Lifting Of Degeneracy Research Articles

Theoretical Investigation of the Interfaces and Mechanisms of Induced Spin Polarization of 1D Narrow Zigzag Graphene- and h-BN Nanoribbons on a SrO-Terminated LSMO(001) Surface

The structure of the interfaces and the mechanisms of induced spin polarization of 1D infinite and finite narrow graphene- and h-BN zigzag nanoribbons placed on a SrO-terminated La1-xSrxMnO3 (LSMO) (001) surface were studied using density functional theory (DFT) electronic structure calculations. It was found that the π-conjugated nanofragments are bonded to the LSMO(001) surface by weak disperse interactions. The types of coordination of the fragments, the strength of bonding, and the rate of spin polarization depend upon the nature of the fragments. Infinite and finite graphene narrow zigzag nanoribbons are characterized by the lift of the spin degeneracy and strong spin polarization caused by interface-induced structural asymmetry and oxygen-mediated indirect exchange interactions with Mn ions of LSMO support. Spin polarization changes the semiconducting nature of infinite graphene nanoribbons to half-metallic state with visible spin-up density of states at the Fermi level. The h-BN nanoribbon binding energy is weaker than graphene nanoribbon ones with noticeably shorter interlayer distance. The asymmetry effect and indirect exchange interactions cause spin polarization of h-BN nanoribbon as well with formation of embedded states inside the band gap. The results show a possibility to use one-atom thick nanofragments to design LSMO-based heterostructures for spintronic nanodevices with h-BN as an inert spacer to develop different potential barriers.

On the resonant state of magnetization in array of interacting nanodots

Development of the interpretation of the phenomenon of the lift of the magnetic resonance frequencies degeneracy caused by the magnetostatic interaction in assemblies of nanodisks has been done. The difference of the resonance behavior of magnetic vortexes in a round and rectangular nanodots has been studied experimentally and explained.

Band-gap generation and excitation of conduction electrons in graphene by THz laser fields

ABSTRACTGraphene is a one-atom-thin 2D layer of hexagonal rings of carbon atoms (or, a giant 2D ‘carbon-molecule’) whose low-energy quasi-particles are charged and massless Dirac fermions which follow the relativistic Dirac equation in 2D. Using a recently developed theory of interaction of graphene with intense laser fields, we briefly discuss two phenomena of interest: (1) the lifting of degeneracy of graphene at the K-points by THz laser interaction and (2) induction of anisotropic electron distributions in the conduction band from the occupied valence band by absorption of one-, two-, or multiple THz photons. The first process is analogous to a phase transition of a pristine graphene from a semi-metal into a semiconductor within a time scale determined by the ultrashort pulse duration of the laser. The second process may permit control of electron currents in graphene whose magnitude and direction may be controlled simultaneously by controlling the THz laser parameters (e.g. pulse duration, field strength or polarisation).

Multigap superconductivity and barrier-driven resonances in superconducting nanofilms with an inner potential barrier

We study the crossover in a zero temperature superconducting nanofilm from a single to a double superconducting slab induced by a tunable insulating potential barrier in the middle. The single phase superconducting ground state of this heterostructure is shown to be intrinsically multigapped and to have a new type of resonance caused by the strength of the barrier, thus distinct from the Thompson-Blatt shape resonance which is caused by tuning the thickness of the film. Single particle electronic states are strongly or weakly affected according to their parity (even or odd) with respect to the insulating barrier. The lift of the parity degeneracy at finite barrier strength reconfigures the pairing interaction and leads to a multigapped superconducting state with interaction driven resonances.

Revealing the band structure of InSb nanowires by high-field magnetotransport in the quasiballistic regime

The charge transport properties of individual InSb nanowires based transistors are studied at 4.2 K in the quasiballistic regime. The energy level separations at zero magnetic field are extracted from a bias voltage spectroscopy. The magnetoconductance under a magnetic field applied perpendicularly to the nanowire axis is investigated up to 50 T. Owing to the magnetic reduction of the backscattering, the electronic states of the quasi-one-dimensional electron gas are revealed by Landauer-Buttiker conductance quantization. The results are compared to theoretical predictions revealing the spin and orbital degeneracy lifting. At sufficiently high magnetic field the measurements show the evolution to the quantum Hall effect regime with the formation of Landau orbits and conducting edge states.

Charge density wave phase transition on the surface of electrostatically doped multilayer graphene

We demonstrate that the charge density wave (CDW) phase transition occurs on the surface of electronically doped multilayer graphene when the Fermi level approaches the M points (also known as van Hove singularities where the density of states diverge) in the Brillouin zone of the graphene band structure. The occurrence of such CDW phase transitions is supported by both the electrical transport measurement and optical measurements in electrostatically doped multilayer graphene. The CDW transition is accompanied with the sudden change of graphene channel resistance at Tm = 100 K, as well as the splitting of Raman G peak (1580 cm−1). The splitting of Raman G peak indicates the lifting of in-plane optical phonon branch degeneracy, and the non-degenerate phonon branches are correlated to the lattice reconstructions of graphene—the CDW phase transition.

