Two-dimensional (2D) materials have attracted much recent attention because they exhibit various distinct intrinsic properties/functionalities, which are, however, usually not interchangeable. Interestingly, here we propose a generic approach to convert 2D semiconductors, which are amply abundant, to 2D topological insulators (TIs), which are less available, via selective atomic adsorption and strain engineering. The approach is underlined by an orbital design principle that involves introducing an extrinsic s-orbital state into the intrinsic sp-bands of a 2D semiconductor, so as to induce s-p band inversion for a TI phase, as demonstrated by tight-binding model analyses. Remarkably, based on first-principles calculations, we apply this approach to convert the semiconducting monolayer CuS and CuTe into a TI by adsorbing Na and K respectively with a proper s-level energy, and CuSe into a TI by adsorbing a mixture of Na and K with a tuned s-level energy or by adsorbing either Na or K on a strained CuSe with a tuned p-level valence band edge. Our findings open a new door to the discovery of TIs by a predictive materials design, beyond finding a preexisting 2D TI.
Chu et al. recently reported extensive results of local density approximation (LDA) and of four (4) different Green function and dressed Coulomb (GW) approximation calculations of electronic properties of several semiconductors and insulators [Phys. Rev. B 93, 125210 (2016)].
A previously unknown effect-giant spatial redistribution of the electric field strength in a crystal under illumination of the structure - was discovered and investigated in real photoresistors on high-resistivity (semi-insulating) semiconductor CdTe crystals (in metal-thin insulator- semiconductor-thin insulator -metal structures). A new concept is proposed for photoelectric phenomena in high- resistivity semiconductor crystals. The concept is based on the idea that the redistribution of the field under such conditions that the carrier lifetime remains unchanged under illumination plays a det…
We have succeeded in growing ferromagnetic metals (Co, Fe, and NiFe)/ Al2O3/ AlGaAs heterostructures with homogeneous and flat interfaces. The electro-luminescence (EL) from the light emitting diode (LED) consisting of the metal/insulator/semiconductor (MIS) structure depends on the magnetization direction of the ferromagnetic electrode at room temperature. This fact shows that a spin-injection from the ferromagnetic metal to the semiconductor is achieved. The spin-injection efficiency is estimated to be the order of 1 % at room temperature.
Here we demonstrate that water-infiltrated nanoporous glass electrically switches an oxide semiconductor from an insulator to metal. We fabricated the field effect transistor structure on an oxide semiconductor, SrTiO3, using 100%-water-infiltrated nanoporous glass - amorphous 12CaO*7Al2O3 - as the gate insulator. For positive gate voltage, electron accumulation, water electrolysis and electrochemical reduction occur successively on the SrTiO3 surface at room temperature, leading to the formation of a thin (~3 nm) metal layer with an extremely high electron concentration of 10^15-10^16 cm^-2, …
Diluted ferromagnetic III-V semiconductors typically show a high degree of compensation. Compensation is connected to the presence of comparable densities of charged defects of either sign. This naturally leads to the development of strong correlations between defect positions during growth and annealing. We show that these correlations are required to understand the experimentally observed transport and magnetic properties as well as the persistence of the energy gap upon doping with magnetic ions.
