Electron-hole Symmetry Breaking Research Articles

Influence of ab initio derived site-dependent hopping parameters on electronic transport in graphene nanoribbons.

Graphene Nano Ribbons (GNRs) have been studied extensively due to their potential applications in electrical transport, optical devices, etc. The Tight Binding (TB) model is a common method used to theoretically study the properties of GNRs. However, the hopping parameters of two-dimensional graphene (2DG) are often used as the hopping parameters of the TB model of GNRs, which may lead to inaccuracies in the prediction of GNRs. In this work, we calculated the site-dependent hopping parameters from density functional theory and construction of Wannier orbitals for use in a realistic TB model. It has been found that due to the edge effect, the hopping parameters of edge C atoms are markedly different from the bulk part, which is prominently observed in narrow GNRs. Compared to graphene, the change of hopping parameter of edge C atoms of zigzag GNRs (ZGNRs) and armchair GNRs (AGNRs) is as high as 0.11 and 0.08 eV, respectively. Moreover, we investigated the impact of the calculated site-dependent (SD) hopping parameters on the electronic transport properties of GNRs in the absence and presence of the perpendicular electric field and dilute charged impurities using the Green function approach, Landauer-Büttiker formalism and self-consistent Born approximation. We find an electron-hole asymmetry in the electronic structure and transport properties of ZGNRs with SD hopping parameters. Furthermore, AGNRs with SD hopping energies show a band gap regardless of their width, while AGNRs with 2DG hopping parameters exhibit metallic or semiconductor phases depending on their width. In addition, electric field-induced 4-ZGNR with SD hopping parameters undergoes a metallic to n-doped semiconducting phase transition whereas for 4-ZGNR with 2DG hopping parameters and 8-AGNRs with 2DG or SD hopping parameters, the application of an electric field opens the band gap in both conduction and valence bands simultaneously. Our findings provide evidence for the electron-hole symmetry breaking in ZGNR with SD hopping parameters and make ZGNRs a suitable candidate in valleytronic devices.

Thermoelectric Power and Hall Effect in Correlated Metals and Doped Mott–Hubbard Insulators: DMFT Approximation

We present comparative theoretical investigation of thermoelectric power and Hall effect in the Hubbard model for correlated metal and Mott insulator (considered as prototype cuprate superconductor) for different concentrations of current carriers. Analysis is performed within standard DMFT approximation. For Mott insulator we consider the typical case of partial filling of the lower Hubbard band (hole doping). We calculate the dependence of thermopower on doping level and determine the critical concentration of carriers corresponding to sign change of thermopower. An anomalous dependence of thermopower on temperature is obtained significantly different from linear temperature dependence typical for the usual metals. The role of disorder scattering is analyzed on qualitative level. The comparison with similar studies of the Hall effect shows, that breaking of electron-hole symmetry leads to the appearance of the relatively large interval of band-fillings (close to the half-filling) where thermopower and Hall effects have different signs. We propose a certain scheme allowing to determine the number of carriers from ARPES data and perform semi-quantitative estimate of both thermopower and Hall coefficient using the usual DFT calculations of electronic spectrum.

Microwave-Assisted Thermoelectricity in S - I - S′ Tunnel Junctions

Asymmetric superconducting tunnel junctions with gaps ${\mathrm{\ensuremath{\Delta}}}_{1}>{\mathrm{\ensuremath{\Delta}}}_{2}$ have been proven to show a peculiar nonlinear bipolar thermoelectric effect. This arises due to the spontaneous breaking of electron-hole symmetry in the system, and it is maximized at the matching-peak bias $|V|={V}_{p}=({\mathrm{\ensuremath{\Delta}}}_{1}\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{2})/e$. In this paper, we investigate the interplay of photon-assisted tunneling (PAT) and bipolar thermoelectric generation. In particular, we show how thermoelectricity, at the matching peak, is supported by photon absorption and emission processes at the frequency-shifted sidebands $V=\ifmmode\pm\else\textpm\fi{}{V}_{p}+n\ensuremath{\hbar}\ensuremath{\omega}$, $n\ensuremath{\in}\mathbb{Z}$. This represents a sort of microwave-assisted thermoelectricity. We show the existence of multiple stable solutions, being associated with different photon sidebands, when a load is connected to the junction. Finally, we discuss how the nonlinear cooling effects are modified by the PAT. The proposed device can detect millimeter-wavelength signals by converting a temperature gradient into a thermoelectric current or voltage.

