Spin Degeneracy Research Articles

Edge-Dependent Electronic and Magnetic Characteristics of Freestanding \u03b212-Borophene Nanoribbons

This work presents an investigation of nanoribbons cut from β12-borophene sheets by applying the density functional theory. In particular, the electronic and magnetic properties of borophene nanoribbons (BNR) are studied. It is found that all the ribbons considered in this work behave as metals, which is in good agreement with the recent experimental results. β12-BNR has significant diversity due to the existence of five boron atoms in a unit cell of the sheet. The magnetic properties of the ribbons are strongly dependent on the cutting direction and edge profile. It is interesting that a ribbon with a specific width can behave as a normal or a ferromagnetic metal with magnetization at just one edge or two edges. Spin anisotropy is observed in some ribbons, and the magnetic moment is not found to be the same in both edges in an antiferromagnetic configuration. This effect stems from the edge asymmetry of the ribbons and results in the breaking of spin degeneracy in the band structure. Our findings show that β12 BNRs are potential candidates for next-generation spintronic devices.

The Kubo-Greenwood spin-dependent electrical conductivity of 2D transition-metal dichalcogenides and group-IV materials: A Green’s function study

The spin-dependent electrical conductivity of counterparts of graphene, transition-metal dichalcogenides (TMDs) and group-IV nanosheets, have investigated by a magnetic exchange field (MEF)-induction to gain the electronic transport properties of charge carriers. We have implemented a k.p Hamiltonian model through the Kubo-Greenwood formalism in order to address the dynamical behavior of correlated Dirac fermions. Tuning the MEF enables one to control the effective mass of carriers in group-IV and TMDs, differently. We have found the Dirac-like points in a new quantum anomalous Hall (QAH) state at strong MEFs for both structures. For both cases, a broad peak in electrical conductivity originated from the scattering rate and entropy is observed. Spin degeneracy at some critical MEFs is another remarkable point. We have found that in the limit of zero or uniform MEFs with respect to the spin-orbit interaction, the large resulting electrical conductivity depends on the spin sub-bands in group-IV and MLDs. Featuring spin-dependent electronic transport properties, one can provide a new scenario for future possible applications.

Edge magnetism impact on electrical conductance and thermoelectric properties of graphenelike nanoribbons

Edge states in narrow quasi two-dimensional nanostructures determine, to a large extent, their electric, thermoelectric and magnetic properties. Non-magnetic edge states may quite often lead to topological insulator type behavior. However another scenario develops when the zigzag edges are magnetic and the time reversal symmetry is broken. In this work we report on the electronic band structure modifications, electrical conductance and thermoelectric properties of narrow zigzag nanoribbons with spontaneously magnetized edges. Theoretical studies based on the Kane-Mele- Hubbard tight-binding model show that for silicene, germanene and stanene both the Seebeck coefficient and the thermoelectric power factor are strongly enhanced for energies close to the charge neutrality point. Perpendicular gate voltage lifts the spin degeneracy of energy bands in the ground state with antiparallel magnetized zigzag edges and makes the electrical conductance significantly spin-polarized. Simultaneously the gate voltage worsens the thermoelectric performance. Estimated room-temperature figures of merit for the aforementioned nanoribbons can exceed a value of 3 if phonon thermal conductances are adequately reduced.

Spinless hourglass nodal-line semimetals

Nodal-line semimetals, one of the topological semimetals, have degeneracy along nodal lines where the band gap is closed. In many cases, the nodal lines appear accidentally, and in such cases it is impossible to determine whether the nodal lines appear or not, only from the crystal symmetry and the electron filling. In this paper, for spinless systems, we show that in specific space groups at $4N+2$ fillings ($8N+4$ fillings including the spin degree of freedom), presence of the nodal lines is required regardless of the details of the systems. Here, the spinless systems refer to crystals where the spin-orbit coupling is negligible and the spin degree of freedom can be omitted because of the SU(2) spin degeneracy. In this case the shape of the band structure around these nodal lines is like an hourglass, and we call this a spinless hourglass nodal-line semimetal. We construct a model Hamiltonian as an example and we show that it is always in the spinless hourglass nodal-line semimetal phase even when the model parameters are changed without changing the symmetries of the system. We also establish a list of all the centrosymmetric space groups, under which spinless systems always have hourglass nodal lines, and illustrate where the nodal lines are located. We propose that Al$_3$FeSi$_2$, whose space-group symmetry is Pbcn (No. 60), is one of the nodal-line semimetals arising from this mechanism.

