Valley Symmetry Research Articles

Adiabatic quantum pumping in graphene with magnetic barriers

We study an adiabatic quantum pump effect in a two terminal graphene device with two oscillating square electric barriers and a stationary magnetic barrier using the scattering matrix approach. The model employs the low-energy Dirac approximation and incorporates the possible existence of a finite band gap in graphene spectrum. We show that in this case valley-polarized and pure valley currents can be pumped due to the valley symmetry breaking. For a \delta-function magnetic barrier we present analytical expressions for bilinear total and valley pumping responses. These results are compared to numerical ones for a double \delta-function, a square and a triple square magnetic barriers.

Zitterbewegung in bilayer graphene: Effects of trigonal warping and electric field

We study the effects of trigonal warping and electric field on the Zitterbewegung of low-energy electrons in bilayer graphene. A time-dependent average velocity of electrons is calculated by using Gaussian wave packets. The Zitterbewegung of electric current shows a transient behavior. The anisotropy of the eigenspectrum due to the trigonal warping distortion breaks the valley symmetry to induce valley-polarized Zitterbewegungs of electric current. An external electric field, applied perpendicular to the layer, opens a band gap and makes the group velocities of electrons at conduction and valence bands slower. Using this feature, we demonstrate that the decay time of the transient Zitterbewegung can be made longer by the electric field. Combining these effects, it is expected that valley-polarized Zitterbewegungs of electric current with longer decay time, which eventually become two valley-polarized constant currents at large times, can exist in a biased bilayer graphene with trigonal warping.

Excitonic instabilities and insulating states in bilayer graphene

The competing ground states of bilayer graphene are studied by applying renormalization group techniques to a bilayer honeycomb lattice with nearest neighbor hopping. In the absence of interactions, the Fermi surface of this model at half-filling consists of two nodal points with momenta $\mathbf{K}$, ${\mathbf{K}}^{\ensuremath{'}}$, where the conduction band and valence band touch each other, yielding a semimetal. Since near these two points the energy dispersion is quadratic with perfect particle-hole symmetry, excitonic instabilities are inevitable if interband interactions are present. Using a perturbative renormalization group analysis up to the one-loop level, we find different competing ordered ground states, including ferromagnetism, superconductivity, spin and charge density wave states with ordering vector $\mathbf{Q}=\mathbf{K}\ensuremath{-}{\mathbf{K}}^{\ensuremath{'}}$, and excitonic insulator states. In addition, two states with valley symmetry breaking are found in the excitonic insulating and ferromagnetic phases. This analysis strongly suggests that the ground state of bilayer graphene should be gapped, and with the exception of superconductivity, all other possible ground states are insulating.

Interaction-Induced Topological Insulator States in Strained Graphene

The electronic properties of graphene can be manipulated via mechanical deformations, which opens prospects for both studying the Dirac fermions in new regimes and for new device applications. Certain natural configurations of strain generate large nearly uniform pseudomagnetic fields, which have opposite signs in the two valleys, and give rise to flat spin- and valley-degenerate pseudo-Landau levels (PLLs). Here we consider the effect of the Coulomb interactions in strained graphene with a uniform pseudomagnetic field. We show that the spin or valley degeneracies of the PLLs get lifted by the interactions, giving rise to topological insulator states. In particular, when a nonzero PLL is quarter or three-quarter filled, an anomalous quantum Hall state spontaneously breaking time-reversal symmetry emerges. At half-filled PLLs, a weak spin-orbital interaction stabilizes the time-reversal-symmetric quantum spin-Hall state. These many-body states are characterized by the quantized conductance and persist to a high temperature scale set by the Coulomb interactions, which we estimate to be a few hundreds Kelvin at moderate strain values. At fractional fillings, fractional quantum Hall states breaking valley symmetry emerge. These results suggest a new route to realizing robust topological states in mesoscopic graphene.

Spontaneously Gapped Ground State in Suspended Bilayer Graphene

Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.

Chiral filtering in graphene with coupled valleys

We analyze the problem of electronic transmission through different regions of a graphene sheet that are characterized by different types of connections between the Dirac points. These valley symmetry breaking Hamiltonians might arise from electronic self-interaction mediated by the dielectric environment of distinct parts of the substrate on which the graphene sheet is placed. We show that it is possible to have situations in which we can use these regions to select or filter states of one desired chirality.