Noncollinear twisted RKKY interaction on the optically driven SnTe(001) surface

The nontrivial spin texture on the (001) surface of topological crystalline insulator SnTe hosts exotic scientific importance and spintronic applications. Here, we study the effects of weak Floquet optical driving on the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities on a doped SnTe(001) surface. Due to peculiar spin-orbit hybridization, we find a noncollinear twisted RKKY interaction with XYZ-Heisenberg, symmetric in-plane, and asymmetric Dzyaloshinskii-Moriya (DM) terms. We see that contributions from the $z$ $(x)$ component of the XYZ-Heisenberg (DM) interaction are dominant for most parameters. The interactions, including DM terms that are responsible for interesting spin textures, require doping in most cases. We propose to modify the interactions in situ via optical control of band structure, and thereby doping. A notable aspect of this control protocol is breaking of electron-hole symmetry, which stems from the DM interaction.

Phase-Coherent Thermoelectricity in Superconducting Hybrids (Brief Review)

We review some recent advances in studies of phase-coherent thermoelectric effects in superconducting hybrid structures such as, e.g., Andreev interferometers. We elucidate a number of mechanisms of electron-hole symmetry breaking in such systems causing dramatic enhancement of thermoelectric effects. We demonstrate that the flux-dependent thermopower exhibits periodic dependence on the applied magnetic flux $\Phi_x$ which in some limits may reduce to either odd or even functions of $\Phi_x$ in accordance with experimental observations. We also show that dc Josephson current in Andreev interferometers can be controlled and enhanced by applying a temperature gradient which may also cause a nontrivial current-phase relation and a transition to a $\pi$-junction state.

Nitrogen-doped nanoporous graphene induced by a multiple confinement strategy for membrane separation of rare earth.

SummaryRare earth separation is still a major challenge in membrane science. Nitrogen-doped nanoporous graphene (NDNG) is a promising material for membrane separation, but it has not yet been tested for rare earth separation, and it is limited by multi-complex synthesis. Herein, we developed a one-step, facile, and scalable approach to synthesize NDNG with tunable pore size and controlled nitrogen content using confinement combustion. Nanoporous hydrotalcite from Zn(NO3)2 is formed between layers of graphene oxide (GO) absorbed with phenylalanine via confinement growth, thus preparing the sandwich hydrotalcite/phenylalanine/GO composites. Subsequently, area-confinement combustion of hydrotalcite nanopores is used to etch graphene nanopores, and the hydrotalcite interlayer as a closed flat nanoreactor induces two-dimensional space confinement doping of planar nitrogen into graphene. The membrane prepared by NDNG achieves separation of Sc3+ from the other rare earth ions with excellent selectivity (∼3.7) through selective electrostatic interactions of pyrrolic-N, and separation selectivity of ∼1.7 for Tm3+/Sm3+.

Superconducting nonlinear thermoelectric heat engine

In a previous work, we predicted that a thermally biased tunnel junction between two different superconductors can display a thermoelectric effect of nonlinear nature in the temperature gradient, under proper conditions. In this work we give a more extended discussion, and we focus on the two main features of the nonlinear contributions: i) the $linear-in-bias$ thermoelectricity, that can be associated to a spontaneous breaking of electron-hole symmetry, ii) the strong contribution at the matching peak singularity, which is typically associated to the maximum output power and efficiency. We discuss the nonlinear origin of the thermoelectricity and its relationship with the non-linear cooling mechanism in superconducting junctions previously discussed in the literature. Finally, we design and characterize the performance of the system as a heat engine, for a realistic design and experimental parameter values. We discuss possible non-idealities demonstrating that the system is amenable to current experimental realization.

Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian

We study the ballistic conductivity of bilayer graphene in the presence of symmetry-breaking terms in effective Hamiltonian for low-energy excitations, such as the trigonal-warping term ($\gamma_3$), the electron-hole symmetry breaking interlayer hopping ($\gamma_4$), and the staggered potential ($\delta_{AB}$). Earlier, it was shown that for $\gamma_3\neq{}0$, in the absence of remaining symmetry-breaking terms (i.e., $\gamma_4=\delta_{AB}=0$), the conductivity ($\sigma$) approaches the value of $3\sigma_0$ for the system size $L\rightarrow{}\infty$ (with $\sigma_0=8e^2/(\pi{}h)$ being the result in the absence of trigonal warping, $\gamma_3=0$). We demonstrate that $\gamma_4\neq{}0$ leads to the divergent conductivity if $\gamma_3\neq{}0$, or to the vanishing conductivity if $\gamma_3=0$. For realistic values of the tight-binding model parameters, $\gamma_3=0.3\,$eV, $\gamma_4=0.15\,$eV (and $\delta_{AB}=0$), the conductivity values are in the range of $\sigma/\sigma_0\approx{}4-5$ for $100\,$nm$\ <L<1\,\mu$m, in agreement with existing experimental results. The staggered potential ($\delta_{AB}\neq{}0$) suppresses zero-temperature transport, leading to $\sigma\rightarrow{}0$ for $L\rightarrow{}\infty$. Although $\sigma=\sigma(L)$ is no longer universal, the Fano factor approaches the pseudodiffusive value ($F\rightarrow{}1/3$ for $L\rightarrow{}\infty$) in any case with non-vanishing $\sigma$ (otherwise, $F\rightarrow{}1$) signaling the transport is ruled by evanescent waves. Temperature effects are briefly discussed in terms of a phenomenological model for staggered potential $\delta_{AB}=\delta_{AB}(T)$ showing that, for $0<T\leqslant{}T_c\approx{}12\,$K and $\delta_{AB}(0)=1.5\,$meV, $\sigma(L)$ is noticeably affected by $T$ for $L\gtrsim{}100\,$nm.

Quantum limit cyclotron resonance in monolayer epitaxial graphene in magnetic fields up to 560 T: The relativistic electron and hole asymmetry

Electron-hole symmetry breaking of Dirac electrons has been evidenced as a well-resolved cyclotron resonance (CR) peak splitting at magnetic fields around 300-500 T in epitaxial monolayer graphene. The magnetic field was swept up to 560 T for the infrared CR by means of the electromagnetic flux compression technique in a 1000-T class megagauss generator. The authors argue that it is the CR mode repulsion, caused by the electron-electron correlation, which is responsible for the observed CR intensity transfer from the hole to the electron.

Nonlinear Thermoelectricity with Electron-Hole Symmetric Systems.

In the linear regime, thermoelectric effects between two conductors are possible only in the presence of an explicit breaking of the electron-hole symmetry. We consider a tunnel junction between two electrodes and show that this condition is no longer required outside the linear regime. In particular, we demonstrate that a thermally biased junction can display an absolute negative conductance, and hence thermoelectric power, at a small but finite voltage bias, provided that the density of states of one of the electrodes is gapped and the other is monotonically decreasing. We consider a prototype system that fulfills these requirements, namely, a tunnel junction between two different superconductors where the Josephson contribution is suppressed. We discuss this nonlinear thermoelectric effect based on the spontaneous breaking of electron-hole symmetry in the system, characterize its main figures of merit, and discuss some possible applications.