We present a fully parameter-free density-functional approach for the accurate description of optical absorption spectra of insulators, semiconductors and metals. We show that this can be achieved within time-dependent current-density-functional theory using a simple dynamical polarization functional. We derive this functional from physical principles that govern optical spectra. Our method is truly predictive because not a single parameter is used. In particular, we do not use an \textit{ad-hoc} material-dependent broadening parameter to compare theory to experiment as is usually done. Our ap…
Spin injection using ferromagnetic semiconductors at room temperature is a building block for the realization of spin-functional semiconductor devices. Nevertheless, this has been very challenging due to the lack of reliable room-temperature ferromagnetism in well-known group IV and III-V based semiconductors. Here, we demonstrate room-temperature spin injection by using spin pumping in a (Ga,Fe)Sb / BiSb heterostructure, where (Ga,Fe)Sb is a ferromagnetic semiconductor (FMS) with high Curie temperature (TC) and BiSb is a topological insulator (TI). Despite the very small magnetization of (Ga,…
We demonstrate highly efficient spin injection at low and room temperature in an AlGaAs/GaAs semiconductor heterostructure from a CoFe/AlOx tunnel spin injector. We use a double-step oxide deposition for the fabrication of a pinhole-free AlOx tunnel barrier. The measurements of the circular polarization of the electroluminescence in the Oblique Hanle Effect geometry reveal injected spin polarizations of at least 24% at 80K and 12% at room temperature.
We investigate the metal-insulator transition occurring in semiconductors with magnetic impurities when lowering temperature. In contrast to the usually considered percolation transition in the non-uniform medium induced by the localization of charge carriers in the fluctuating \emph{electric} potential, the studied transition is connected with their localization in the fluctuating \emph{magnetic} potential produced by magnetized impurities (more accurately - in the combined fluctuating potential). When decreasing temperature, the magnetization of magnetic impurities in the semiconductor becom…
We present an analytical study of the spatial decay rate $γ$ of the one-particle density matrix $ρ(\vec r,\vec r')\sim\exp(-γ|\vec r-\vec r'|)$ for systems described by single particle orbitals in periodic potentials in arbitrary dimensions. This decay reflects electronic locality in condensed matter systems and is also crucial for O(N) density functional methods. We find that $γ$ behaves contrary to the conventional wisdom that generically $γ\propto\sqrtΔ$ in insulators and $γ\propto\sqrt{T}$ in metals, where $Δ$ is the direct band gap and $T$ the temperature. Rather, in semiconductors $γ\pro…
Topological phase transitions between a conventional insulator and a state of matter with topological properties have been proposed and observed in mercury telluride - cadmium telluride quantum wells. We show that a topological state can be induced in such a device, initially in the trivial phase, by irradiation with microwave frequencies, without closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. The velocity of the edge states can be tuned by adjusting the intensity of the microwave radiation. We discuss th…
We show that a semiconductor thin film can acquire a non-trivial spin texture due to the proximity effect induced by a topological insulator. The effect stems from coupling to the topological surface states and is present even when the insulator is doped. We propose a semiconductor/topological insulator heterostructure as a device that allows measuring interface properties and probing surface states in uncompensated samples. We also find that the topological insulator surface modes can be significantly broadened and shifted by the presence of metallic contacts.
Two-dimensional (2D) topological crystalline insulators (TCIs) were recently predicted in thin films of the SnTe class of IV-VI semiconductors, which can host metallic edge states protected by mirror symmetry. As thickness decreases, quantum confinement effect will increase and surpass the inverted gap below a critical thickness, turning TCIs into normal insulators. Surprisingly, based on first-principles calculations, here we demonstrate that (001) monolayers of rocksalt IV-VI semiconductors XY (X=Ge, Sn, Pb and Y= S, Se, Te) are 2D TCIs with the fundamental band gap as large as 260 meV in mo…
Tuning the spin-orbit coupling strength via foreign element doping and/or modifying bonding strength via strain engineering are the major routes to convert normal insulators to topological insulators. We here propose an alternative strategy to realize topological phase transition by tuning the orbital level. Following this strategy, our first-principles calculations demonstrate that a topological phase transition in some cubic perovskite-type compounds CsGeBr$_3$ and CsSnBr$_3$ could be facilitated by carbon substitutional doping. Such unique topological phase transition predominantly results …
We show that by nullifying the short-wave response to the long-wave excitation (local-field-effects), the adiabatic time-dependent density-functional theory (TDDFT) of optics of semiconductors and insulators can be brought into excellent agreement with experiment. This indicates that the wing elements [($\Gv,\0v)$ and $(\0v,\Gv)$, $\Gv\ne\0v$] of both the Kohn-Sham (KS) density-response function $χ^s$ and the exchange-correlation kernel $f^{xc}$ are greatly overestimated by the existing approximations to the static DFT and TDDFT, respectively, to the extent that zero is a better approximation …
