双层石墨烯材料中无序导致超导-绝缘体相变的数值研究

本文利用一种新的数值方法研究了在较大的双层石墨烯样品中杂质的无序 效应对超导态特性的影响. 采用核多项式方法 (Kernel Polynomial Method) 来自洽求解双层石墨烯系统的Bogoliubov-de-Gennes (BdG) 方程, 从而得到了由无序效应所引起的超导序参量的空间涨落精确解. 进一步, 计算了系统处于超导态时的态密度、光电导和广义逆参与率 (inverse participation ratio) 等物理量, 并发现随着无序强度的不断增大态密度中的能隙被 完全抑制, 同时光电导的Drude权重也迅速减小并最终降为零, 这表明双层石墨烯中的低能电子态发生了安德森局域化, 系统因而发生了由无序效应诱导的超导-绝缘体相变. 关键词： 双层石墨烯 安德森局域化 超导-绝缘体相变 核多项式方法     

Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.     

Effect of Holstein phonons on the optical conductivity of gapped graphene

We study the optical conductivity of a doped graphene when a sublattice symmetry breaking is occurred in the presence of the electron-phonon interaction. Our study is based on the Kubo formula that is established upon the retarded self-energy. We report new features of both the real and imaginary parts of the quasiparticle self-energy in the presence of a gap opening. We find an analytical expression for the renormalized Fermi velocity of massive Dirac Fermions over broad ranges of electron densities, gap values and the electron-phonon coupling constants. Finally we conclude that the inclusion of the renormalized Fermi energy and the band gap effects are indeed crucial to get reasonable feature for the optical conductivity.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

Charge and spin Hall conductivity in metallic graphene

Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity sigma(xy)(SH). In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to sigma(xy)(SH) values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.     

Angular position of nodes in the superconducting gap of quasi-2D heavy-fermion superconductor CeCoIn5

The thermal conductivity of the heavy-fermion superconductor CeCoIn5 has been studied in a magnetic field rotating within the 2D planes. A clear fourfold symmetry of the thermal conductivity which is characteristic of a superconducting gap with nodes along the ( +/- pi,+/- pi) directions is resolved. The thermal conductivity measurement also reveals a first-order transition at H(c2), indicating a Pauli limited superconducting state. These results indicate that the symmetry most likely belongs to d(x(2)-y(2)), implying that the anisotropic antiferromagnetic fluctuation is relevant to the superconductivity.     

Metal insulator transition in modulated quantum Hall systems

The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where the states are extended are identified. We find that the critical energies, which are distributed to each of the subbands, combine into one when the disorder becomes strong, in the way depending on the symmetry of the disorder and/or the periodic potential.     

A generalized RPA theory of the nuclear response function

A new method of calculating the response function is proposed. The new method gives the response which is explicitly a generalization of the RPA response in a perturbative sense.When we calculate the transition amplitude of a one-body operator from the ground state to a particle-hole (p-h) state, the new response function provides all the second-order effects in addition to the first-order ones which can be obtained in the RPA theory. The new response function is obtained by the following procedure. Firstly, we consider the second RPA theory which is a generalization of the usual RPA theory. It is found that the second RPA misses some of the second-order effects. Secondly, we formulate a modified second RPA equation from the equation of motion of the operators, and then derive the p-h response function from it. It is found that the newly derived p-h response function is obtained by adding new terms to the self-energy of the p-h response function derived from the second RPA theory. Lastly, we introducd vertex functions which take into account the transitions from a particle (hole) state to a particle (hole) state. Note that the p-h response function deals with only the transition amplitudes from a particle (hole) state to a hole (particle) state.     

Impurity Effects at Surfaces of a Photon-Dressed Bi_2Se_3 Thin Film

We investigate the impurity effects on surfaces of a thin film topological insulator, applied by an off-resonant circular polarized light. It is found that the off-resonant driving induces a quantized total Hall conductivity, when the driving strength is larger than a critical value and the Fermi level lies in the band gap, indicating that our system is converted into the topological phase. We also find that with the increasing disorder strength, the Dirac masses of top and bottom surfaces are renormalized and then fixed to half of their initial values, respectively,which will shrink the widths of the half-integer plateau of anomalous Hall conductivities.     

Conductivity of disordered graphene at half filling

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity 4e²/πh in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma-model including a topological term with θ=π. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e²/h. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.     

Polaronic conductivity in the photoinduced phase of 1T-TaS2

The transient optical conductivity of photoexcited 1T-TaS2 is determined over a three-order-of-magnitude frequency range. Prompt collapse and recovery of the Mott gap is observed. However, we find important differences between this transient metallic state and that seen across the thermally driven insulator-metal transition. Suppressed low-frequency conductivity, Fano phonon line shapes, and a midinfrared absorption band point to polaronic transport. This is explained by noting that the photoinduced metallic state of 1T-TaS2 is one in which the Mott gap is melted but the lattice retains its low-temperature symmetry, a regime only accessible by photodoping.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Line nodes in the superconducting gap function of noncentrosymmetric CePt3Si

The superconducting gap structure of recently discovered heavy fermion CePt(3)Si without spatial inversion symmetry was investigated by thermal transport measurements down to 40 mK. In zero field a residual T-linear term was clearly resolved as T --> 0, with a magnitude in good agreement with the value expected for a residual normal fluid with a nodal gap structure, together with a T2 dependence at high temperatures. With an applied magnetic field, the thermal conductivity grows rapidly, in dramatic contrast to fully gapped superconductors, and exhibits one-parameter scaling with T/sqrt[H]. These results place an important constraint on the order parameter symmetry; that is, CePt(3)Si is most likely to have line nodes.     

