Temperature effects on edge magnetoplasmons in the quantum Hall regime

Abstract

A microscopic treatment of edge magnetoplasmons (EMPs) is presented for the case of not-toolow temperatures in which the inequality kBT ≫hvg/ℓ0, where vg is the group velocity of the edge states and ℓ0 is the magnetic length, is fulfilled, and for filling factors ν = 1(2). We have obtained independent EMP modes spatially symmetric and antisymmetric with respect to the edge. We describe in detail the spatial structure and dispersion relations of the new edge waves (edge helicons, dipole, quadrupole and octupole EMPs), which have the characteristic length ℓT = ℓ 2 0 kBT /hvg. We have found that, in contrast to well-known results for a spatially homogeneous dissipation within the channel, the damping of the fundamental EMP at not-too-low temperatures is not quantized and has a T −1 dependence. PACS 73.20.Dx, 73.40.Hm I. INTRODUCTION.Edge magnetoplasmons (EMPs) in the two-dimensional electron system (2DES) have received much attention in recent years. Experimental studies have been performed to determine the dispersion relation and the role of edge states in the transport properties of the 2DES both on liquid helium [1-3] as in high-mobility AlGaAs-GaAs heterostructures [4][5][6][7][8][9][10][11]. The interest have even increased with the advent of time-resolved transport experiments [7,9,10]. From a theoretical point of view, a lot of work have been also devoted to study the characteristics of these collective excitations propagating along the edge of the 2DES in the presence of a normal magnetic field B and different edge-wave mechanisms have been proposed [12][13][14][15][16][17][18][19][20][21][22][23]. First, the EMPs dispersion were determined theoretically within essentially classical models [13,16] in which the charge density varies at the edge, but the edge position of the 2DES is kept constant. Other, distinctly different, quantum-mechanical edge-wave mechanisms was proposed [14,15,17,18] in which only the edge change and the density profile is taken as the unperturbed 2DES with respect to the fluctuating edge.Recently a microscopic model was proposed in Refs. [21,22] that effectively incorporates the edge-wave mechanisms mentioned above in the quantum Hall effect (QHE) regime. Even though EMPs have been studied in the limit of low temperatures k B T ≪hv g /ℓ 0 , where v g is the group velocity of the edge states and the magnetic length ℓ 0 = h/m * ω c with ω c = |e|B/m * c, in the calculation of the current density J was assumed that the components of the electric field E of the wave are smooth on the ℓ 0 scale. However, this assumption can not be well justified for EMPs at very low temperatures. Here, we extend the approach of Refs. [21,22] for not-too-low temperatures, wherehω c ≫ k B T ≫hv g /ℓ 0 . In this regime the typical scales of in-plane components of E are of the order of ℓ T = ℓ 2 0 k B T /hv g , which is much larger than ℓ 0 . Our model to treat EMPs consists in considering a 2DES, of width W , length L x = L, and negligible thickness, in the presence of a strong B parallel to the z axis, such ...

Edge magnetoplasmons in wide armchair graphene ribbons

“…Our study shows that the relevant condition L em x 1µm is realistic. The EMPs that we find near a graphene edge are very different from those EMPs treated previously in conventional 2DES, in particular in the integral QHE regime 18,[21][22][23][24][25][26][27] .…”

“…We expect that the charge excitation due to EMPs at the right part of channel will be strongly localized at y u r (ρ ru (t, r)) and y d r (ρ rd (t, r)), in case (i), and at y u,1 r (ρ r,u1 (t, r)) in case (ii). Then for case (i) the components of the current density j(y), in the low-frequency limit ω ≪ v F /ℓ 0 , are 24,25…”

“…where we suppressed the factor exp[−i(ωt − k x x)] common to all terms in Eqs. (25) and (26). From Eqs.…”

Terahertz resonances due to edge magnetoplasmons in a wide armchair graphene ribbon with a weak superlattice potential

“…They are counterpropagating and with essential spatial overlap. This is in contrast with EMPs for conventional two-dimensional electron systems (2DES) which give only one fundamental EMP at the ν = 2 QHE regime; for conventional 2DES different types of EMPs have been studied theoretically [16][17][18][19][20][21][22] and experimentally. [23][24][25] These two counterpropagating EMPs can be on resonance if a strong coupling of the EMPs holds at the ends of the segment L em x ≤ L x , where L x is the length of graphene channel.…”

Edge magnetoplasmons in a wide armchair graphene ribbon with a weak superlattice potential: Finite-frequency gaps and zero group velocity

“…16) four degenerate states of the zero LL at one location and two degenerate states of this LL at a different location, two fundamental EMPs are present: counterpropagating and with essential spatial overlap. This is in contrast with EMPs in conventional two-dimensional electron systems (2DES) which give only one fundamental EMP at the ν = 2 QHE regime, with negligible spin-splitting; for conventional 2DES different types of EMPs have been studied theoretically [17][18][19][20][21][22][23] and experimentally. [24][25][26] Above two counterpropagating EMPs can be on resonance if a strong coupling of the EMPs holds at the ends of the segment L em x ≤ L x , where L x is the length of graphene channel.…”