A nonmagnetic topological Weyl semimetal in quaternary Heusler compound CrAlTiV

We predict that the paramagnetic state of inversion-breaking quaternary Heusler alloy CrVTiAl is a Weyl semimetal candidate. There are 24 Weyl nodes (WN) appearing at the same energy in the first Brillouin zone without spin-orbit coupling (SOC). One WN splits into a pair of Weyl nodes (WN1 and WN2) of the same chirality when considering SOC because SOC removes the spin degeneracy. Clear surface state Fermi arc structures on the (111) surface are also obtained. The formation mechanism of the Weyl nodes is independent of point symmetries, i.e., the number and chirality of Weyl nodes are not affected when the point symmetries are broken slightly.

Defect-induced large spin-orbit splitting in monolayer PtSe2

The effect of spin-orbit coupling (SOC) on the electronic properties of monolayer (ML) PtSe$_2$ is dictated by the presence of the crystal inversion symmetry to exhibit spin polarized band without characteristic of spin splitting. Through fully-relativistic density-functional theory calculations, we show that large spin-orbit splitting can be induced by introducing point defects. We calculate stability of native point defects such as a Se vacancy (V$_{\texttt{Se}}$), a Se interstitial (Se$_{i}$), a Pt vacancy (V$_{\texttt{Pt}}$), and a Pt interstitial (Pt$_{i}$), and find that both the V$_{\texttt{Se}}$ and Se$_{i}$ have the lowest formation energy. We also find that in contrast to the Se$_{i}$ case exhibiting spin degeneracy in the defect states, the large spin-orbit splitting up to 152 meV is observed in the defect states of the V$_{\texttt{Se}}$. Our analyses of orbital contributions to the defect states show that the large spin splitting is originated from the strong hybridization between Pt-$d_{x{^2}+y{^2}}+d_{xy}$ and Se-$p_{x}+p_{y}$ orbitals. Our study clarifies that the defects play an important role in the spin splitting properties of the PtSe$_2$ ML, which is important for designing future spintronic devices.

Magnetotransport in heterostructures of transition metal dichalcogenides and graphene

We use a van-der-Waals pickup technique to fabricate different heterostructures containing WSe$_2$(WS$_2$) and graphene. The heterostructures were structured by plasma etching, contacted by one-dimensional edge contacts and a topgate was deposited. For graphene/WSe$_2$/SiO$_2$ samples we observe mobilities of $\sim$12 000 cm$^2$/Vs. Magnetic field dependent resistance measurements on these samples show a peak in the conductivity at low magnetic field. This dip is attributed to the weak antilocalization (WAL) effect, stemming from spin-orbit coupling. Samples where graphene is encapsulated between WSe$_2$(WS$_2$) and hBN show a much higher mobility of up to $\sim$120 000 cm$^2$/Vs. However, in these samples no WAL peak can be observed. We attribute this to a transition from the diffusive to the quasiballistic regime. At low magnetic field a resistance peak appears, which we ascribe to a size effect, due to boundary scattering. Shubnikov-de Haas oscillations in fully encapsulated samples show all integer filling factors, due to complete lifting of the spin and valley degeneracy.

Electronic structure and topological properties of centrosymmetric MoAs2/WAs2 from first principles

We investigate the electronic structure of group VI-B transition metal di-arsenides (TAs2, T = Mo, W). By comparing the formation energies, the centrosymmetric di-arsenides compounds are energetically more stable, in contrast to the di-phosphorides (MoP2/WP2). Both compounds can be well described by a two-band model with a pair of well-separated electron/hole bands. The electron/hole carrier density is nearly compensated in MoAs2 (|ne − nh|/nh < 1%). The {{mathscr{Z}}}_{2} classification for all partially occupied bands are topologically strong (1;001), and therefore robust surface states are expected in these materials. Using the adaptive K-mesh method, no energy degenerate state could be found except the spin degeneracy in the whole Brillouin zone, excluding the possibility of intrinsic Dirac or Weyl points near the Fermi level in the system.

