Spontaneous parity breaking of graphene in the Quantum Hall regime

We propose that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic-field-dependent Peierls distortion. This leads to valley splitting of the n=0 Landau level but not of the other Landau levels. Compared to Quantum Hall valley ferromagnetism recently discussed in the literature, lattice distortion provides an alternative explanation to all of the currently observed Quantum Hall plateaus in graphene.     

磁场中的拓扑绝缘体边缘态性质

用数值方法研究了拓扑绝缘体薄膜体系在外加垂直磁场 作用下其边缘态的性质. 磁场的加入通过耦合k+eA, 即Peierls势替换关系和 该作用导致的Zeeman交换场体现在哈密顿量中. 考虑窄条圆环状结构的二维InAs/GaSb/AlSb薄膜量子阱材料, 当其处于拓扑非平庸状态, 即量子自旋霍尔态时, 会出现受时间反演对称性保护的两支简并边缘态, 而在垂直磁场的作用下, 时间反演对称性被破坏, 这时能带将形成一条条的朗道能级, 原来简并的两支边缘态也会分开到朗道能级谱线的两侧, 从电子态密度的空间分布情况则可以看到边缘态分别局域在材料的两个边界. 随着磁场的增大, 位于同一边界上的不同 自旋极化的边缘态将出现分离: 一支仍然局域在边缘, 另一支则随外加磁场的增加而有逐渐演化到材料内部的趋势. 文中还计算了同一边界上的两支边缘态之间的散射, 结果表明由于两个边缘态在空间发生分离, 相互之间的散射被很大的压制, 得到了其散射随磁场增加没有明显变化的结论, 所以磁场并不会增强散射过程, 也没有破坏体拓扑材料的性质, 说明了量子自旋霍尔态在没有时间反演对称的情况下也可以有较强的稳定性.     

Magnetoresistance measurements of graphene at the charge neutrality point

We report on transport measurements of the insulating state that forms at the charge neutrality point of graphene in a magnetic field. Using both conventional two-terminal measurements, sensitive to bulk and edge conductance, and Corbino measurements, sensitive only to the bulk conductance, we observed a vanishing conductance with increasing magnetic fields. By examining the resistance changes of this insulating state with varying perpendicular and in-plane fields, we probe the spin-active components of the excitations in total fields of up to 45?T. Our results indicate that the ν=0 quantum Hall state in single layer graphene is not spin-polarized.     

Spontaneous quantum Hall states in chirally stacked few-layer graphene systems

Chirally stacked N-layer graphene systems with N≥2 exhibit a variety of distinct broken symmetry states in which charge density contributions from different spins and valleys are spontaneously transferred between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We argue that valley Hall states have [N/2] edge channels per spin valley.     

Stable Pfaffian state in bilayer graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.     

Electronic states on the surface of graphite

Graphite consists of graphene layers in an AB (Bernal) stacking arrangement. The introduction of defects can reduce the coupling between the top graphene layers and the bulk crystal producing new electronic states that reflect the degree of coupling. We employ low temperature high magnetic field scanning tunneling microscopy (STM) and spectroscopy (STS) to access these states and study their evolution with the degree of coupling. STS in magnetic field directly probes the dimensionality of electronic states. Thus two-dimensional states produce a discrete series of Landau levels while three-dimensional states form Landau bands providing a clear distinction between completely decoupled top layers and ones that are coupled to the substrate. We show that the completely decoupled layers are characterized by a single sequence of Landau levels with square-root dependence on field and level index indicative of massless Dirac fermions. In contrast weakly coupled bilayers produce special sequences reflecting the degree of coupling, and multilayers produce sequences reflecting the coexistence of massless and massive Dirac fermions. In addition we show that the graphite surface is soft and that an STM tip can be quite invasive when brought too close to the surface and that there is a characteristic tip-sample distance beyond which the effect of sample-tip interaction is negligible.     