Observation of Dirac surface states in the noncentrosymmetric superconductor BiPd

Materials with strong spin-orbit coupling (SOC) have in recent years become a subject of intense research due to their potential applications in spintronics and quantum information technology. In particular, in systems which break inversion symmetry, SOC facilitates the Rashba-Dresselhaus effect, leading to a lifting of spin degeneracy in the bulk and intricate spin textures of the Bloch wave functions. Here, by combining angular resolved photoemission (ARPES) and low temperature scanning tunneling microscopy (STM) measurements with relativistic first-principles band structure calculations, we examine the role of SOC in single crystals of noncentrosymmetric BiPd. We report the detection of several Dirac surface states, one of which exhibits an extremely large spin splitting. Unlike the surface states in inversion-symmetric systems, the Dirac surface states of BiPd have completely different properties at opposite faces of the crystal and are not trivially linked by symmetry. The spin-splitting of the surface states exhibits a strong anisotropy by itself, which can be linked to the low in-plane symmetry of the surface termination.

Generic model for the hyperkagome iridateNa4Ir3O8in the local-moment regime

Hyperkagome iridate, Na$_4$Ir$_3$O$_8$, has been regarded as a promising candidate material for a three-dimensional quantum spin liquid. Here the three-dimensional network of corner-sharing triangles forms the hyperkagome lattice of Ir$^{4+}$ ions. Due to strong spin-orbit coupling, the local moments of Ir$^{4+}$ ions are described by the pseudospin $j_{\rm eff} = 1/2$ Kramers doublet. The Heisenberg model on this lattice is highly frustrated and quantum/classical versions have been studied in earlier literature. In this work, we derive a generic local-moment model beyond the Heisenberg limit for the hyperkagome iridate by considering multi-orbital interactions for all the $t_{2g}$ orbitals and spin-orbit coupling. The lifting of massive classical degeneracy in the Heisenberg model by various spin-anisotropy terms is investigated at the classical level and the resulting phase diagram is presented. We find that different anisotropy terms prefer distinct classes of magnetically ordered phases, often with various discrete degeneracy. The implications of our results for recent $\mu$SR and NMR experiments on this material and possible quantum spin liquid phases are discussed.

Landau Level Splittings, Phase Transitions, and Nonuniform Charge Distribution in Trilayer Graphene.

We report on magnetotransport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the 12-fold degeneracy of the zeroth Landau level. As a function of perpendicular electric field, our data exhibit a sequence of phase transitions between all integer quantum Hall states in the filling factor interval -8<ν<0. We develop a theoretical model and argue that, in contrast to monolayer and bilayer graphene, the observed Landau level splittings and quantum Hall phase transitions can be understood within a single-particle picture, but imply the presence of a charge density imbalance between the inner and outer layers of TLG, even at charge neutrality and zero transverse electric field. Our results indicate the importance of a previously unaccounted band structure parameter which, together with a more accurate estimate of the other tight-binding parameters, results in a significantly improved determination of the electronic and Landau level structure of TLG.

Output polarization characteristics of a GaN microcavity diode polariton laser

We report the steady state output polarization characteristics of GaN-based microcavity polariton lasers operated with electrical injection at room temperature. The output is unpolarized below the nonlinear threshold injection current and is linearly polarized above it with a maximum degree of polarization of $\ensuremath{\sim}22%$. The results have been analyzed theoretically, and the calculated results are in agreement with the measured data. We have also measured the polarization-resolved output light current characteristics, wherein a distinct lowering of the non-linear threshold is observed in one device. This is interpreted in terms of spatially inhomogeneous lifting of degeneracy and polarization splitting in the microcavity.

Magneto-optical transport properties of monolayerWSe2

The recent experimental realization of a high quality WSe$% _{2} $ leads to the possibility of magneto-optical measurements and the manipulation of the spin and valley degrees of freedom. We study the influence of the very strong spin-orbit coupling and of the anisotropic lifting of the valley pseudospin degeneracy on its magnetotransport properties. The energy spectrum of WSe$_{2} $ is derived and discussed in the presence of a perpendicular magnetic field $B$. Correspondingly we evaluate the magneto-optical Hall conductivity and the optical longitudinal conductivity as functions of the frequency, magnetic field, and Fermi energy. They are strongly influenced by the field $B$ and the strong spin splitting. The former exhibits valley polarization and the latter beatings of oscillations. The magneto-optical responses can be tuned in two different regimes: the mictrowave-to-terahertz regime and the visible-frequency one. The absorption peaks involving the $n=0$ LL appear in between these two regimes and show a magnetic control of the spin and valley splittings. We also evaluate the power absorption spectrum.

