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The possibility of superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is studied. Quadratic coupling of electrons with out-of-plane phonons is considered in details, taking into account both deformation potential and bond-stretch contributions. The order parameter of electron-electron pairing can have different structures due to four-component spinor character of electrons wave function. We consider s-wave pairing, diagonal on conduction and valence bands, but having arbitrary structure with respect to valley degree of freedom. The sign and magnitude of contribution of each phonon mode to effective electron-electron interaction turns out to depend on both the symmetry of phonon mode and the structure of the order parameter. Unconventional orbital-spin symmetry of the order parameter is found.
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The photoresponse of graphene at mid-infrared frequencies is of high technological interest and is governed by fundamentally different underlying physics than the photoresponse at visible frequencies, as the energy of the photons and substrate phonons involved have comparable energies. Here we perform a spectrally resolved study of the graphene photoresponse for mid-infrared light by measuring spatially resolved photocurrent over a broad frequency range (1000-1600 cm$^{-1}$). We unveil the different mechanisms that give rise to photocurrent generation in graphene on a polar substrate. In particular, we find an enhancement of the photoresponse when the light excites bulk or surface phonons of the SiO$_2$ substrate. This work paves the way for the development of graphene-based mid-infrared thermal sensing technology.
We consider ground state of electron-hole graphene bilayer composed of two independently doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only conduction band of electron-doped layer and valence band of hole-doped layer, thus the ground state is similar to ordinary BCS condensate. At strong coupling, an ultrarelativistic character of electron dynamics reveals and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. The analysis of instability of unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. A relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of separable potential. It is shown that, if characteristic width of the pairing region is of the order of magnitude of chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However, if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.
Conduction between graphene layers is suppressed by momentum conservation whenever the layer stacking has a rotation. Here we show that phonon scattering plays a crucial role in facilitating interlayer conduction. The resulting dependence on orientation is radically different than previously expected, and far more favorable for device applications. At low temperatures, we predict diode-like current-voltage characteristics due to a phonon bottleneck. Simple scaling relationships give a good description of the conductance as a function of temperature, doping, rotation angle, and bias voltage, reflecting the dominant role of the interlayer beating phonon mode.
The superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is considered. It is shown that the structure of the order parameter in the valley space substantially affects conditions of the pairing. Electron-hole pairing in graphene bilayer in the strong coupling regime is also considered. Taking into account retardation of the screened Coulomb pairing potential shows a significant competition between the electron-hole direct attraction and their repulsion due to virtual plasmons and single-particle excitations.
Vertical heterostructures combining different layered materials offer novel opportunities for applications and fundamental studies of collective behavior driven by inter-layer Coulomb coupling. Here we report heterostructures comprising a single-layer (or bilayer) graphene carrying a fluid of massless (massive) chiral carriers, and a quantum well created in GaAs 31.5 nm below the surface, supporting a high-mobility two-dimensional electron gas. These are a new class of double-layer devices composed of spatially-separated electron and hole fluids. We find that the Coulomb drag resistivity significantly increases for temperatures below 5-10 K, following a logarithmic law. This anomalous behavior is a signature of the onset of strong inter-layer correlations, compatible with the formation of a condensate of permanent excitons. The ability to induce strongly-correlated electron-hole states paves the way for the realization of coherent circuits with minimal dissipation and nanodevices including analog-to-digital converters and topologically protected quantum bits.
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