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A Tunable Phonon-Exciton Fano System in Bilayer Graphene

Interference between different possible paths lies at the heart of quantum physics. Such interference between coupled discrete and continuum states of a system can profoundly change its interaction with light as seen in Fano resonance. Here we present a unique many-body Fano system composed of a discrete phonon vibration and continuous electron-hole pair transitions in bilayer graphene. Mediated by the electron-phonon interactions, the excited state is described by new quanta of elementary excitations of hybrid phonon-exciton nature. Infrared absorption of the hybrid states exhibit characteristic Fano lineshapes with parameters renormalized by many-body interactions. Remarkably, the Fano resonance in bilayer graphene is continuously tunable through electrical gating. Further control of the phonon-exciton coupling may be achieved with an optical field exploiting the excited state infrared activity. This tunable phonon-exciton system also offers the intriguing possibility of a 'phonon laser' with stimulated phonon amplification generated by population inversion of band-edge electrons.

Interference between different possible paths lies at the heart of quantum physics. Such interference between coupled discrete and continuum states of a system can profoundly change its interaction with light as seen in Fano resonance 1,2 .
Here we present a unique many-body Fano system composed of a discrete phonon vibration and continuous electron-hole pair transitions in bilayer graphene 3 Two dimensional (2D) graphene exhibits remarkable electrical 3,4 , vibrational [8][9][10][11] , and optical properties [12][13][14][15][16] . Many of these properties can be modified in graphene through electrical gating, which enables control of the intricate interplay between electrons, phonons, and photons. Such control is exemplified in gated bilayer graphene structures, where an gating electrical field can modify phonon-light interactions by inducing infrared (IR) activity in an otherwise IR-inactive phonon vibration (Fig. 1a, b), as well as electron-light interactions by generating a tunable electronic bandgap 5,[16][17][18][19][20][21] (Fig. 1c, d). In this way electron-phonon interactions are also modified through the electronic structure and phonon dipole changes [9][10][11] . This tunable coupling between electrons, vibrations, and light offers exciting opportunities in exploring new physical phenomena. One example is the control of quantum interference between vibration-and electron-mediated optical absorption (Fig. 1e), which provides an unusual tunable Fano system involving three different elementary excitations: photon, exciton, and phonon.
A Fano resonance describes the quantum interference of optical absorption through coupled discrete and continuum transitions, where the excited eigenstates are mixtures of the discrete and continuum states 1,2 . It gives rise to a characteristic asymmetric lineshapes in absorption spectra 1 . First introduced to describe atomic photoionization 2 , the Fano lineshape has been observed ubiquitously in neutron scattering 22 , Raman scattering 23 , photoabsorption in quantum wells 24 , and electrical transport through nanostructures 25,26 .
However, a tunable Fano system characterized by interference between many-body excitations is difficult to achieve. Here bilayer graphene provides a unique many body system where Fano interference between coupled phonon and electron-hole pair excitations can be realized and controlled through electrical gating . Unlike the relatively  simple Fano resonances characterized by single-electron transitions in atoms and   quantum dots, the bilayer graphene Fano resonance describes a collective phonon   vibration coupled to a continuum of electron-hole excitations through electron-phonon interactions. Such coupling leads to new elementary excitations described by hybrid phonon-exciton states, in which the 'dressed' phonon component has a strongly renormalized center frequency, line width, and infrared activity due to the many-body interactions. This hybrid phonon-exciton excitation and the associated tunable Fano resonance in bilayer graphene can be continuously tuned through electrical gating and are described quantitatively using a tight-binding model. This microscopic understanding of the couplings between electron, phonon, and light in bilayer graphene can lead to novel applications exploiting the tunable bandgap of bilayer graphene.
In our studies, we used dual-gated bilayer graphene samples. Fig. 1f shows an optical microscopy image of a typical device. A pristine A-B stacked graphene bilayer has inversion symmetry, but an electrical field normal to the graphene plane breaks this symmetry and profoundly changes the graphene electronic and vibrational properties.
Electronically, bilayer graphene is intrinsically an undoped gapless semiconductor. A normal electrical field, however, induces a non-zero energy gap and charge carrier doping.
These two key parameters, electronic bandgap (Δ) and carrier doping concentration (n), can be controlled independently in a dual-gate graphene device. This is achieved by controlling both the top and bottom displacement fields D t and D b with the corresponding gates ( Fig. 1g) : the discontinuity of the displacement field ΔD=D b -D t determines the carrier doping concentration, while the average displacement field D = (D b +D t )/2 determines the tunable bandgap 16 (see supplementary information). For phonon vibrations, we focus on the symmetric G-mode phonon 6,11 (Fig. 1a). It carries zero dipole moment and is therefore infrared inactive in the pristine symmetric bilayer. A normal electric field, however, breaks the symmetry between the upper and lower layers, resulting in different charges on the carbon atoms at the A site of the bottom layer and the B site of the top layer (Fig. 1b). These atoms now appear like oppositely charged ions in a polar crystal and their vibrations become infrared active.
The field-induced electronic bandgap and phonon infrared activity lead to dramatic changes in graphene bilayer infrared absorption spectra.

