The Kondo semiconductor $Yb B_{12}$ exhibits a spin and charge gap of approximately 15 meV. Close to the gap energy narrow dispersive collective excitations were identified by previous inelastic neutron scattering experiments. We present a theoretical analysis of these excitations. Starting from a periodic Anderson model for crystalline electric field (CEF) split 4f states we derive the hybridized quasiparticle bands in slave boson mean-field approximation and calculate the momentum dependent dynamical susceptibility in random phase approximation (RPA). We show that a small difference in the hybridization of the two CEF (quasi-) quartets leads to the appearance of two dispersive spin resonance excitations at the continuum threshold. Their intensity is largest at the antiferromagnetic (AF) zone boundary point and they have an upward dispersion which merges with the continuum less than halfway into the Brillouin zone. Our theoretical analysis explains the most salient features of previously unexplained experiments on the magnetic excitations of $Yb B_{12}$.
A recombination radiation line of real excitons in dense two-dimensional electron gas at the [100] silicon surface is observed in luminescence spectra of metal-oxide-semiconductor (MOS) structures. A new effect of anisotropic paramagnetic reduction of the luminescence line indicates a strong influence of the Kondo correlations on electron paramagnetism of the excitons.
An interplay of the Kondo scattering and exciton effects (d-f Coulomb interaction) in the intermediate valence systems and Kondo lattices is demonstrated to lead to an essential change of the scaling behavior in comparison with the standard Anderson model. In particular, a marginal regime can occur where characteristic fluctuation rate is proportional to flow cutoff parameter. In this regime the "Kondo temperature" itself is strongly temperature dependent which may give a key to the interpretation of controversial experimental data for heavy fermion and related systems.
In the Anderson lattice model for a mixed-valent system, the $d-f$ hybridization can possess a $p$-wave symmetry. The strongly-correlated insulating phase in the mean-field approximation is shown to be a $p$-wave Bose condensate of excitons with a spontaneous lattice deformation. We study the equilibrium and linear response properties across the insulator-metal transition. Our theory supports the empirical correlation between the lattice deformation and the magnetic susceptibility and predicts measurable ultrasonic and high-frequency phonon behavior in mixed-valent semiconductors.
Kondo insulating materials lie outside the usual dichotomy of weakly versus correlated - band versus Mott - insulators. They are metallic at high temperatures but resemble band insulators at low temperatures because of the opening of an interaction induced band gap. The first discovered Kondo insulator (KI) SmB$_6$ has been predicted to form a topological KI (TKI) which mimics a topological insulator at low temperatures. However, since its discovery thermodynamic and transport anomalies have been observed that have defied a theoretical explanation. Enigmatic signatures of collective modes insi…
The compound SmB$_6$ is a Kondo Insulator, where the lowest-energy bulk electronic excitations are spin excitons. It also has surface states that are subjected to strong spin-orbit coupling. It has been suggested that SmB$_6$ is also a topological insulator. Here we show that, despite the absence of time-reversal symmetry breaking and the presence of strong spin-orbit coupling, the chiral spin texture of the Weyl cone is not completely protected. In particular, we show that the spin-exciton mediated scattering produces features in the surface electronic spectrum at energies separated from the …
Using inelastic neutron scattering, we map a 14 meV coherent resonant mode in the topological Kondo insulator SmB6 and describe its relation to the low energy insulating band structure. The resonant intensity is confined to the X and R high symmetry points, repeating outside the first Brillouin zone and dispersing less than 2 meV, with a 5d-like magnetic form factor. We present a slave-boson treatment of the Anderson Hamiltonian with a third neighbor dominated hybridized band structure. This approach produces a spin exciton below the charge gap with features that are consistent with the observ…
The quantum chromodynamics (QCD) Kondo effect is a quantum phenomenon in which heavy quarks ($c$, $b$) exist as impurity particles in quark matter composed of light quarks ($u$, $d$, $s$) at extremely high density. This is analogous to the famous Kondo effect in condensed matter physics. In the present paper, we show theoretically the existence of the "QCD Kondo excitons", i.e., the bound states of light quarks and heavy quarks, as the lowest-excitation modes above the ground state of the quark matter governed by the QCD Kondo effect. These are neutral for color and electric charges, similarly…
We have performed the bulk-sensitive high-resolution soft x-ray photoemission study of a Kondo semiconductor CeRhAs and related compounds CeNiSn and CePdSn. The comparison of the spectra of polycrystalline CePdSn on the fractured and scraped surfaces shows that the fracturing of the samples is much better than the scraping in order to obtain intrinsic photoemission spectra. The Ce 4d core-level spectra show clear differences in the electronic states among the materials.
We report Hall, magnetic, heat capacity and doping studies from single crystals of Yb_14MnSb_11 and Yb_13.3La_0.7MnSb_11. These heavily doped semiconducting compounds are ferromagnetic below 53 K and 39 K respectively. The renormalization of the carrier mass from 2 me near room temperature to 15 me at 5 K, plus the magnetic evidence for partial screening of the Mn magnetic moments suggest that these compounds represent rare examples of an underscreened Kondo lattice with T_K = 350 K.