Attractive and driven interactions in quantum dots: Mechanisms for geometric pumping

We analyze time-dependent transport through a quantum dot with electron-electron interaction that is statically tunable to both repulsive and attractive regimes, or even dynamically driven. Motivated by the recent experimental realization [Hamo et. al, Nature 535, 395 (2016)] of such a system in a static double quantum dot we compute the geometric pumping of charge in the limit of weak tunneling, high temperature and slow driving. We analyze the pumping responses for all pairs of driving parameters (gate voltage, bias voltage, tunnel coupling, electron-electron interaction). We show that the responses are analytically related when these different driving protocols are governed by the same pumping mechanism, which is characterized by effective driving parameters that differ from the experimental ones. For static attractive interaction we find a characteristic pumping resonance despite the 'attractive Coulomb blockade' that hinders stationary transport. Moreover, we identify a pumping mechanism that is unique to driving of the interaction. Finally, although a single-dot model with orbital pseudo-spin describes most of the physics of the mentioned experimental setup, it is crucial to account for the additional (real-) spin degeneracies of the double dot and the associated electron-hole symmetry breaking. This is necessary because the pumping response is more sensitive than DC transport measurements and detects this difference through pronounced qualitative effects.

Bilayer graphene under pressure: Electron-hole symmetry breaking, valley Hall effect, and Landau levels

The electronic structure of bilayer graphene under pressure develops very interesting features with an enhancement of the trigonal warping and a splitting of the parabolic touching bands at the K point of the reciprocal space into four Dirac cones, one at K and three along the T symmetry lines. As pressure is increased, these cones separate in reciprocal space and in energy, breaking the electron-hole symmetry. Due to their energy separation, their opposite Berry curvature can be observed in valley Hall effect experiments and in the structure of the Landau levels. Based on the electronic structure obtained by Density Functional Theory, we develop a low energy Hamiltonian that describes the effects of pressure on measurable quantities such as the Hall conductivity and the Landau levels of the system.

Boundary conditions for transition-metal dichalcogenide monolayers in the continuum model

We derive the boundary conditions for MoS$_2$ and similar transition-metal dichalcogenide honeycomb (2H polytype) monolayers with the same type of $\mathbf{k}\!\cdot\!\mathbf{p}$ Hamiltonian within the continuum model around the K points. In an effective 2-band description, the electron-hole symmetry breaking quadratic terms are also taken into account. We model the effect of the edges with a linear edge constraint method that has been applied previously to graphene. Focusing mainly on zigzag edges, we find that different reconstruction geometries with different edge-atoms can generally be described with one scalar parameter varying between 0 and $2\pi$. We analyze the edge states and their dispersion relation in MoS$_2$ in particular, and we find good agreement with the results of previous density functional theory calculations for various edge types.

Monolayer MoS2: Trigonal warping, theΓvalley, and spin-orbit coupling effects

We use a combined ab-initio calculations and k.p theory based approach to derive a low-energy effective Hamiltonian for monolayer MoS2 at the K point of the Brillouin zone. It captures the features which are present in first-principles calculations but not explained by the theory of Xiao et al. [Phys Rev Lett 108, 196802 (2012)], namely the trigonal warping of the valence and conduction bands, the electron-hole symmetry breaking, and the spin-splitting of the conduction band. We also consider other points in the Brillouin zone which might be important for transport properties. Our findings lead to a more quantitative understanding of the properties of this material in the ballistic limit.

Tight-binding model for grapheneπ-bands from maximally localized Wannier functions

The electronic properties of graphene sheets are often understood by starting from a simple phenomenological $\ensuremath{\pi}$-band tight-binding model. We provide a perspective on these models that is based on a study of ab initio maximally localized Wannier wave functions centered at carbon sites. Hopping processes in graphene can be separated into intersublattice contributions responsible for band dispersion near the Dirac point, and intrasublattice contributions responsible for electron-hole symmetry breaking. Both types of corrections to the simplest near-neighbor model can be experimentally relevant. We find that distant neighbor hopping parameters increase the ratio of the full $\ensuremath{\pi}$-band width to the Dirac point velocity and flatten bands along the $KM$ Brillouin-zone edge. We propose a five-parameter model which achieves a good compromise between simplicity and accuracy, and an alternate 15-parameter model achieves better accuracy with some loss of simplicity.

Charges driving under the influence

An investigation of Coulomb drag in graphene integrated into a stacked heterostructure unveils unexpected electron–hole symmetry-breaking in two-dimensional electronic crystals.