Phenomenologically a Fano resonance absorption lineshape is described by
, where A e , q, E ! , ! are the fitting parameters (fits are shown in Fig. 2a as red traces). In the relatively narrow spectral range around the Fano resonance, A e has been approximated as a constant. The Fano lineshape is seen to change dramatically when the energy gap Δ is increased, first as a weak absorption dip, then as a dispersive interference, and finally as an absorption peak. The critical parameter describing these lineshapes is q. In these spectra, q is negative and its magnitude increases by an order of magnitude as Δ increases. This increase of |q| can be qualitatively understood by noting that the phonon gains infrared activity from the field-induced symmetry breaking and its dipole moment increases monotonically with the field strength. At the same time electronic transitions at E E ! = get weaker with increasing field strength once the gap energy is larger than E ! .
Instead of varying the electronic bandgap, we can also modify the Fano resonance infrared absorption by changing the carrier concentration. This is achieved experimentally by fixing the bottom gate voltage and sweeping the top gate voltage. In such measurements, the bandgap also changes slightly, but the dominant effects are from carrier doping. Fig. 2b shows Fano absorption spectra (with the broad electronic absorption background subtracted) at different carrier concentrations. We observe that electron doping can also lead to a continuous change from a dip to a peak in the absorption spectrum around the phonon energy. In this case, the increase in |q| is mainly due to a reduction of electronic transition strength from Pauli blocking: with the increase of the electron density, the Fermi energy shifts up and the electronic transitions at E ! become forbidden when the final states for such transitions are already filled.
The detailed dependence of Fano resonance parameters on electrical gating reveals not only the changes of electron and phonon optical dipole strengths contained in A e and q, but also the renormalization of the 'dressed' phonon vibration frequency E ! and broadening ! . Displayed in Fig. 3a- We show in Fig. 3

Methods
The fabrication procedure for creating the dual-gate devices was described in Ref. 16 .
Briefly, bilayer graphene was connected to 20nm thick Au source and drain electrodes. The authors declare no competing financial interests.  This phonon softening also arises from stronger coupling to electronic transitions with energy larger than Δ. (d) Phonon linewidth is broadened by the electron-phonon coupling.
The linewidth reaches a maximum at Δ=E Ω when the electron-phonon interactions are the strongest.
Supplementary Material:

Determine the gate induced bandgap and carrier concentration.
The field induced bandgap and carrier concentration in bilayer graphene are independently varied by controlling the both the top and bottom displacement electrical fields D t and D b with the corresponding gates. The relation between the displacement electrical field and gate voltages is described by where the top gate dielectric layer has a dielectric constant ε t = 7.

Detailed calculations of the many body Fano system in bilayer graphene.
We will focus on the tunable Fano resonance in bilayer graphene at different induced bandgap but with zero carrier doping. The Hamiltonian describing low energy excitations in this many body system with one dominant active phonon mode is where the elementary excitations are described by the phonon creation operator a + and electron-hole pair creation operator  (Fig. 1a in the main text) couples to electron-hole excitations when n ≈ 0 (due to electron-hole symmetry) and needs to be considered in our Fano system 6 .
Since there is only one phonon which is relevant in the problem, to deal with the large