We have performed density functional calculations using a range of local and semi-local as well as hybrid density functional approximations of the structure and elastic constants of 18 semiconductors and insulators. We find that most of the approximations have a very small error in the lattice constants, of the order of 1\%, while the error in the elastic constants and bulk modulus are much larger, at about 10\%. In addition, we find that the error in the elastic constants, $c_{ij}$, are larger compared to the error in the bulk modulus. Depending on the functional and which error estimate that…
The unidirectional magnetoresistance (UMR) is one of the most complex spin-dependent transport phenomena in ferromagnet/non-magnet bilayers, which involves spin injection and accumulation due to the spin Hall effect (SHE) or Rashba-Edelstein effect (REE), spin-dependent scattering, and magnon scattering at the interface or in the bulk of the ferromagnet. While UMR in metallic bilayers has been studied extensively in very recent years, its magnitude is as small as 10$^-$$^5$, which is too small for practical applications. Here, we demonstrate a giant UMR effect in a heterostructure of BiSb topo…
Over the past several years, the inherent scaling limitations of electron devices have fueled the exploration of high carrier mobility semiconductors as a Si replacement to further enhance the device performance. In particular, compound semiconductors heterogeneously integrated on Si substrates have been actively studied, combining the high mobility of III-V semiconductors and the well-established, low cost processing of Si technology. This integration, however, presents significant challenges. Conventionally, heteroepitaxial growth of complex multilayers on Si has been explored. Besides compl…
We demonstrate that first-principles based adiabatic continuation approach is a very powerful and efficient tool for constructing topological phase diagrams and locating non-trivial topological insulator materials. Using this technique, we predict that the ternary intermetallic series Li$_2M'X$ where $M'$=Cu, Ag, Au, or Cd, and $X$=Sb, Bi, or Sn, hosts a number of topological insulators with remarkable functional variants and tunability. We also predict that several III-V semimetallic compounds are topologically non-trivial. We construct a topological phase diagram in the parameter space of th…
Electron correlation in semiconductors and insulators via symbolic regression
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）；Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）
We study the magnetic susceptibility of a layered semiconductor BiTeI with giant Rashba spin splitting both theoretically and experimentally to explore its orbital magnetism. Apart from the core contributions, a large temperature-dependent diamagnetic susceptibility is observed when the Fermi energy E_F is near the crossing point of the conduction bands, while the susceptibility turns to be paramagnetic when E_F is away from it. These features are consistent with first-principles calculations, which also predict an enhanced orbital magnetic susceptibility with both positive and negative signs …
We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Though the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional si…
We report a numerical analysis of Anderson localization in a model of a doped semiconductor. The model incorporates the disorder arising from the random spatial distribution of the donor impurities and takes account of the electron-electron interactions between the carriers using density functional theory in the local density approximation. Preliminary results suggest that the model exhibits a metal-insulator transition.
A self-consistent model of bipolar charge-carrier injection and transport processes in a semiconductor/insulator/conductor system is developed which incorporates space-charge effects in the description of the injection process. The amount of charge-carriers injected is strongly determined by the energy barrier emerging at the contact, but at the same time the electrostatic potential generated by the injected charge-carriers modifies the height of this injection barrier itself. In our model, self-consistency is obtained by assuming continuity of the electric displacement and of the electrochemi…
We use a random gap model to describe a metal-insulator transition in three-dimensional semiconductors due to doping and find a conventional phase transition, where the effective scattering rate is the order parameter. Spontaneous symmetry breaking results in metallic behavior, whereas the insulating regime is characterized by the absence of spontaneous symmetry breaking. The transition is continuous for the average conductivity with critical exponent equal to 1. Away from the critical point the exponent is roughly 0.6, which may explain experimental observations of a crossover of the exponent…
The generalized boundary conditions for the envelope wave function that take into account the real structure of an interface were used to investigate the hole spectrum of the semiconductor quantum dot embedded in an insulator matrix. An essential influence of the interface levels, which could exist at the top of the valence band, on the hole spectrum has been demonstrated. It is found that usually applied boundary conditions, wherein all components of the envelope wave function vanish at the interface, can be used only in the absence of the interface levels close to the band edge.