Thermally excited spin current and giant magnetothermopower in metals with embedded ferromagnetic nanoclusters

We show that a thermally excited spin current naturally appears in metals with embedded ferromagnetic nanoclusters. When such materials are subjected to a magnetic field, a spin current can be generated by a temperature gradient across the sample as a signature of electron-hole symmetry breaking in a metal due to the electron spin-flip scattering from polarized magnetic moments. Such a spin current can be observed via a giant magnetothermopower which tracks the polarization state of the magnetic subsystem and is proportional to the magnetoresistance. Our theory explains the recent experiment on Co clusters in copper by S. Serrano-Guisan et al. [Nat. Mater.5, 730 (2006)].

Can the spin-orbit interaction break the channel degeneracy (conservation) of the two-channel orbital Kondo problem?

Two-level systems (TLS) interacting with conduction electrons are possibly described by the two-channel Kondo Hamiltonian. In this case the channel degeneracy is due to the real spin of the electrons. The possibility of breaking that degeneracy has interest on his own. In fact, we show that the interaction of the conduction electrons with a spin-orbit scatterer nearby the TLS leads to the breaking of the channel degeneracy only in the case of electron-hole symmetry breaking. The generated channel symmetry breaking TLS-electron couplings are, however, too weak to result in any observable effects. Our analysis is also relevant for heavy fermion systems.

Dimensional change as a function of charge injection in graphite intercalation compounds: A density functional theory study

Charge-induced dimensional changes as a function of charge injection are predicted for graphite intercalation compounds by the means of geometry optimization with density functional theory. A plane wave basis set with periodic boundary condition and ultrasoft pseudopotentials are used in the generalized gradient approximation. Agreement with experiment is obtained for the calculated strain-charge relationship for the graphite sheet and for the calculated inter-layer distances of ${\mathrm{KC}}_{8},$ $X{\mathrm{C}}_{6}$ $(X=\mathrm{K},$ Li, Ca, and Ba), ${\mathrm{C}}_{6}\mathrm{Cl},$ ${\mathrm{C}}_{18}{\mathrm{PF}}_{6},$ and ${\mathrm{C}}_{24}{\mathrm{AsF}}_{6}.$ When the interlayer distances are increased from the optimized values up to 10 \AA{}, the charge transfer and basal plane strain in ${\mathrm{KC}}_{6}$ decrease whereas they remain unchanged in ${\mathrm{C}}_{6}\mathrm{Cl}.$ The results of the full calculations, which include specific counterions, are consistent with the results from jellium calculations (in which the counterions are represented by a uniformly distributed background charge). This shows that hybridization between the ions and the graphite sheets is not significant. All of the investigated models provide calculated charge-strain relationships for graphite that are asymmetric with respect to the sign of charge transfer. Expansion occurs for negative charge injection and contraction occurs for positive charge injection, due to the electron-hole symmetry breaking effect of second neighbor antibonding interactions.

Instability of the marginal commutative model of tunneling centers interacting with a metallic environment: Role of the electron-hole symmetry breaking

The role of the electron-hole symmetry breaking is investigated for a symmetrical commutative two-level system in a metal using the multiplicative renormalization group in a straightforward way. The role of the symmetries of the model and the path integral technique are also discussed in detail. It is shown that the electron-hole symmetry breaking may make the model non-commutative and generate the assisted tunneling process which is, however, too small itself to drive the system into the vicinity of the two-channel Kondo fixed point. While these results are in qualitative agreement with those of Moustakas and Fisher (Phys. Rev. B 51, 6908 (1995), ibid 53, 4300 (1996)) the scaling equations turn out to be essentially different. We show that the main reason for this difference is that the procedure for the elimination of the high energy degrees of freedom used by Moustakas and Fisher leaves only the free energy invariant, however, the couplings generated are not connected to the dynamical properties in a straightforward way and should be interpreted with care. These latter results might have important consequences in other cases where the path integral technique is used to produce the scaling equations and calculate physical quantities.