Novel anisotropy in the superconducting gap structure of Bi2Sr2CaCu2O(8+delta) probed by quasiparticle heat transport

Since the nature of pairing interactions is manifested in the superconducting gap symmetry, the exact gap structure, particularly any deviation from the simple d(x(2)-y(2)) symmetry, would help in elucidating the pairing mechanism in high- T(c) cuprates. Anisotropic heat transport measurement in Bi(2)Sr(2)CaCu(2)O(8+delta) reveals that the quasiparticle populations are different for the two nodal directions and thus the gap structure must be uniquely anisotropic, suggesting that pairing is governed by interactions with a rather complicated anisotropy. Intriguingly, it is found that the "plateau" in the magnetic-field dependence of the thermal conductivity is observed only in the b-axis transport.     

Inhomogeneous metallic phase in a disordered Mott insulator in two dimensions

We show that, with increasing randomness, the spectral gap in a 2D Mott-Hubbard insulator is destroyed first at a disorder V(c1), while antiferromagnetism persists up to a higher V(c2). Most unexpectedly, between V(c1) and V(c2) the system is metallic and is sandwiched between the Mott insulator below V(c1) and the Anderson insulator above V(c2). The metal is formed when the spectral gap gets destroyed locally in regions where the disorder potential is high enough to overcome the interelectron repulsion. This generates puddles with enhanced charge fluctuations that percolate with increasing disorder, resulting in a spatially inhomogeneous metallic phase.     

Gap opening in single-layer graphene in the presence of periodic scalar and vector potentials within the continuum model

Gap opening at the Dirac point of the single-layer graphene with periodic scalar and vector potentials has been theoretically investigated under the continuum model. The symmetry analysis indicates that the two-fold degeneracy at the Dirac point can be lifted when the potentials break both the chiral symmetry and the time-reversal symmetry. With the perturbation theory, we derive an analytical expression (gap equation) for gap opening at the Dirac point. Furthermore, the bandgap from the gap equation agrees well with the exact result, when the applied potentials are weak.     

Thermoelectric power of mixed electronic-ionic conductors II. Case of titanium dioxide

The purpose of the present work is the determination of the thermopower components corresponding to different charge carriers (electrons, electron holes and ions) for TiO₂ and the use of these data for evaluation of the effect of symmetry between these two properties. The procedure of the determination of these components was based on the following two approximations:

The first approximation is based on a symmetrical model assuming a consistency between thermopower and electrical conductivity within the n-p transition (minimum of electronic component of the electrical conductivity corresponds to zero value of the electronic component of thermopower).

The second approximation is based on the apparent asymmetry between thermopower and electrical conductivity within the n-p transition as determined from the first approximation.

The analysis, based on the data of the electronic components of thermopower and electrical conductivity for TiO₂ single crystal, results in the band gap (using the Jonker formalism). The determined band gap is equal to 2.77 eV and 2.57 eV at the first and the second approximations, respectively, while the band gap determined from the experimentally measured data is equal 3.35 eV. These values are consistent with the band gap determined from the data of electrical conductivity corresponding to the n-p transition point (E_g=3.16 eV) and for the data measured experimentally and those free of the ionic conductivity component (E_g=2.79 eV). The obtained results indicate that thermopower and electrical conductivity most likely exhibit the effect of symmetry.     

准一维多链无序体系跳跃电导特性

在单电子紧束缚近似下,建立了准一维多链无序体系直流、交流电子跳跃输运模型,通过计算探讨了无序模式、维度效应、温度及外场对其直流、交流电导率的影响.计算结果表明:准一维多链无序体系的直流、交流电导率随着格点能量无序度的增大而减小,非对角无序具有增强体系电子输运能力的作用.随着链数的增加,体系的直流、交流电导率增大,但格点能量无序度较小时,维度效应的影响不明显.在对角无序情况下准一维多链无序体系的交流电导率随温度的升高而增大,而在非对角无序模式下却随温度的升高而减小,但对于直流情况,体系的直流电导率随温度的升     

Optical conductivity of single-layer graphene induced by temporal mass-gap fluctuations

We consider the dynamics of charge carriers in single-layer graphene that are subject to random temporal fluctuations of their mass gap. The optical conductivity is calculated by incorporating the quantum-stochastic time evolution into the standard linear-response (Kubo) theory. We find that, for an intermediate range of frequencies below the average gap size, electron transport is enhanced by fluctuations. At the same time, in the limit of high as well as low frequencies, the conductivity is suppressed as the variance of gap fluctuations increases. In particular, the dc conductivity is always suppressed by a random temporal mass with nonvanishing mean value and vanishes in the zero-temperature limit. Our results are complementary to those obtained recently for static random-gap disorder in finite-size systems.     

Twofold spontaneous symmetry breaking in the heavy-fermion superconductor UPt3

The field-orientation dependent thermal conductivity of the heavy-fermion superconductor UPt3 was measured down to very low temperatures and under magnetic fields throughout the distinct superconducting phases: B and C phases. In the C phase, a striking twofold oscillation of the thermal conductivity within the basal plane is resolved reflecting the superconducting gap structure with a line of node along the a axis. Moreover, we find an abrupt vanishing of the oscillation across a transition to the B phase, as a clear indication of a change of gap symmetries. We also identify extra two line nodes below and above the equator in both B and C phases. From these results together with the symmetry consideration, the gap function of UPt3 is determined as a E(1u) representation characterized by a combination of two line nodes at the tropics and point nodes at the poles.