Optical conductivity [$σ(ω)$] of the Kondo semiconductor YbB$_{12}$ has been measured over wide ranges of temperature ($T$=8$-$690 K) and photon energy ($\hbar ω\geq$ 1.3 meV). The $σ(ω)$ data reveal the entire crossover of YbB$_{12}$ from a metallic electronic structure at high $T$ into a semiconducting one at low $T$. Associated with the gap development in $σ(ω)$, a clear onset is newly found at $\hbarω$=15 meV for $T \leq$ 20 K. The onset energy is identified as the gap width of YbB$_{12}$ appearing in $σ(ω)$. This gap in σ(ω)$ is interpreted as the indirect gap, which has been predicted in…
We report the anisotropic changes in the electronic structure of a Kondo semiconductor CeOs$_2$Al$_{10}$ across an anomalous antiferromagnetic ordering temperature ($T_0$) of 29 K, using optical conductivity spectra. The spectra along the $a$- and $c$-axes indicate that a $c$-$f$ hybridization gap emerges from a higher temperature continuously across $T_0$. Along the b-axis, on the other hand, a different energy gap with a peak at 20 meV appears below 39 K, which is higher temperature than $T_0$, because of structural distortion. The onset of the energy gap becomes visible below $T_0$. Our obs…
We report the temperature-dependent three-dimensional angle-resolved photoemission spectra of the Kondo semiconductor SmB$_6$. We found a difference in the temperature dependence of the peaks at the X and $Γ$ points, due to hybridization between the Sm 5d conduction band and the nearly localized Sm 4f state. The peak intensity at the X point has the same temperature dependence as the valence transition below 120 K, while that at the $Γ$ point is consistent with the magnetic excitation at Q=(0.5,0.5,0.5) below 30 K. This suggests that the hybridization with the valence transition mainly occurs …
We present a theory to model carrier mediated ferromagnetism in concentrated or diluted local moment systems. The electronic subsystem of the Kondo lattice model is described by a combined equation of motion / coherent potential approximation method. Doing this we can calculate the free energy of the system and its minimum according to the magnetization of the local moments. Thus also the Curie temperature can be determined and its dependence on important model parameters. We get qualitative agreement with the Curie temperatures' experimental values of Ga$_{1-x}$Mn$_x$As for a proper hole dens…
Spin dynamics in the new Kondo insulator compound CeRu2Al10 has been studied using unpolarized and polarized neutron scattering on single crystals. In the unconventional ordered phase forming below T0 = 27.3 K, two excitation branches are observed with significant intensities, the lower one of which has a gap of 4.8 +/- 0.3 meV and a pronounced dispersion up to about 8.5 meV. Comparison with RPA magnon calculations assuming crystal-field and anisotropic exchange couplings captures major aspects of the data, but leaves unexplained discrepancies, pointing to a key role of direction-specific hybr…
A microscopic theory is developed to analyze the dynamics of exciton formation out of incoherent carriers in semiconductor heterostructures. The carrier Coulomb and phonon interaction is included consistently. A cluster expansion method is used to systematically truncate the hierarchy problem. By including all correlations up to the four-point (i.e. two-particle) level, the fundamental fermionic substructure of excitons is fully included. The analysis shows that the exciton formation is an intricate process where Coulomb correlations rapidly build up on a picosecond time scale while phonon dyn…
A variational calculation of the ground-state energy of neutral excitons and of positively and negatively charged excitons (trions) confined in a single-quantum well is presented. We study the dependence of the correlation energy and of the binding energy on the well width and on the hole mass. The conditional probability distribution for positively and negatively charged excitons is obtained, providing information on the correlation and the charge distribution in the system. A comparison is made with available experimental data on trion binding energies in GaAs-, ZnSe-, and CdTe-based quantum…
We report measurements of the thermal conductivity $κ$ on single crystalline CeRu$_4$Sn$_6$ in the temperature range between 80mK and 80K, along the main crystallographic directions. $κ$ is phonon-dominated in the whole temperature range and is found to be essentially isotropic. At low temperatures the data are well approximated by $κ\propto T^2$, which is attributed to a predominant scattering of phonons on electrons. We describe the data with a Callaway fit in the whole temperature range giving good agreement at low and high temperatures.