Gap states and edge properties of rectangular graphene quantum dot in staggered potential

We investigate edge properties of a gapful rectangular graphene quantum dot in a staggered potential. In such a system gap states with discrete and closely spaced energy levels exist that are spatially located on the left or right zigzag edge. We find that, although the bulk states outside the energy gap are nearly unaffected, spin degeneracy of each gap state is lifted by the staggered potential. We have computed the occupation numbers of spin-up and -down gap states at various values of the strength of the staggered potential. The electronic and magnetic properties of the zigzag edges depend sensitively on these numbers. We discuss the possibility of applying this system as a single electron spintronic device.

Optical and microwave control of germanium-vacancy center spins in diamond

A solid-state system combining a stable spin degree of freedom with an efficient optical interface is highly desirable as an element for integrated quantum optical and quantum information systems. We demonstrate a bright color center in diamond with excellent optical properties and controllable electronic spin states. Specifically, we carry out detailed optical spectroscopy of a Germanium Vacancy (GeV) color center demonstrating optical spectral stability. Using an external magnetic field to lift the electronic spin degeneracy, we explore the spin degree of freedom as a controllable qubit. Spin polarization is achieved using optical pumping, and a spin relaxation time in excess of 20 $\mu$s is demonstrated. Optically detected magnetic resonance (ODMR) is observed in the presence of a resonant microwave field. ODMR is used as a probe to measure the Autler-Townes effect in a microwave-optical double resonance experiment. Superposition spin states were prepared using coherent population trapping, and a pure dephasing time of about 19 ns was observed. Prospects for realizing coherent quantum registers based on optically controlled GeV centers are discussed.

Valence band energy spectrum of HgTe quantum wells with an inverted band structure

The energy spectrum of the valence band in $\mathrm{HgTe}/{\mathrm{Cd}}_{x}{\mathrm{Hg}}_{1\ensuremath{-}x}\mathrm{Te}$ quantum wells of a width ($8--20$) nm has been studied experimentally by magnetotransport effects and theoretically in the framework of a four-band $kP$ method. Comparison of the Hall density with the density found from a period of the Shubnikov--de Haas (SdH) oscillations clearly shows that the degeneracy of states of the top of the valence band is equal to 2 at the hole density $p&lt;5.5\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Such degeneracy does not agree with the calculations of the spectrum performed within the framework of the four-band $kP$ method for symmetric quantum wells. These calculations show that the top of the valence band consists of four spin-degenerate extremes located at $k\ensuremath{\ne}0$ (valleys) which gives the total degeneracy $K=8$. It is shown that taking into account the ``mixing of states'' at the interfaces leads to the removal of the spin degeneracy that reduces the degeneracy to $K=4$. Accounting for any additional asymmetry, for example, due to the difference in the mixing parameters at the interfaces, the different broadening of the boundaries of the well, etc., leads to reduction of the valleys degeneracy, making $K=2$. It is noteworthy that for our case twofold degeneracy occurs due to degeneracy of two single-spin valleys. The hole effective mass (${m}_{h}$) determined from analysis of the temperature dependence of the amplitude of the SdH oscillations shows that ${m}_{h}$ is equal to $(0.25\ifmmode\pm\else\textpm\fi{}0.02){m}_{0}$ and weakly increases with the hole density. Such a value of ${m}_{h}$ and its dependence on the hole density are in a good agreement with the calculated effective mass.

Quantum correlations at infinite temperature: The dynamical Nagaoka effect

Do quantum correlations play a role in high temperature dynamics of many-body systems? A common expectation is that thermal fluctuations lead to fast decoherence and make dynamics classical. In this paper, we provide a striking example of a single particle created in a featureless, infinite temperature spin bath which not only exhibits non-classical dynamics but also induces strong long-lived correlations between the surrounding spins. We study the non-equilibrium dynamics of a hole created in a fermionic or bosonic Mott insulator in the atomic limit, which corresponds to a degenerate spin system. In the absence of interactions, the spin correlations arise purely from quantum interference, and the correlations are both antiferromagnetic and ferromagnetic, in striking contrast to the equilibrium Nagaoka effect. These results are relevant for several condensed matter spin systems, and should be observable using state of the art bosonic or fermionic quantum gas microscopes.

Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement

The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals’ in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present article, with potent applications in the field of quantum information processing, provide a deeper understanding of the electronic von Neumann entropy and hybrid entanglement that occurs in two-dimensional nanodots.

Negative magnetoresistance in Weyl semimetals NbAs and NbP: Intrinsic chiral anomaly and extrinsic effects

Chiral anomaly induced negative magnetoresistance (NMR) has been widely used as a critical transport evidence on the existence of Weyl fermions in topological semimetals. In this mini review, we discuss the general observation of the NMR phenomena in non-centrosymmetric NbP and NbAs. We show that NMR can be contributed by intrinsic chiral anomaly of Weyl fermions and/or extrinsic effects, such as superimposition of Hall signals, field-dependent inhomogeneous current flow in the bulk, i.e. current jetting, and weak localization (WL) of coexistent trivial carriers. Such WL controlled NMR is heavily dependent on sample quality, and is characterized by pronounced crossover from positive to negative MR growth at elevated temperatures, as a result of the competition between the phase coherence time and the spin-orbital scattering constant of the bulk trivial pockets. Thus, the correlation of NMR and chiral anomaly needs to be scrutinized, without the support of other complimentary techniques. Due to the lifting of spin degeneracy, the spin orientations of Weyl fermions are either parallel or antiparallel to the momentum, a unique physical property known as helicity. The conservation of helicity provides strong protection for the transport of Weyl fermions, which can only be effectively scattered by magnetic impurities. Chemical doping of magnetic and non-magnetic impurities are thus more convincing in probing the existence of Weyl fermions than the NMR method.

Effect of excitation power on voltage induced local magnetization dynamics in an ultrathin CoFeB film

Voltage or electric field induced magnetization dynamics promises low power spintronics devices. For successful operation of some spintronics devices such as magnetic oscillators and magnetization switching devices a clear understanding of nonlinear magnetization dynamics is required. Here, we report a detailed experimental and micromagnetic simulation study about the effect of excitation power on voltage induced local magnetization dynamics in an ultrathin CoFeB film. Experimental results show that the resonance line-width and frequency remains constant, whereas cone angle of the magnetization precession increases linearly with square-root of excitation power below threshold value, known as linear excitation regime. Above threshold power, the dynamics enters into nonlinear regime where resonance line-width monotonically increases and resonance frequency monotonically decreases with increasing excitation power. Simulation results reveal that a strong nonlinear and incoherent magnetization dynamics are observed in our experiment above the threshold power which reduces dynamic magnetic signal by suppressing large cone angle of magnetization precession. Moreover, a significant transfer of spin angular momentum from uniform FMR mode to its degenerate spin waves outside of excitation area further restrict the cone angle of precession within only few degrees in our device. Our results will be very useful to develop all-voltage-controlled spintronics devices.

Unconventional superconductivity and anomalous response in hole-doped transition metal dichalcogenides

Two-dimensional transition metal dichalcogenides entwine interaction, spin-orbit coupling, and topology. Hole-doped systems lack spin degeneracy: states are indexed with spin and valley specificity. This unique structure offers new possibilities for correlated phases and phenomena. We realize an unconventional superconducting pairing phase which is an equal mixture of a spin singlet and the $m = 0$ spin triplet. It is stable against large in-plane magnetic fields, and its topology allows quasiparticle excitations of net nonzero Berry curvature via pair-breaking circularly polarized light.

Topological superconductivity in monolayer transition metal dichalcogenides

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological because of the near spin degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favours two topological superconducting states: interpocket paired state with Chern number 2 and intrapocket paired state with finite pair momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device-friendly platform of monolayer TMDs.

