Superconductivity and other collective phenomena in a hybrid Bose-Fermi mixture formed by a polariton condensate and an electron system in two dimensions

Ovidiu Cotleţ, Sina Zeytinoǧlu, Manfred Sigrist, Eugene Demler, and Ataç Imamoǧlu

Phys. Rev. B 93, 054510 – Published 9 February 2016

Abstract

Interacting Bose-Fermi systems play a central role in condensed matter physics. Here, we analyze a novel Bose-Fermi mixture formed by a cavity exciton-polariton condensate interacting with a two-dimensional electron system. We show that that previous predictions of superconductivity [F. P. Laussy, Phys. Rev. Lett. 104, 106402 (2010)] and excitonic supersolid formation [I. A. Shelykh, Phys. Rev. Lett. 105, 140402 (2010)] in this system are closely intertwined, resembling the predictions for strongly correlated electron systems such as high-temperature superconductors. In stark contrast to a large majority of Bose-Fermi systems analyzed in solids and ultracold atomic gases, the renormalized interaction between the polaritons and electrons in our system is long-ranged and strongly peaked at a tunable wave vector, which can be rendered incommensurate with the Fermi momentum. We analyze the prospects for experimental observation of superconductivity and find that critical temperatures on the order of a few kelvins can be achieved in heterostructures consisting of transition metal dichalcogenide monolayers that are embedded in an open cavity structure. All-optical control of superconductivity in semiconductor heterostructures could enable the realization of new device concepts compatible with semiconductor nanotechnology. In addition the possibility to interface quantum Hall physics, superconductivity, and nonequilibrium polariton condensates is likely to provide fertile ground for investigation of completely new physical phenomena.

Received 8 October 2015
Revised 15 January 2016

DOI:https://doi.org/10.1103/PhysRevB.93.054510

Physics Subject Headings (PhySH)

Bose-Einstein condensates Bose-Fermi mixtures Charge density waves Exciton polariton

Supersolids Two-dimensional electron gas

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ovidiu Cotleţ^1,*, Sina Zeytinoǧlu^1,2, Manfred Sigrist², Eugene Demler³, and Ataç Imamoǧlu¹

¹Institute of Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
²Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
³Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA

^*ocotlet@phys.ethz.ch

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Issue

Vol. 93, Iss. 5 — 1 February 2016

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Images

Figure 1
Upper panel: The schematic of the semiconductor heterostructure that is analyzed. The pumping laser that induces and sustains the BEC in the lower QW is not shown in the schematic in order not to complicate the figure. Lower panel: Bare polariton (blue) and electron (red) dispersion in logarithmic scale. The vertical dashed lines are at the photon wave vector $k_{p h} = 3.3 E_{c} (0) / (ℏ c)$ (corresponding to the maximal momenta that we can investigate optically; the $3.3$ factor comes from the GaAs index of refraction) and at $k_{p h} / 10$ (roughly corresponding to the momentum where the polariton dispersion switches from photonic to excitonic). The parameters used are typical GaAs parameters: $g_{0} = 2 meV, m_{e} = 0.063 m_{0}, m_{h} = 0.046 m_{0}, n_{e} = 2 \times 10^{11} {cm}^{- 2}, E_{c} (0) = E_{x} (0) = 1.518 eV$ .
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Figure 2
Upper panel: Bare polariton dispersion (blue) versus renormalized polariton dispersion (red). Lower panel: Screened electron-polariton matrix element $M (q) = \sqrt{N_{0}} V_{X} (k) / ε (k)$ (blue) versus screened and renormalized electron-polariton matrix element $\tilde{M} (q)$ (red). The parameters used for the solid lines are typical GaAs parameters: $d = a_{B} = 10 nm, L = 20 nm, g_{0} = 2 meV, ε = 13 ε_{0}, m_{e} = 0.063 m_{0}, m_{h} = 0.046 m_{0}, n_{e} = 2 \times 10^{11} {cm}^{- 2}, U = 0.209 μ eV μ m^{2}, n_{0} = 4 \times 10^{11} {cm}^{- 2}$ . The parameters used for the dashed lines are the same as for the solid lines except for $L^{'} = 1.5 L$ and $n_{0}^{'} = 2 n_{0}$ . The quantization area is taken to be $1 μ m^{2}$ .
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Figure 3
Upper-left panel: Critical temperature (solid purple line) for a typical TMD monolayer as a function of polariton density $n_{0}$ . The dashed green line is at the critical polariton density $n_{c} = 2.169 \times 10^{13} {cm}^{- 2}$ and can be regarded as dividing the BEC (blue region) and supersolid (green region) phases of the polaritons. Upper-right panel: The polariton spectral function at the roton minimum $B (q_{r}, ω)$ . Lower-left panel: Polariton dispersion renormalization (in purple is the bare dispersion). Lower-right panel: $λ_{q}$ . The different colors of the lines in the upper-right, lower-left, and lower-right panels correspond to different values of $n_{0}$ denoted by the colored dots in the upper-left panel. Expressed in percentages of $n_{c}$ these are $n_{0} = 100 % n_{c}$ (blue), $n_{0} = 99.7 % n_{c}$ (green), $n_{0} = 99.3 % n_{c}$ (red), $n_{0} = 98.8 % n_{c}$ (black).The rest of the parameters are typical TMD monolayer parameters: $d = a_{B} = 1 nm, L = 1.5 a_{B} = 1.5 nm, g_{0} = 10 \sqrt{4} meV$ (4 exciton layers are used), $ε = 4 ε_{0}, m_{e} = m_{h} = 0.2 m_{0}, n_{e} = 10^{13} {cm}^{- 2}, U = 0.12 μ eV μ m^{2}$ .
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Figure 4
First vertex correction diagram. In blue are the electron propagators while in red are the polariton propagators.
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Figure 5
The total interaction $\tilde{V} (r)$ (blue) compared to the screened Coulomb repulsion ${\tilde{V}}_{C} (r)$ (green) for the parameters used in Fig. 3 with $n_{0} = n_{c}$ .
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Figure 6
Comparison between $V^{F} (ɛ)$ (blue), $V^{B C S} (ɛ)$ (red), and $V^{S} (ɛ)$ (green). For the BCS potential we choose $ω_{D} = g_{0}$ . For simulations we used typical GaAs parameters, the same parameters used for the solid lines in Fig. 2.
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