The great obstacle for practical applications of the quantum anomalous Hall (QAH) effect is the lack of suitable QAH materials (Chern insulators) with large non-trivial band gap, room-temperature magnetic order and high carrier mobility. The Nickle chloride (NiCl3) monolayer characteristics are investigated herein using first-principles calculations. It is reported that NiCl3 monolayers constitute a new class of Dirac materials with Dirac spin-gapless semiconducting and high-temperature ferromagnetism (~400K). Taking into account the spin-orbit coupling, the NiCl3 monolayer becomes an intrinsi…
Lead (Pb) halide perovskites have achieved great success in recent years due to their excellent optoelectronic properties, which is largely attributed to the lone-pair s orbital-derived antibonding states at the valence band edge. Guided by the key band-edge orbital character, a series of ns2-containing (i.e., Sn2+, Sb3+, Bi3+) Pb-free perovskite alternatives have been explored as potential photovoltaic candidates. On the other hand, based on the band-edge orbital components (i.e., M2+ s and p/X- p orbitals), a series of strategies have been proposed to optimize their optoelectronic properties…
The effect of disorder on transport and magnetization in ferromagnetic III-V semiconductors, in particular (Ga,Mn)As, is studied theoretically. We show that Coulomb-induced correlations of the defect positions are crucial for the transport and magnetic properties of these highly compensated materials. We employ Monte Carlo simulations to obtain the correlated defect distributions. Exact diagonalization gives reasonable results for the spectrum of valence-band holes and the metal-insulator transition only for correlated disorder. Finally, we show that the mean-field magnetization also depends c…
Zero dimensional graphene quantum dots (GQDs) exhibit interesting physical and chemical properties due to the edge effect and quantum confinement. As the number of carbon atoms in edge is more than on basal plane, GQDs are more reactive. Room temperature XRD pattern confirms the formation of the GQDs. UV-Visible spectra confirm that GQDs show optical absorption in the visible region. The emission peaks in the photoluminescence spectra are red shifted with the increase of excitation wavelength. Dynamic light scattering (DLS) analysis shows that the average size of the particles is found to be 6…
Significant field emission is found theoretically possible from nanorods of semiconductors of wide energy band gaps. If the nanorod has a thin surface layer containing a large number of localized states, a part of nanorod can exhibit an insulator-to-semimetal transition under high enough fields of direction parallel to its axis, so that field emission occurs at the apex of the metal like tip. The field emission property of silicon carbide nanorods is studied as an example and found to be in qualitative agreement with the experimental findings.