Weakly Anisotropic Noncentrosymmetric Superconductors with Radial Line Nodes and the Origin of the Anomalous Thermodynamic Data

In noncentrosymmetric superconductors (NCSs), the inversion symmetry (IS) is most commonly broken by an antisymmetric spin-orbit coupling (SOC) removing the spin degeneracy and splitting the Fermi surface (FS) into two branches. A two component condensate is then produced with a doublet pair potential mixing an even singlet and an odd triplet. When the triplet and the singlet strengths are comparable, the pair potential can have rich nodes. The angular line nodes (ALNs) are associated with strong anisotropy and they are widely studied in the literature. When the anisotropy is not strong, they can be replaced by other types of nodes in closed or open forms affecting the low temperature properties. Here, we focus on the weakly anisotropic case and the line nodes in the superconducting plane which become circular in the limit of full isotropy. We study the topology of these radial line nodes (RLNs) and show that it is characterized by the $Z_2$ classification similar to the Quantum-Spin-Hall Insulators. From the thermodynamical perspective, the RLNs cause, even in the topological phases, an exponentially suppressed low temperature behaviour which can be mistaken by nodeless s-wave pairing, thus, providing an explanation to a number of recent experiments with contraversial pairing symmetries. In the rare case when the RLN is on the Fermi surface, the exponential suppression is replaced by a linear temperature dependence. The RLNs are difficult to detect, and for this reason, they may have escaped experimental attention. We demonstrate that Andreev conductance measurements with clean interfaces can efficiently probe the weakly anisotropic samples where the RLNs are expected to be found.

Generation of spin polarized currents with coherent trapping in magnetic semiconductors

A semiconductor heterostructure consisting of two quantum wells, one of them magnetically doped, is proposed for the generation of spin currents by two lasers tuned at the resonances formed between two lowest energy states (1 and 2) and the continuum (3), which are set by design to be in a like configuration. By numerically simulating the proposed structure under the action of the laser fields, we are able to observe the formation of a quasi-dark state near the resonance. The structure’s design has been idealized as to place state 2 in the magnetically doped quantum-well, where a constant magnetic field breaks the electronic spin degeneracy, leading to the giant Zeeman splitting. This ensures that only one of the electronic spins is driven into a dark resonance, thus blocking it from escaping the system. The other spin is free to escape, so that a spin polarized photocurrent is generated. The polarization can be switched by changing the frequency of the controlling laser. Since this kind of trapping is based on quantum interference, the switching times are expected to be fast. In our simulation, we do not simplify the structure down to level modeling, rather we simulate the full structure under time dependent oscillating laser fields and then identify the signatures that indicate a three-level like behavior. We based our search for the structure on real doping parameters found in real materials used in the literature, however the idea relies on the potential profiles studied, and the presence of the giant splitting, regardless of the underlying material that may be used.

Superconducting instability of a non-centrosymmetric system

The Fermi gas approach to the weak-coupling superconductivity in the non-centrosymmetric systems lead to a conclusion of an approximately spin-orbit coupling independent critical temperature of the singlet states as well as the triplet states defined by the order parameter aligned with the antisymmetric spin-orbit coupling vector. We indicate that the above results follow from a simplified approximation of a density of states by a constant Fermi surface value. Such a scenario does not properly account for the spin-split quasiparticle energy spectrum and reduces the spin-orbit coupling influence on superconductivity to the bare pair-breaking effect of a lifted spin degeneracy. Applying the tight-binding model, which captures the primary features of the spin-split energy band, i.e., its enhanced width and the spin-orbit coupling induced redistribution of the spectral weights in the density of states, we calculate the critical temperature of a non-centrosymmetric superconductor. We report a general tendency of the critical temperature to be suppressed by the antisymmetric spin-orbit coupling. We indicate that, the monotonic decrease of the critical temperature may be altered by the spin-orbit coupling induced van Hove singularities which, when driven to the Fermi level, generate maxima in the phase diagram. Extending our considerations to the intermediate-coupling superconductivity we point out that the spin-orbit coupling induced change of the critical temperature depends on the structure of the electronic energy band and both – the strength and symmetry of the pair potential. Finally, we discuss the mixed singlet-triplet state superconducting instability and establish conditions concerning the symmetry of the singlet and triplet counterparts as well as the range of the spin-orbit coupling energy which make such a phase transition possible.