Neotectonic evolution of the northern Laborec drainage basin (northeastern part of Slovakia)

This study investigates the influence of neotectonic activity on river and basin patterns in a mountainous area located in the northeastern part of the Carpathian Belt (the Laborecká vrchovina and Bukovské vrchy Mts. in eastern Slovakia). This area evolved within the accretionary wedge of the Carpathians during the Neogene, and it was alsowas affected by Middle to Late Miocene thrusting of the External Carpathians. Morphometric analysis, longitudinal and transverse river valley profiles, analysis of basin and valley symmetries, and investigation of alluvial terraces were carried out on the northern Laborec River and its tributaries. This was done to detect a possible relationship between their river courses and any ongoing neotectonic activity, which is otherwise difficult to detect by methods of structural geology because of the poorly exposed area. The general topography of the basin is characterized by a stepwise inclination to the SW as a result of differential uplift and subsidence. The reorganization of the river network in the Laborec drainage basin was influenced by tectonic activity along the NE–SW up to N–S fault structures during the neotectonic phase (Pliocene–Quaternary). The movement along these fault structures is predominantly normal to transtensive. The obtained data assumes that the region is under approximately NE–SW oriented S H compression and NW–SE trending S h tension. The Laborec drainage basin is characterized by a very high degree of asymmetry that sharply increases from the upper to the lower courses of the river. The right-bank tributaries of the Laborec River are < 12 km in length; however, the left-bank tributaries such as Vydraňka, Ol'šava, Výrava, Udava, and Cirocha Streams are up to 50 km long with a high potential of headward erosion and capturing. The valley asymmetry is also very variable in the upper and lower portions of the basin. Based on these presented results, the ancient river thalweg was located along the axis of the Hostovice–Habura depression, and it was captured by the Ol'šava, Výrava, and Udava Streams. The asymmetric pattern of the drainage basin is the result of active tectonics, the continual subsidence of the Transcarpathian Basin, and by the uplift of the Laborecká vrchovina and Bukovské vrchy Mts. These events caused rejuvenation of the headward erosion of streams in the southern part. Favorable lithology was also essential in the process of river capture.

Magnetotransport Properties of Quasi-Free-Standing Epitaxial Graphene Bilayer on SiC: Evidence for Bernal Stacking

We investigate the magnetotransport properties of quasi-free-standing epitaxial graphene bilayer on SiC, grown by atmospheric pressure graphitization in Ar, followed by H(2) intercalation. At the charge neutrality point, the longitudinal resistance shows an insulating behavior, which follows a temperature dependence consistent with variable range hopping transport in a gapped state. In a perpendicular magnetic field, we observe quantum Hall states (QHSs) both at filling factors (ν) multiples of four (ν = 4, 8, 12), as well as broken valley symmetry QHSs at ν = 0 and ν = 6. These results unambiguously show that the quasi-free-standing graphene bilayer grown on the Si-face of SiC exhibits Bernal stacking.

Valley symmetry breaking and gap tuning in graphene by spin doping

We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic singularity appears in the Hall conductivity when the frequency of the external field agrees with the width of the gap.

Hierarchy of spin and valley symmetry breaking in quantum Hall single-layer graphene

We explore several microscopic mechanisms for breaking the $n=0$ fourfold Landau level degeneracy in a single-layer graphene. Valley-scattering random potential, Zeeman interaction, and electron-phonon coupling are considered in the presence of SU(4)-symmetric Coulomb exchange interaction. Among all the mechanisms considered, it is the electron-phonon coupling combined with the Zeeman interaction which leads to the full splitting of the $n=0$ Landau levels. A recent controversy of "valley-first" or "spin-first" breaking of SU(4) symmetry of the $n=0$ graphene Landau level is examined in light of our results. Existence of midgap states between Landau levels of opposite valley polarity are demonstrated.

Valley Symmetry Breaking in Bilayer Graphene: A Test of the Minimal Model

Physical properties reflecting the valley asymmetry of Landau levels in a biased bilayer graphene under a magnetic field are discussed. Within the 4-band continuum model with a Hartree-corrected self-consistent gap and finite damping factor we predict the appearance of anomalous steps in quantized Hall conductivity due to the degeneracy lifting of Landau levels. Moreover, the valley symmetry breaking effect appears as a nonsemiclassical de Haas-van Alphen effect where the reduction of the oscillation period to half cannot be accounted for through quasiclassical quantization of the orbits in reciprocal space.