The role of orbital ordering on metal-insulator transition of transition-metal oxides is investigated by the cluster self-consistent field approach in the strong correlation regime. A clear dependence of the insulating gap on the orbital order parameter is found in the single-particle excitation spectra. The thermal fluctuation drives the orbital order-disorder transition, diminishes the gap and leads to the metal-insulator transition. The interplay between spins and orbits results in unusual temperature dependence of the orbital polarization in the orbital insulator, which can be seen in the …
Point defects have a strong impact on the performance of semiconductor and insulator materials used in technological applications, spanning microelectronics to energy conversion and storage. The nature of the dominant defect types, how they vary with processing conditions, and their impact on materials properties are central aspects that determine the performance of a material in a certain application. This information is, however, difficult to access directly from experimental measurements. Consequently, computational methods, based on electronic density functional theory (DFT), have found wi…
The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expressio…
Motivated by the fact that septuple-atomic-layer MnBi$_2$Te$_4$ can be structurally viewed as the combination of double-atomic-layer MnTe intercalating into quintuple-atomic-layer Bi$_2$Te$_3$, we present a general approach of constructing twelve septuple-atomic-layer $α_i$- and $β_i$-$MA_2Z_4$ monolayer family (\emph{i} = 1 to 6) by intercalating MoS$_2$-type $MZ$$_2$ monolayer into InSe-type A$_2$Z$_2$ monolayer. Besides reproducing the experimentally synthesized $α_1$-MoSi$_2$N$_4$, $α_1$-WSi$_2$N$_4$ and $β_5$-MnBi$_2$Te$_4$ monolayer materials, another 66 thermodynamically and dynamically…
To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration $n_c$ for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of p…
We point out that the effective channel for the interfacial thermal conductance, the inverse of Kapitza resistance, of metal-insulator/semiconductor interfaces is governed by the electron-phonon interaction mediated by the surface states allowed in a thin region near the interface. Our detailed calculations demonstrate that the interfacial thermal conductance across Pb/Pt/Al/Au-diamond interfaces are only slightly different among these metals, and reproduce well the experimental results of the interfacial thermal conductance across metal-diamond interfaces observed by Stoner et al. [Phys. Rev.…
The dispersion law of plasmons running along thin wires with radius $a$ is known to be practically linear. We show that in a wire with a dielectric constant $κ$ much larger than that of its environment $κ_e$, such dispersion law crosses over to a dispersionless three-dimensional-like law when the plasmon wavelength becomes shorter than the length $(a/2) \sqrt{(κ/κ_e)\ln(κ/2κ_e)}$ at which the electric field lines of a point charge exit from the wire to the environment. This happens both in trivial semiconductor wires and wires of three-dimensional topological insulators.
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion. We show that the appearance of corner states does not depend solely on the cry…
We discuss a new mechanism of orbital ordering, which in charge transfer insulators is more important than the usual exchange interactions and which can make the very type of the ground state of a charge transfer insulator, i.e. its orbital and magnetic ordering, different from that of a Mott-Hubbard insulator. This purely electronic mechanism allows us to explain why orbitals in Jahn-Teller materials typically order at higher temperatures than spins, and to understand the type of orbital ordering in a number of materials, e.g. K_2CuF_4, without invoking the electron-lattice interaction.
Hybrid semiconductor-ferromagnetic insulator heterostructures are interesting due to their tunable electronic transport, self-sustained stray field and local proximitized magnetic exchange. In this work, we present lattice matched hybrid epitaxy of semiconductor - ferromagnetic insulator InAs/EuS heterostructures and analyze the atomic-scale structure as well as their electronic and magnetic characteristics. The Fermi level at the InAs/EuS interface is found to be close to the InAs conduction band and in the bandgap of EuS, thus preserving the semiconducting properties. Both neutron and X-ray …
We consider the effect of the Rashba spin-orbital interaction and space charge in a ferromagnet-insulator/semiconductor/insulator-ferromagnet junction where the spin current is severely affected by the doping, band structure and charge screening in the semiconductor. In diffusion region, if the the resistance of the tunneling barriers is comparable to the semiconductor resistance, the magnetoresistance of this junction can be greatly enhanced under appropriate doping by the co-ordination between the Rashba effect and screened Coulomb interaction in the nonequilibrium transport processes within…
