Density of states in randomly shaped graphene quantum dots

By numerical diagonalization of honeycomb-lattice tight-binding Hamiltonian we calculate the density of state (DOS) of irregularly shaped graphene quantum dots fabricated in the form of graphene nano-flakes. The finite-size electron confinement and the edge states result in the central peak of DOS that is located at the zero-energy Dirac point. The amplitude and width of the peak are provided by the form of the graphene cluster, but no regular correlation with its shape was found.     

Broken-symmetry states of Dirac fermions in graphene with a partially filled high Landau level

We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wave vectors +/-q*. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, which suggests an instability toward a charge density wave. A symmetry broken stripe phase is formed at large system size limit, which is robust against perturbation from disorder scattering. Such a quantum phase is experimentally observable through transport measurements. Associated with the special wave functions of the Dirac LL, both stripe and bubble phases become possible candidates for the ground state of the Dirac fermions in graphene with lower filling factors in the N=3 LL.     

Echoes of relativistic Landau levels in graphene and bilayer graphene

The problem of echo effects that can originate in graphene and bilayer graphene upon the generation of relativistic Landau levels in a quantizing magnetic field is considered. Graphene (bilayer graphene) is considered in a long-wave approximation near the Dirac points. It is proposed that the echo effect be used for the quantum memory of optical states in the far infrared.     

Landau damping and inhomogeneous reference states

Landau damping is a fundamental phenomenon in plasma physics, which also plays an important role in astrophysics, and sometimes under different names, in fluid dynamics, and other fields. Its theoretical discussion in the framework of the Vlasov equation often assumes that the reference stationary state is homogeneous in space. However, Landau damping around an inhomogeneous reference stationary state, a natural setting in astrophysics for instance, induces new mathematical difficulties and physical phenomena. The goal of this article is to provide an introduction to these problems and the questions they raise.     

Effect of a nonuniform magnetic field on the Landau states in a biased AA-stacked graphene bilayer

We study the Landau states in the biased AA-stacked graphene bilayer under an exponentially decaying magnetic field along one spatial dimension. The results show that the energy eigenvalues of the system are strongly dependent on the inhomogeneity of the magnetic field and the bias voltage between the graphene layers, and in particular the reordering and mixing of finite Landau states could occur. Moreover, we also demonstrate that the current carrying states induced by the decaying magnetic field propagate vertically to the magnetic-field gradient within the graphene sample and can be further modulated by the bias voltage between the layers.     

Infrared spectroscopy of Landau levels of graphene

We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.     

Density of states in the bilayer graphene with the excitonic pairing interaction

In the present paper, we consider the excitonic effects on the single particle normal density of states (DOS) in the bilayer graphene (BLG). The local interlayer Coulomb interaction is considered between the particles on the non-equivalent sublattice sites in different layers of the BLG. We show the presence of the excitonic shift of the neutrality point, even for the noninteracting layers. Furthermore, for the interacting layers, a very large asymmetry in the DOS structure is shown between the particle and hole channels. At the large values of the interlayer hopping amplitude, a large number of DOS at the Dirac’s point indicates the existence of the strong excitonic coherence effects between the layers in the BLG and the enhancement of the excitonic condensation. We have found different competing orders in the interacting BLG. Particularly, a phase transition from the hybridized excitonic insulator phase to the coherent condensate state is shown at the small values of the local interlayer Coulomb interaction.     

Collapse of Landau levels in gated graphene structures

We describe a new regime of magnetotransport in two-dimensional electron systems in the presence of a narrow potential barrier. In such systems, the Landau level states, which are confined to the barrier region in strong magnetic fields, undergo a deconfinement transition as the field is lowered. Transport measurements on a top-gated graphene device are presented. Shubnikov-de Haas (SdH) oscillations, observed in the unipolar regime, are found to abruptly disappear when the strength of the magnetic field is reduced below a certain critical value. This behavior is explained by a semiclassical analysis of the transformation of closed cyclotron orbits into open, deconfined trajectories.     

Quantum capacitance of the armchair-edge graphene nanoribbon

The quantum capacitance, an important parameter in the design of nanoscale devices, is derived for armchair-edge single-layer graphene nanoribbon with semiconducting property. The quantum capacitance oscillations are found and these capacitance oscillations originate from the lateral quantum confinement in graphene nanoribbon. Detailed studies of the capacitance oscillations demonstrate that the local channel electrostatic potential at the capacitance peak, the height and the number of the capacitance peak strongly depend on the width, especially a few nanometres, of the armchair-edge graphene nanoribbon. It implies that the capacitance oscillations observed in the experiments can be utilized to measure the width of graphene nanoribbon. The results also show that the capacitance oscillations are not seen when the width is larger than 30 nm.     

Dissipation and criticality in the lowest Landau level of graphene

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance sigma_{xy} and the longitudinal conductance sigma_{xx} are computed. We demonstrate that bond disorder can produce a plateaulike feature centered at nu=0, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between +/-E_{c}, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be 2.47+/-0.04. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between approximately 1.0 and approximately 7/3.     