Observation of broken time-reversal symmetry with Andreev bound state tunneling spectroscopy

Quasiparticle (QP) planar tunneling spectroscopy is used to investigate the density of states (DoS) of YBa₂Cu₃O₇ (YBCO). Temperature, crystallographic orientation, doping, damage and magnetic field dependencies confirm that the observed zero-bias conductance peak (ZBCP) is an Andreev bound state (ABS), an intrinsic property of a d-wave superconducting order parameter (OP) at an interface. In zero applied field, the splitting of the ZBCP below 8 K confirms a near-surface phase transition into a superconducting state with spontaneously broken time-reversal symmetry (BTRS). Tunneling into the ABS provides a phase-sensitive spectroscopy that can be used to measure a variety of DoS properties in an unconventional superconductor.     

Local compressibility measurements of correlated states in suspended bilayer graphene

Bilayer graphene has attracted considerable interest due to the important role played by many-body effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors ν= ± 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zero-field ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of broken-symmetry states at ν=0, ± 1, and ± 2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.     

Band structure and transport property of graphene/h-BN heterostructure under local potentials

We investigate band structure and transport property of lattice-matched graphene/hexagonal boron nitride (h-BN) heterostructure using the tight-binding approach. It shows that local potentials can significantly modify the band structure and the transport property. A method to individually manipulate the edge states by local potentials is proposed, including shifts and other deformations of edge bands. The two-terminal conductance of each layer is quantized but the interlayer conductance is non-quantized due to band mixing. In addition, we explore the Landau level spectrum in graphene/h-BN nanoribbons under both magnetic field and local potentials. The plateaus-like behavior of the interlayer conductance is observed.     

Polar Kerr effect and time reversal symmetry breaking in bilayer graphene

The unique sensitivity of optical response to different types of symmetry breaking can be used to detect and identify spontaneously ordered many-body states in bilayer graphene. We predict a strong response at optical frequencies, sensitive to electronic phenomena at low energies, which arises because of nonzero interband matrix elements of the electric current operator. In particular, the polar Kerr rotation and reflection anisotropy provide fingerprints of the quantum anomalous Hall state and the nematic state, characterized by spontaneously broken time-reversal symmetry and lattice rotation symmetry, respectively. These optical signatures, which undergo a resonant enhancement in the near-infrared regime, lie well within reach of existing experimental techniques.     

Spin-polarized to valley-polarized transition in graphene bilayers at ν=0 in high magnetic fields

We investigate the transverse electric field (E) dependence of the ν=0 quantum Hall state (QHS) in dual-gated graphene bilayers in high magnetic fields. The longitudinal resistivity ρ(xx) measured at ν=0 shows an insulating behavior which is strongest in the vicinity of E=0, as well as at large E fields. At a fixed perpendicular magnetic field (B), the ν=0 QHS undergoes a transition as a function of the applied E, marked by a minimum, temperature-independent ρ(xx). This observation is explained by a transition from a spin-polarized ν=0 QHS at small E fields to a valley- (layer-)polarized ν=0 QHS at large E fields. The E field value at which the transition occurs follows a linear dependence on B.     

Asymmetric Tunneling Conductance and the Non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.     

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.     

Quantum Hall effect in twisted bilayer graphene

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.     

Exploring the electronic band structure of individual carbon nanotubes under 60 T