We performed optical-pump terahertz-probe measurements of a Mott insulator YTiO$_{3}$ and a band semiconductor Si using a laser diode (1.47 eV) and a femtosecond pulse laser (1.55 eV). Both samples possess long energy-relaxation times (1.5 ms for YTiO$_{3}$ and 15 $μ$s for Si); therefore, it is possible to extract terahertz complex conductivities of photoinduced carriers under equilibrium. We observed highly contrasting behavior - Drude conductivity in Si and localized conductivity possibly obeying the Jonscher law in YTiO$_{3}$. The carrier number at the highest carrier-concentration layer in…
The recent discovery of topological insulators with exotic metallic surface states has garnered great interest in the fields of condensed matter physics and materials science. A number of spectacular quantum phenomena have been predicted when the surface states are under the influence of magnetism and superconductivity, which could open up new opportunities for technological applications in spintronics and quantum computing. To achieve this goal, material realization of topological insulators with desired physical properties is of crucial importance. Based on first-principles calculations, her…
We study steady-states of semiconductor nanowires subjected to strong resonant time-periodic drives. The steady-states arise from the balance between electron-phonon scattering, electron-hole recombination via photo-emission, and Auger scattering processes. We show that tuning the strength of the driving field drives a transition between an electron-hole metal (EHM) phase and a Floquet insulator (FI) phase. We study the critical point controlling this transition. The EHM-to-FI transition can be observed by monitoring the presence of peaks in the density-density response function which are asso…
Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum Hall effect in that all the states below the gap contribute and there occurs no dissipation. However the spin Hall conductance is not quan…
Topological crystalline insulators (TCI) are new topological phases of matter protected by crystal symmetry of solids. Recently, the first realization of TCI has been predicted and observed in IV-VI semiconductor SnTe and related alloys Pb_{1-x}Sn_{x}(Te, Se). By combining k.p theory and band structure calculation, we present a unified approach to study topological surface states on various crystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.p Hamiltonian for topological surface states from electronic structure of the bulk, thereby providing a microscopic understanding of b…
We present evidence that the insulator to metal transition in (La,Ca)MnO3 near x~0.2 is driven by the suppression of coherent Jahn-Teller distortions, originating from d type orbital ordering. The orbital ordered state is characterised by large long-range Q2 distortions below To*-o'. Above To*-o' we find evidence for coexistence between an orbital-ordered and -disordered state. This behaviour is discussed in terms of electronic phases of an orbital ordered insulating and orbital-disordered metallic states.
The synthesis of self-organized quantum dots (QD's) can be achieved through bottom up layer by layer deposition processes as chemical vapor deposition (CVD) or physical vapor deposition (PVD). However, QD's may also be synthesized via sol-gel route, which involves a spontaneous evolution from thin films to discrete QD's without further deposition. The aim of the paper is to discuss and compare the physical phenomena involved in QD's formation which initiate from thin film surface roughening between PVD-CVD and sol-gel synthesis approaches. We propose two simple physical models which are releva…
Films of ZnO doped with magnetic ions, Mn and Co and, in some cases, with Al have been fabricated with a very wide range of carrier densities. Ferromagnetic behaviour is observed in both insulating and metallic films, but not when the carrier density is intermediate. Insulating films exhibit variable range hopping at low temperatures and are ferromagnetic at room temperature due to the interaction of the localised spins with static localised states. The magnetism is quenched when carriers in the localised states become mobile. In the metallic (degenerate semiconductor) range, robust ferromagne…
We study the temperature dependence of the orbital susceptibility of an excitonic insulator on the basis of a two-band model. It is shown that a drastic change (an anomalous enhancement) in susceptibility as a function of temperature occurs owing to the occurrence of additional orbital susceptibility due to the excitonic gap. We calculate explicitly the temperature dependence of orbital susceptibility for a model of Ta$_2$NiSe$_5$, and show that the result is consistent with experimental results.
Within the ionic Hubbard model, electron correlations transmute the single-particle gap of a band insulator into a Mott gap in the strong correlation limit. However understanding the nature of possible phases in between these two extreme insulating phases remains an outstanding challenge. We find two strongly correlated insulating phases in between the above extremes: (i) The insulating phase just before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons through staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons an…
