Thermal detection of single photons using Dirac fermions.

The content of this work is the study of electromagnetic interaction in single-layer graphene by means of the perturbation theory. The interaction of electromagnetic field with Dirac fermions in single-layer graphene has a peculiarity: Dirac fermions in graphene interact not only with the electromagnetic wave propagating within the graphene sheet, but also with electromagnetic field propagating from a location outside the graphene sheet and illuminating this sheet. The interaction Hamiltonian of the system comprising electromagnetic field and Dirac fermions fields contains the limits at graphene plane of electromagnetic field vector and scalar potentials which can be shortly called boundary electromagnetic field. The study of S-matrix requires knowing the limits at graphene plane of 2-point Green functions of electromagnetic field which also can be shortly called boundary 2-point Green functions of electromagnetic field. As the first example of the application of perturbation theory, the second order terms in the perturbative expansions of boundary 2-point Green functions of electromagnetic field as well as of 2-point Green functions of Dirac fermion fields are explicitly derived. Further extension of the application of perturbation theory is also discussed.

We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies $\omega_1$ and $\omega_2=r \omega_1$. We show that such drives may be used to tune towards dynamics induced freezing where the wavefunction of the state of the system after a drive cycle at time $T= 2\pi/\omega_1$ has almost perfect overlap with the initial state. We locate regions in the $(\omega_1 ,r)$ plane where the freezing is near exact for a class of integrable and a specific non-integrable model. The integrable models that we study encompass Ising and XY models in $d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a topological insulator surface whereas the non-integrable model studied involves the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of $(\omega_1,r)$ plane where the freezing is near-exact. We supplement our numerical analysis with semi-analytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.

After the discovery of Dirac fermions in graphene, it has become a natural question to ask whether it is possible to realize Dirac fermions in other two-dimensional (2D) materials as well. In this work, we report the discovery of multiple Dirac-like electronic bands in ultrathin Ge films grown on Au(1 1 1) by angle-resolved photoelectron spectroscopy. By tuning the thickness of the films, we are able to observe the evolution of their electronic structure when passing through the monolayer limit. Our discovery may signify the synthesis of germanene, a 2D honeycomb structure made of Ge, which is a promising platform for exploring exotic topological phenomena and enabling potential applications.

Effects of long-range correlated disorder on Dirac fermions in graphene

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $\phi^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $\phi^6$ potential, can significantly change the fate of the Landau pole in the $\phi^4$ theory. We obtain the coupled beta functions of a $\phi^4 + \phi^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $\phi^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $\phi^4$ theory, so graphene is free from Landau poles if the $\phi^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

Graphene plasmons, which are collective oscillations of Dirac fermions in graphene, are of broad interests in both fundamental research and technological applications. In this talk, we present the first nano-infrared (IR) imaging studies of graphene plasmons using the scattering-type scanning near-field optical microscopy—a unique technique allowing efficient excitation and high-resolution imaging of graphene plasmons. With this technique, we were able to show that common graphene/SiO 2 /Si back-gated structures support propagating surface plasmons in the IR frequencies. The observed plasmons are highly confined surface modes with a wavelength around 200nm that are conveniently tunable by the back gate voltages [1]. In addition, we were able to map and characterize grain boundaries inside CVD graphene film by examining the distinct plasmonic interference patterns triggered by these line defects. Our modeling and analysis unveiled unique electronic properties associated with grain boundaries [2]. Furthermore, we investigate the plasmonic properties of Bernal-stacking bilayer graphene (BLG) and find that BLG supports gate-tunable IR plasmons with higher confinement compared to graphene and randomly stacked graphene layers. We also found that BLG plasmons can be turned off completely in a wide voltage range close to the charge neutrality point. Those unique plasmonic properties are attributed to both interlayer electron tunneling and bandgap opening in BLG [3]. Finally, we observed peculiar one-dimensional edge plasmons propagating strictly along the edges of patterned graphene nanostructures. Compared to commonly known two-dimensional surface plasmons, these one-dimensional edge modes have shown a slightly smaller plasmon wavelength [4].