Universal conductance fluctuations in graphene

Universal conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance is very sensitive to the elastic scattering that breaks the valley symmetry. In the absence of such scattering (disorder potential is smooth at atomic scales and trigonal warping is negligible), the variance is four times greater than in conventional metals, which explains a recent unexpected numerical finding. Strong intravalley scattering and/or warping reduces this factor to two and only the intervalley scattering leads to same result as for conventional metals. Different universal values of the variance, when compared with experimental data, can provide important information about disorder in the system.

Midgap states and charge inhomogeneities in corrugated graphene

We study the changes induced by the effective gauge field due to ripples on the low energy electronic structure of graphene. We show that zero-energy Landau levels will form, associated with the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that ${h}^{2}∕la\ensuremath{\gtrsim}1$, where $a$ is the lattice constant. The existence of localized levels gives rise to a large compressibility at zero energy and to the enhancement of instabilities arising from electron-electron interactions including electronic phase separation. The combined effect of the ripples and an external magnetic field breaks the valley symmetry of graphene, leading to the possibility of valley selection.

Weak-Localization Magnetoresistance and Valley Symmetry in Graphene

Because of the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalization and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks p-->-p symmetry of the Fermi line in each valley) suppresses antilocalization, while intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways of breaking a "hidden" valley symmetry of the system.

Binding energies of ground and excited donor states bound toXvalleys in GaAs/AlAs type-II quantum wells

We calculate the binding energies of $1s,$ $2s,$ ${2p}_{x},$ ${2p}_{y},$ and ${2p}_{z}$ donor states bound to X valleys in type-II GaAs-AlAs quantum well structures using an anisotropic variational method that enables us to take into account the effective-mass anisotropy and the quantum confinement. These binding energies present a strong dependence on the effective mass and the valley symmetry. Intradonor $1\stackrel{\ensuremath{\rightarrow}}{s}2p$ transitions energies are shown to be up to 1000 ${\mathrm{cm}}^{\ensuremath{-}1},$ which is well above the energies usually observed for donors in type-I quantum structures.

Piezo‐Hall Effect in n‐Type Germanium

AbstractThe piezo‐Hall effect has been measured at room temperature in germanium specimens doped with ≈︁1015 and ≈︁1018 Sb atoms per cm3. An experimental arrangement was used in which the stress and magnetic field were along a 〈111〉 valley symmetry direction and the current and Hall probes in the normal plane. The experimental results for ≈︁1018 cm−3 material are in accord with the simple electron transfer model with a mobility anisotropy of 7. The ≈︁1015 cm−3 material shows an anomalously small variation of Hall coefficient with stress. Possible explanations in terms of constancy of the net carrier concentration and intervalley scattering are discussed and rejected.

INTRAVALLEY VARIATION IN SLOPE ANGLES RELATED TO MICROCLIMATE AND EROSIONAL ENVIRONMENT

East- or west-trending stream valleys that have erosional slopes have been reported to be (1) asymmetrical with the north-facing slopes steeper, (2) asymmetrical with the south-facing slopes steeper, and (3) symmetrical, with both sides of equal mean slope angle. A series of measurements of angles of erosional slopes, taken in three east-trending, low-gradient valleys in the Laramie Range, Wyoming, shows that north-facing slopes there tend to be 4.4° steeper than opposed south-facing slopes; slope angle is further affected by nearness to the channel. In valleys that have channel gradients greater than 6° and greatly differing vegetation density across the valley, measurements of slope angles definitely show valley symmetry. The interpretation given is that unless the channel has been maintained against the base of the north-facing slope by greater slope wash from the south-facing slope, vegetation differences and resulting rates of slope erosion alone do not produce asymmetric valleys. Valley asymmetry that results from a variety of basic causes can be attributed to a single mechanism, asymmetric lateral corrosion by the stream. Difference in frost action on north-and south-facing valley sides is rejected as a cause of valley asymmetry in the areas studied because (1) the asymmetry is opposite that reported in tundra regions elsewhere, and (2) the degree of asymmetry in two widely separated areas does not reflect differences in the degree of frost activity in the two areas.