interactions in biased bilayer graphene

We investigate the effect that the intrinsic spin-orbit and the inter- and intra-layer Rashba interactions have on the energy spectrum of either an unbiased or a biased graphene bilayer. We find that under certain conditions, a Dirac cone is formed out of a parabolic band and that it is possible to create a "Mexican hat"-like energy dispersion in an unbiased bilayer. In addition, in the presence of only an intralayer Rashba interaction, the K (K') point splits into four distinct ones, contrarily to the case in single-layer graphene, where the splitting also takes place, but the low-energy dispersion at these points remains identical.Comment: 10 pages, 10 figure

Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach

We study the quantum Hall effect in graphene at filling factors \nu = 0 and \nu = \pm, concentrating on the quantum Hall ferromagnetic regime, within a non-perturbative bosonization formalism. We start by developing a bosonization scheme for electrons with two discrete degrees of freedom (spin-1/2 and pseudospin-1/2) restricted to the lowest Landau level. Three distinct phases are considered, namely the so-called spin-pseudospin, spin, and pseudospin phases. The first corresponds to a quarter-filled (\nu =-1) while the others to a half-filled (\nu = 0) lowest Landau level. In each case, we show that the elementary neutral excitations can be treated approximately as a set of n-independent kinds of boson excitations. The boson representation of the projected electron density, the spin, pseudospin, and mixed spin-pseudospin density operators are derived. We then apply the developed formalism to the effective continuous model, which includes SU(4) symmetry breaking terms, recently proposed by Alicea and Fisher. For each quantum Hall state, an effective interacting boson model is derived and the dispersion relations of the elementary excitations are analytically calculated. We propose that the charged excitations (quantum Hall skyrmions) can be described as a coherent state of bosons. We calculate the semiclassical limit of the boson model derived from the SU(4) invariant part of the original fermionic Hamiltonian and show that it agrees with the results of Arovas and co-workers for SU(N) quantum Hall skyrmions. We briefly discuss the influence of the SU(4) symmetry breaking terms in the skyrmion energy.Comment: 16 pages, 4 figures, final version, extended discussion about the boson-boson interaction and its relation with quantum Hall skyrmion

Celebrating Haldane's `Luttinger liquid theory'

This short piece celebrates Haldane's seminal J. Phys. C 14, 2585 (1981) paper laying the foundations of the modern theory of Luttinger liquids in one-dimensional systems.Comment: Viewpoint for Journal of Physics: Condensed Matte

Quantum Brownian motion in a Landau level

Motivated by questions about the open-system dynamics of topological quantum matter, we investigated the quantum Brownian motion of an electron in a homogeneous magnetic field. When the Fermi length $l_F=\hbar/(v_Fm_{\text{eff}})$ becomes much longer than the magnetic length $l_B=(\hbar c/eB)^{1/2}$, then the spatial coordinates $X,Y$ of the electron cease to commute, $[X,Y]=il_B^2$. As a consequence, localization of the electron becomes limited by Heisenberg uncertainty, and the linear bath-electron coupling becomes unconventional. Moreover, because the kinetic energy of the electron is quenched by the strong magnetic field, the electron has no energy to give to or take from the bath, and so the usual connection between frictional forces and dissipation no longer holds. These two features make quantum Brownian motion topological, in the regime $l_F\gg l_B$, which is at the verge of current experimental capabilities. We model topological quantum Brownian motion in terms of an unconventional operator Langevin equation derived from first principles, and solve this equation with the aim of characterizing diffusion. While diffusion in the noncommutative plane turns out to be conventional, with the mean displacement squared being proportional to $t^\alpha$ and $\alpha=1$, there is an exotic regime for the proportionality constant in which it is directly proportional to the friction coefficient and inversely proportional to the square of the magnetic field: in this regime, friction helps diffusion and the magnetic field suppresses all fluctuations. We also show that quantum tunneling can be completely suppressed in the noncommutative plane for suitably designed metastable potential wells, a feature that might be worth exploiting for storage and protection of quantum information

Conformal QED in two-dimensional topological insulators

It has been shown recently that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). In this work, we provide a first-principle derivation of this non-Fermi-liquid phase based on the gauge-theory approach. Firstly, we derive a gauge theory for the edge states by simply assuming that the interactions between the Dirac fermions at the edge are mediated by a quantum dynamical electromagnetic field. Here, the massless Dirac fermions are confined to live on the one-dimensional boundary, while the (virtual) photons of the U(1) gauge field are free to propagate in all the three spatial dimensions that represent the physical space where the topological insulator is embedded. We then determine the effective 1+1-dimensional conformal field theory (CFT) given by the conformal quantum electrodynamics (CQED). By integrating out the gauge field in the corresponding partition function, we show that the CQED gives rise to a 1+1-dimensional Thirring model. The bosonized Thirring Hamiltonian describes exactly a HLL with a parameter K and a renormalized Fermi velocity that depend on the value of the fine-structure constant $\alpha$.Comment: (5+4) pages, 2 figure