Optical flux pump in the quantum Hall regime

Letter

Optical flux pump in the quantum Hall regime

Bin Cao, Tobias Grass, Glenn Solomon, and Mohammad Hafezi

Phys. Rev. B 103, L241301 – Published 28 June 2021

Abstract

A seminal gedankenexperiment by Laughlin describes the charge transport in quantum Hall systems via the pumping of flux. Here, we propose an optical scheme which probes and manipulates quantum Hall systems in a similar way: When light containing orbital angular momentum interacts with electronic Landau levels, it acts as a flux pump which radially moves the electrons through the sample. We investigate this effect for a graphene system with Corbino geometry and calculate the radial current in the absence of any electric potential bias. Remarkably, the current is robust against the disorder which is consistent with the lattice symmetry, and in the weak excitation limit, the current shows a power-law scaling with intensity characterized by the novel exponent 2/3.

Received 19 April 2021
Revised 7 June 2021
Accepted 8 June 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L241301

Physics Subject Headings (PhySH)

Angular momentum of light Integer quantum Hall effect Transport phenomena

Disordered systems Graphene

Exact diagonalization Photoexcitation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bin Cao ¹, Tobias Grass², Glenn Solomon¹, and Mohammad Hafezi^1,3

¹Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
²ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona) 08860, Spain
³IREAP, University of Maryland, College Park, Maryland 20742, USA

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Issue

Vol. 103, Iss. 24 — 15 June 2021

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Images

Figure 1
(a) The illustration of the proposed setup. The Corbino-structured sample is concentric with the OAM beam. The OAM-induced current is measured between the inner and the outer electric contacts. (b) In a pristine system, the orbitals in each Landau level (LL) are degenerate in energy. The optical selection (red arrows) leads to an increase in OAM (for positive $ℓ$ ) and phonon relaxations (blue arrows) maintain the OAM. This equivalently leads to a directional transport of electrons. (c) In a system with disorder and confinement, the LLs are broadened in the bulk whereas the energy of the edge orbitals (shaded region) rises quickly. Only the edge states couple and relax pair wisely whereas the disordered bulk eigenstate may couple and relax to more than one eigenstate.
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Figure 2
(a) We illustrate the model used in the simulation. In total 100 orbitals are considered. The confinement is chosen such that 80 are bulk states whereas ten are outer edge states and ten are inner edge states. At $t = 0$ , the bulk states in ${LL}_{0}$ are filled below the Fermi level $E_{F}$ , whereas others are empty. We use $ℓ = + 1$ to illustrate the optical selection rules. In the bulk, states can couple to many others, whereas on the edge only the states with OAM difference equal to $ℓ$ are strongly coupled. (b) The wave function of a bulk state in real space is shown. The bulk state is localized, and the phase of the wave function is disordered as shown in (c). (d) The edge state is delocalized, and the twisted phase of the wave-function (e) shows a well-defined OAM.
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Figure 3
(a) We plot the occupation of ${LL}_{1}$ as a function of time for different $ℓ$ 's. We observe Rabi oscillations which are damped. (b) For the average relaxation time $τ = 50 fs$ , one does not see Rabi oscillation because of the fast relaxation compared to the Rabi frequency. (c) The average radial position of electrons as a function of time for various OAM excitations for $τ = 50 fs$ . (d) The semiclassical current corresponding to (c) for various OAM excitations.
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Figure 4
(a) We plot the average current as a function of disorder strength $γ$ with various bias voltages $V_{b} = 0$ , 10, 30 mV. Increasing $γ$ leads to a decrease in the average current. We apply a DC voltage bias $V_{b}$ across the sample to recover the current. We find a bias increases the average current. Here we use $ℓ = + 1, τ = 50 fs$ . (b) We plot the average current for $OAM = + 1, τ = 50 fs$ as a function of total number of orbitals (system size) considered in the simulation. The average current stays constant. (c) We plot the simulated current $I$ as a function of pump intensity on log-log scales and compare with the reference current $I_{r}$ multiplied by a constant 0.21 (orange line). (d) We plot the simulated $I$ as a function of average relaxation rate $Γ = 1 / τ$ on log-log scales and compare with the reference current $I_{r}$ multiplied by a constant 0.22 (orange line). The simulated results' scalings match very well with the analytical predictions.
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