Spin splitting of Dirac fermions in graphene on Ni intercalated with alloy of Bi and Au

The charge carriers in graphene are massless Dirac fermions and exhibit a relativistic Landau-level quantization in a magnetic field. Recently, it has been reported that, without any external magnetic field, quantized energy levels have been also observed from strained graphene nanobubbles on a platinum surface, which were attributed to the Landau levels of massless Dirac fermions in graphene formed by a strain-induced pseudomagnetic field. Here we show the generation of the Landau levels of massless Dirac fermions on a partially potassium-intercalated graphite surface without applying external magnetic field. Landau levels of massless Dirac fermions indicate the graphene character in partially potassium-intercalated graphite. The generation of the Landau levels is ascribed to a vector potential induced by the perturbation of nearest-neighbour hopping, which may originate from a strain or a gradient of on-site potentials at the perimeters of potassium-free domains.

Two dimensional honeycomb ferromagnets host massless Dirac magnons which are a bosonic analogue of Dirac fermions in graphene. The Dirac magnons may become massive and topological when the time reversal symmetry breaks and an energy gap opens up at the Dirac point, which was experimentally observed in -based van der Waals magnets. Here, we investigate the spin wave excitations in the 3d magnetic oxide with electrons (). Using inelastic neutron scattering, we observe two magnon bands separated by a 1.2-meV gap at the Dirac points indicating that its Dirac magnons are massive. Using the linear spin-wave and density functional theory calculations, we find that the spin-orbit-coupled antisymmetric Dzyaloshinskii-Moriya exchanges can best account for the observed Dirac gap opening. The associated Berry curvature and Chern number () indicate that hosts topological spin excitations via time-reversal symmetry breaking of Dirac magnons.

In this paper, we develop a new approach for analyzing collective quantum excitations in graphene, based on the quantum multistream model. We explore a range of phenomena, including the energy band structure of collective modes, linear and nonlinear excitations, statistical characteristics, and the linear dielectric response of quasiparticle excitations in graphene. A modified Wigner quasiprobability distribution is derived, enabling the study of phase-space dynamics for linear excitations. Our results reveal that quasiparticle excitations of massless Dirac fermions are governed by three distinct characteristic wavenumbers. Notably, we identify a broad energy bandgap associated with the collective effects, below which quasiparticle excitations become unstable. The thermodynamic analysis, encompassing internal pressure and heat capacity, uncovers several intriguing deviations from the behavior of a conventional Fermi electron gas. Furthermore, we demonstrate that massless Dirac fermions in graphene can sustain both large-amplitude cnoidal waves and solitary structures. By examining the dielectric response within the Lindhard framework, incorporating a quasiparticle energy dispersion that accounts for both single-particle and wave-like contributions, we gain new insights into the frequency-dependent response, loss-function spectrum, and static charge screening, highlighting key differences from the ordinary Fermi gas. This theory offers a unified approach to capturing both the particle-like and wave-like aspects of massless Dirac Fermion excitations, clearly distinguishing their individual contributions to various physical properties. It also extends beyond the conventional many-body theories incorporating the mean field approximations by appropriately linking the single-electron dynamics to collective behavior through the hybrid nature of quasiparticle matter-wave dispersion.

We investigate near-degenerate four-wave mixing in graphene using femtosecond laser pulse shaping microscopy. Intense near-degenerate four-wave mixing signals on either side of the exciting laser spectrum are controlled by amplitude and phase shaping. Quantitative signal modeling for the input pulse parameters shows a spectrally flat phase response of the near-degenerate four-wave mixing due to the linear dispersion of the massless Dirac Fermions in graphene. Exploiting these properties we demonstrate that graphene is uniquely suited for the intrafocus phase characterization and compression of broadband laser pulses, circumventing disadvantages of common methods utilizing second or third harmonic light.

We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.

Quantum transport of Dirac fermions in graphene with a spatially varying Rashba spin–orbit coupling

A theory of electron states for graphene nanoribbons with a smoothly varying width is developed. It is demonstrated that the standard adiabatic approximation allowing to neglect the mixing of different standing waves is more restrictive for the massless Dirac fermions in graphene than for the conventional electron gas. For the case of zigzag boundary conditions, one can expect a well-pronounced conductance quantization only for highly excited states. This difference is related to the relativistic Zitterbewegung effect in graphene.

Kohn anomaly by massive Dirac fermions in graphene