Large transverse Hall-like signal in topological Dirac semimetal Cd3As2.

Cadmium arsenide (Cd3As2) is known for its inverted band structure and ultra-high electron mobility. It has been theoretically predicted and also confirmed by ARPES experiments to exhibit a 3D Dirac semimetal phase containing degenerate Weyl nodes. From magneto-transport measurements in high quality single crystals of Cd3As2, a small effective mass m* ≈ 0.05 me is determined from the Shubnikov-de Haas (SdH) oscillations. In certain field orientations, we find a splitting of the SdH oscillation frequency in the FFT spectrum suggesting a possible lifting of the double degeneracy in accord with the helical spin texture at outer and inner Fermi surfaces with opposite chirality predicted by our ab initio calculations. Strikingly, a large antisymmetric magnetoresistance with respect to the applied magnetic fields is uncovered over a wide temperature range in needle crystal of Cd3As2 with its long axis along [112] crystal direction. It reveals a possible contribution of intrinsic anomalous velocity term in the transport equation resulting from a unique 3D Rashba-like spin splitted bands that can be obtained from band calculations with the inclusion of Cd antisite defects.

Angular momentum and topology in semiconducting single-wall carbon nanotubes

Semiconducting single-wall carbon nanotubes are classified into two types by means of orbital angular momentum of valley state, which is useful to study their low energy electronic properties in finite-length. The classification is given by an integer $d$, which is the greatest common divisor of two integers $n$ and $m$ specifying the chirality of nanotubes, by analyzing cutting lines. For the case that $d$ is equal to or greater than four, two lowest subbands from two valleys have different angular momenta with respect to the nanotube axis. Reflecting the decoupling of two valleys, discrete energy levels in finite-length nanotubes exhibit nearly fourfold degeneracy and its small lift by the spin-orbit interaction. For the case that $d$ is less than or equal to two, in which two lowest subbands from two valleys have the same angular momentum, discrete levels exhibit lift of fourfold degeneracy reflecting the coupling of two valleys. Especially, two valleys are strongly coupled when the chirality is close to the armchair chirality. An effective one-dimensional lattice model is derived by extracting states with relevant angular momentum, which reveals the valley coupling in the eigenstates. A bulk-edge correspondence, relationship between number of edge states and the winding number calculated in the corresponding bulk system, is analytically shown by using the argument principle, which enables us to estimate the number of edge states from the bulk property. The number of edge states depends not only on the chirality but also on the shape of boundary.

Ab-initio calculation of electronic structure and optical properties of AB-stacked bilayer α-graphyne

Monolayer α-graphyne is a new two-dimensional carbon allotrope with many special features. In this work the electronic properties of AA- and AB-stacked bilayers of this material and then the optical properties are studied, using first principle plane wave method. The electronic spectrum has two Dirac cones for AA stacked bilayer α-graphyne. For AB-stacked bilayer, the interlayer interaction changes the linear bands into parabolic bands. The optical spectra of the most stable AB-stacked bilayer closely resemble to that of the monolayer, except for small shifts of peak positions and increasing of their intensity. For AB-stacked bilayer, a pronounced peak has been found at low energies under the perpendicular polarization. This peak can be clearly ascribed to the transitions at the Dirac point as a result of the small degeneracy lift in the band structure.

Degeneracy Lifting Effect in the FTIR Spectrum of Fluoroform Trapped in a Nitrogen Matrix. An Experimental and Car–Parrinello Molecular Dynamics Study

The FTIR spectra of fluoroform trapped in argon and nitrogen matrixes are studied at T ∼ 10-30 K. The bands of E symmetry show the splitting effect in a nitrogen matrix, which is absent in an argon matrix. The effect is the most prominent in the case of the ν4 CH bending vibration. It decreases slightly with increasing temperature. Both static and Car-Parrinello molecular dynamic simulations suggest that the degeneracy lifting is due to C3v symmetry lowering caused by interactions between fluoroform and all neighbor N2 matrix molecules.

Quantization and anomalous structures in the conductance of Si/SiGe quantum point contacts