Spectral singularities and zero energy bound states

Single particle scattering around zero energy is re-analysed in view of recent experiments with ultra-cold atoms, nano-structures and nuclei far from the stability valley. For non-zero orbital angular momentum the low energy scattering cross section exhibits dramatic changes depending on the occurrence of either a near resonance or a bound state or the situation in between, that is a bound state at zero energy. Such state is singular in that it has an infinite scattering length, behaves for the eigenvalues but not for the eigenfunctions as an exceptional point and has no pole in the scattering function. These results should be observable whenever the interaction or scattering length can be controlled.     

Landau levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.     

Electric- and magnetic-field-tuned Landau levels and Hall conductivity in AA-stacked bilayer graphene

We theoretically study the combined effect of magnetic and electric fields on the Landau levels and Hall conductivity in AA-stacked bilayer graphene. From the analytic expressions derived, we obtain explicit criterions for determining the zero-energy Landau level and different level crossings in the graphene bilayer. For providing a scheme of experimental verification, we further explore the quantum Hall effect in such a biased bilayer. It is found that the zero-conductance Hall plateau in this system can vanish at certain specific combinations of magnetic and electric fields, accompanying with the occurrence of resonance Hall conductivity steps.     

Tunable quantum capacitance and magnetic oscillation in bilayer graphene device

We address the quantum capacitance of a bilayer graphene device in the presence of Rashba spin–orbit interaction (SOI) by applying external magnetic fields and interlayer biases. Quantum capacitance reflects the mixing of the spin-up and spin-down states of Landau levels and can be effectively modulated by the interlayer bias. The interplay between interlayer bias and Rashba SOI strongly affects magnetic oscillations. The typical beating pattern changes tuned by Rashba SOI strength, interlayer bias energy, and temperature are examined as well.     

Landau quantization and equatorial states on the surface of a nanosphere

The Landau quantization for the electron gas on the surface of a sphere is considered. It is shown that in the regime of strong fields the lowest energy states are those with magnetic quantum numbers m of order of Φ /Φ₀, the number of magnetic flux quanta piercing the sphere. For an electron gas of low density (semiconducting situation) it leads to the formation of an electronic stripe on the equator of the sphere in high fields. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 405–409 (25 September 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Superconducting states of pure and doped graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states; s wave and an exotic p+ip that is possible because of the special structure of the honeycomb lattice. At half filling, the p+ip phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.     

Josephson current through a quantum dot molecule with a Majorana zero mode and Andreev bound states

Based on the Green's function method, we investigate the interplay between Majorana zero mode (MZM) and Andreev bound states (ABSs) in a quantum dot molecule side coupled to a topological superconducting nanowire with a pair of MZMs forming a Josephson junction. Since the strong electron–hole asymmetry induced by the nanowire with a topologically non-trivial phase, the MZM suppress the ABSs. The suppression induced by the MZM is robust against the Coulomb repulsion. The interplay between the MZM and the ABSs in Josephson junction presents a feasible experimental means for distinguish between the presence of MZM and ABSs.     

非简谐振动对石墨烯量子电容和热稳定性的影响

采用固体物理理论和方法,研究了单层石墨烯的量子电容和它的温度稳定性随温度和电压的变化规律,探讨原子非简谐振动对它的影响.结果表明:(1)当电压一定时,单层石墨烯的量子电容和温度稳定性系数均随温度升高发生非线性变化,电压小于2.3 V时,量子电容随温度升高而增大,温度稳定性系数随温度升高由缓慢变化到很快增大,电压高于2.3 V时,量子电容随温度升高先增大后减小,而其温度稳定性系数随温度升高由缓慢变化到很快减小.温度一定时,量子电容只在电压值为0.4～2.8 V范围内才变化较小,而电压值大于2.8 V时,量子电容迅速减小并趋于0;(2)与简谐近似相比,非简谐项会使石墨烯量子电容有所增大,且温度愈高,两者的差愈大,非简谐效应愈显著,温度为300 K时,非简谐的量子电容要比简谐近似的值大0.33%,而温度为1 000 K时,差值增大到1.47%;(3)电压在1.5～1.8 V之间,而温度低于800 K时,石墨烯量子电容的温度稳定性系数最小且不随温度而变,储能性能的温度稳定性最好;(4)非简谐项会使它的量子电容热稳定性系数比简谐近似的值增大,且增大的情况与温度有关,当温度为400 K时量子电容热...     

不同N掺杂构型石墨烯的量子电容研究

超级电容器是一种利用界面双电层储能或在电极材料表面及近表面发生快速可逆氧化还原反应而储能的装置, 其特点是功率密度高、循环寿命长. 制备出兼有高能量密度的电极材料是当前超级电容器研究的重点. 以提高电容储能为目标, 通过掺杂N原子来调制石墨烯的电子结构, 使用基于密度泛函理论的第一原理计算了不同N掺杂构型石墨烯的态密度和能带结构, 拟合出了石墨烯的量子电容, 分析了量子电容储能提升的原因.