Nano-sciences, and in particular nano-physics, constitute a fascinating world of investigations where the experimental challenges are to synthesize, to address (for instance optically or electrically) to explore and promote the remarkable physical properties of new nano-materials. Somehow, one of the most promising realization of nano-sciences lies in carbon-based nano-materials with sp² covalent bonds. In particular, carbon nanotubes, graphene and more recently ultra-narrow graphene nano-ribbons are envisioned as elementary bricks of the future of nano-electronics. However, prior to such an achievement, the first steps consist in understanding their fundamental electronic properties when they constitute the drain–source channel of a gated device or inter-connexion elements. In this article, we present the richness of challenging experiments combining single-object measurements with an extreme magnetic environment. We demonstrate that an applied magnetic field (B), along with a control of the electrostatic doping, drastically modifies the electronic band structure of a carbon nanotube based transistor. Several examples will be addressed in this presentation. When B is applied parallel to the tube axis, a quantum flux threading the tube induces a giant Aharonov–Bohm conductance modulation mediated by Schottky barriers whose profile is magnetic field dependent. In the perpendicular configuration, the applied magnetic field breaks the revolution symmetry along the circumference and non-conventional Landau states develop in the high field regime. By playing with a carbon nanotube based electronic Fabry–Perot resonator, the field dependence of the resonant states of the cavity reveals the onset of the first Landau state at zero energy. These experiments enlighten the outstanding efficiency of magneto-conductance experiments to probe the electronic properties of carbon based nano-materials. To cite this article: S. Nanot et al., C. R. Physique 10 (2009).     

Universal quantized spin-Hall conductance fluctuation in graphene

We report theoretical investigations of the quantized spin-Hall conductance fluctuation of graphene in the presence of disorder. Two graphene models that exhibit the quantized spin-Hall effect (QSHE) are analyzed. Model I is with unitary symmetry under an external magnetic field B not = 0 but with a zero spin-orbit interaction, t(SO)=0. Model II is with symplectic symmetry where B=0 but t(SO) not = 0. The two models give exactly the same universal QSHE conductance fluctuation value 0.285+/-0.005e/4pi regardless of symmetry. We also examined a third model that exhibits QSHE but with quadratic dispersion and obtained the same results. Finally, all three models of QSHE have a one-sided log-normal distribution for spin-Hall conductance. Our results strongly suggest that the quantized spin-Hall conductance fluctuation belongs to a new universality class.     

Distinguishing spontaneous quantum Hall states in bilayer graphene

Chirally stacked N-layer graphene with N≥2 is susceptible to a variety of distinct broken symmetry states in which each spin-valley flavor spontaneously transfers charge between layers. In mean-field theory, one of the likely candidate ground states for a neutral bilayer is the layer antiferromagnet that has opposite spin polarizations in opposite layers. In this Letter, we analyze how the layer antiferromagnet and other competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using Zeeman responses and edge state signatures to identify the character of the bilayer ground state experimentally.     

Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene

We investigate electronic transport in dual-gated twisted-bilayer graphene. Despite the subnanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite interlayer screening and extract the capacitance between the atomically spaced layers. At zero filling factor, we observe an insulating state at large displacement fields, which can be explained by the presence of counterpropagating edge states with interlayer coupling.     

Observation of Spin and Valley Splitting of Landau Levels under Magnetic Tunneling in Graphene/Boron Nitride/Graphene Structures

Resonance magnetic tunneling in heterostructures formed by graphene single sheets separated by a hexagonal boron nitride barrier and bounded by two gates has been investigated in a strong magnetic field, which has allowed observing transitions between spin- and valley-split Landau levels with various indices belonging to different graphene sheets. An unexpected increase with the temperature in the interlayer tunneling conductance owing to transitions between the Landau levels in strong magnetic fields cannot be explained by existing theories.     

Magnetoconductance oscillations and evidence for fractional quantum Hall states in suspended bilayer and trilayer graphene

We report pronounced magnetoconductance oscillations observed on suspended bilayer and trilayer graphene devices with mobilities up to 270,000 cm2/V s. For bilayer devices, we observe conductance minima at all integer filling factors ν between 0 and -8, as well as a small plateau at ν=1/3. For trilayer devices, we observe features at ν=-1, -2, -3, and -4, and at ν～0.5 that persist to 4.5 K at B=8 T. All of these features persist for all accessible values of Vg and B, and could suggest the onset of symmetry breaking of the first few Landau levels and fractional quantum Hall states.