Quantum point contacts (QPCs) are fabricated on modulation-doped Si/SiGe heterostructures and ballistic transport is studied at low temperatures. We observe quantized conductance with subband separations up to 4 meV and anomalies in the first conductance plateau at 4e2/h. At a temperature of T = 22 mK in the linear transport regime, a weak anomalous kink structure arises close to 0.5(4e2/h), which develops into a distinct plateau-like structure as temperature is raised up to T = 4 K. Under magnetic field parallel to the wire up to B = 14 T, the anomaly evolves into the Zeeman spin-split level at 0.5(4e2/h), resembling the "0.7 anomaly" in GaAs/AlGaAs QPCs. Additionally, a zero-bias anomaly (ZBA) is observed in nonlinear transport spectroscopy. At T = 22 mK, a parallel magnetic field splits the ZBA peak up into two peaks. At B = 0, elevated temperatures lead to similar splitting, which differs from the behavior of ZBAs in GaAs/AlGaAs QPCs. Under finite dc bias, the differential resistance exhibits additional plateaus approximately at 0.8(4e2/h) and 0.2(4e2/h) known as "0.85 anomaly" and "0.25 anomaly" in GaAs/AlGaAs QPCs. Unlike the first regular plateau at 4e2/h, the 0.2(4e2/h) plateau is insensitive to dc bias voltage up to at least VDS = 80 mV, in-plane magnetic fields up to B = 15 T, and to elevated temperatures up to T = 25 K. We interpret this effect as due to pinching off one of the reservoirs close to the QPC. We do not see any indication of lifting of the valley degeneracy in our samples.

Interatomic Coulomb interaction and electron nematic bond order in FeSe

Despite having the simplest atomic structure, bulk FeSe has an observed electronic structure with the largest deviation from the band theory predictions among all Fe-based superconductors and exhibits a low temperature nematic electronic state without intervening magnetic order. We show that the Fe-Fe interatomic Coulomb repulsion $V$ offers a natural explanation for the puzzling electron correlation effects in FeSe superconductors. It produces a strongly renormalized low-energy band structure where the van Hove singularity sits remarkably close to Fermi level in the high-temperature electron liquid phase as observed experimentally. This proximity enables the quantum fluctuations in $V$ to induce a rotational symmetry breaking electronic bond order in the $d$-wave channel. We argue that this emergent low-temperature $d$-wave bond nematic state, different from the commonly discussed ferro-orbital order and spin-nematicity, has been observed recently by several angle resolved photoemission experiments detecting the lifting of the band degeneracies at high symmetry points in the Brillouin zone. We present a symmetry analysis of the space group and identify the hidden antiunitary $T$-symmetry that protects the band degeneracy and the electronic order/interaction that can break the symmetry and lift the degeneracy. We show that the $d$-wave nematic bond order, together with the spin-orbit coupling, provide a unique explanation of the temperature dependence, momentum space anisotropy, and domain effects observed experimentally. We discuss the implications of our findings on the structural transition, the absence of magnetic order, and the intricate competition between nematicity and superconductivity in FeSe superconductors.

Lifting of the Landau level degeneracy in graphene devices in a tilted magnetic field

We report on transport and capacitance measurements of graphene devices in magnetic fields up to 30 T. In both techniques, we observe the full splitting of Landau levels and we employ tilted field experiments to address the origin of the observed broken symmetry states. In the lowest energy level, the spin degeneracy is removed at filling factors $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}1$ and we observe an enhanced energy gap. In the higher levels, the valley degeneracy is removed at odd filling factors while spin polarized states are formed at even $\ensuremath{\nu}$. Although the observation of odd filling factors in the higher levels points towards the spontaneous origin of the splitting, we find that the main contribution to the gap at $\ensuremath{\nu}=\ensuremath{-}4,\ensuremath{-}8$, and $\ensuremath{-}12$ is due to the Zeeman energy.

Momentum-dependent sign inversion of orbital order in superconducting FeSe

We investigate the electronic reconstruction across the tetragonal-orthorhombic structural transition in FeSe by employing polarization-dependent angle-resolved photoemission spectroscopy (ARPES) on detwinned single crystals. Across the structural transition, the electronic structures around the G and M points are modified from four-fold to two-fold symmetry due to the lifting of degeneracy in dxz/dyz orbitals. The dxz band shifts upward at the G point while it moves downward at the M point, suggesting that the electronic structure of orthorhombic FeSe is characterized by a momentum-dependent sign-changing orbital polarization. The elongated directions of the elliptical Fermi surfaces (FSs) at the G and M points are rotated by 90 degrees with respect to each other, which may be related to the absence of the antiferromagnetic order in FeSe.

ESR study of the spin ladder with uniform Dzyaloshinskii-Moriya interaction

Evolution of the ESR absorption in a strong-leg spin ladder magnet (C$_7$H$_{10}$N$_2$)$_2$CuBr$_4$ (abbreviated as DIMPY) is studied from 300K to 400mK. Temperature dependence of the ESR relaxation follows a staircase of crossovers between different relaxation regimes. We ague that the main mechanism of ESR line broadening in DIMPY is uniform Dzyaloshinskii-Moria interaction ($|\vec{D}|=0.20$K) with an effective longitudinal component along an exchange bond of Cu ions within the legs resulting from the low crystal symmetry of DIMPY and nontrivial orbital ordering. The same Dzyaloshinskii-Moriya interaction results in the lifting of the triplet excitation degeneracy, revealed through the weak splitting of the ESR absorption at low temperatures.