We report temperature-dependent polarized optical conductivity [$σ(ω)$] spectra of CeFe$_2$Al$_{10}$, which is a reference material for CeRu$_2$Al$_{10}$ and CeOs$_2$Al$_{10}$ with an anomalous magnetic transition at 28 K. The $σ(ω)$ spectrum along the b-axis differs greatly from that in the $ac$-plane, indicating that this material has an anisotropic electronic structure. At low temperatures, in all axes, a shoulder structure due to the optical transition across the hybridization gap between the conduction band and the localized $4f$ states, namely $c$-$f$ hybridization, appears at 55 meV. Ho…
The occupancy of the 4f^n contributions in the Kondo semiconductors CeM2Al10(M = Ru, Os and Fe) has been quantitatively determined by means of bulk-sensitive hard x-ray photoelectron spectroscopy (HAXPES) on the Ce 3d core levels. Combining a configuration interaction scheme with full multiplet calculations allowed to accurately describe the HAXPES data despite the presence of strong plasmon excitations in the spectra. The configuration interaction parameters obtained from this analysis -- in particular the hybridization strength V_eff and the effective f binding energy Delta_f -- indicate a s…
IVC characteristics as well as their derivatives were recorded for contacts on the base of CeNiSn, known as Kondo semiconductor, in the metallic and the tunnelling regime at temperatures between 0.1-8 K and in magnetic fields up to 8 T using mechanically controllable break junctions (MCBJ). It was found that CeNiSn behaves like a compound with typical metallic properties instead of the expected semiconducting behaviour. The main spectral feature is a pronounced zero-bias conductance minimum of about 10 meV width both for metallic and tunnel regime, which appears to be of magnetic nature. The e…
Spontaneously formed excitonic density wave with vortex-antivortex lattice in twisted semiconductor bilayers
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理系）；Department of Physics, University of Massachusetts（马萨诸塞大学物理系）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Physical Science Research Center, Nanjing University（南京大学江苏物理科学研究中心）；Hefei National Laboratory（合肥国家实验室）
The region surrounding the excitonic insulator phase is a three-component plasma composed of electrons, holes, and excitons. Due to the extended nature of the excitons, their presence influences the surrounding electrons and holes. We analyze this correlation. To this end, we calculate the density of bound electrons, the density of electrons in the correlated state, the momentum-resolved exciton density, and the momentum-resolved density of electron-hole pairs that are correlated but unbound. We find qualitative differences in the electron-hole correlations between the weak-coupling and the st…
Semimetallic CeNiSn is shown to transform into a Kondo semiconductor upon the substitution of few percent of Sb for Sn. The full-gap formation is not decisively influenced by the atomic disorder introduced by the substitution. Instead, the extra valence electrons introduced with the Sb doping (one per Sb atom) contribute to the formation of the collective Kondo spin-singlet state at low temperatures, as seen by a reduction of magnetic susceptibility. The definition of the Kondo semiconductor is provided and the difference with either the band-Kondo or the Mott-Hubbard insulators is stressed.
Using NRG, we show that a system containing a quantum impurity (QI), strongly coupled to a semiconductor (gap $2 Δ$) and weakly coupled to a metal, displays a 'reentrant' Kondo stage at low temperatures. The NRG analysis of the corresponding Single Impurity Anderson Model (SIAM) shows that the reentrant stage is characterized by a second sequence of SIAM fixed points: free orbital (FO) > local moment (LM) > strong coupling (SC). In the first stage, the SC fixed point (Kondo temperature $T_{K1}$) is unstable, while the second stage exhibits a much lower Kondo temperature $T_{K2}$, associated to…
Dependence of the spectral functions on temperature and rare-earth substitution was examined in detail for Kondo semiconductor alloys Sm1-xEuxB6 and Yb1-xLuxB12 by bulk-sensitive photoemission. It is found that the 4f lattice coherence and intrinsic (small) energy gap are robust for SmB6 against the Eu substitution up to x = 0.15 while both collapse by Lu substitution already at x = 0.125 for YbB12. Our results suggest that the mechanism of the intrinsic gap formation is different between SmB6 and YbB12 although they were so far categorized in the same kind of Kondo semiconductors.
We study nuclear relaxation in the presence of localized electrons in a two-dimensional electron gas in a disordered delta-doped semiconductor heterostructure and show that this method can reliably probe their magnetic interactions and possible long-range order. In contrast, we argue that transport measurements, the commonly employed tool, may not sometimes distinguish between spatial disorder and long-range order. We illustrate the utility of using the nuclear relaxation method to detect long-range order by analyzing a recent proposal made on the basis of transport measurements, on the sponta…
The build-up of exciton populations in resonantly laser excited semiconductors is studied microscopically. For excitation at the $2s$-exciton resonance, it is shown that polarization with a strict $s$-type radial symmetry can be efficiently converted into an incoherent $p$-type population. As a consequence, inversion between the $2p$ and $1s$ exciton states can be obtained leading to the appearance of significant terahertz gain.
We review the topic of Bose-Einstein condensation of excitons in semiconductors, focusing on the signatures of the macroscopic order of the exciton condensate.
This theoretical paper offers an explicit expression for the binding energy of excitons in a two-dimensional semiconductor with a flat valence band. The formula has been derived quasiclassically assuming that the exciton is tightly bound; i.e., its ground-state radius is determined by the intrinsic polarizability of the semiconductor rather than by the dielectric properties of the environment. The model is relevant to a few two-dimensional semiconductors discovered recently, including distorted 1T-TiSe$_2$, with a supposedly unstable electronic ground state. The valence band flatness reduces t…
Semiconductor excitons are commonly seen as hydrogen atom. This analogy requires a unique hole mass. In reality, this is not so due to the complexity of the semiconductor band structure. The precise consequences on the exciton physics of the Coulomb coupling between heavy and light holes remain a tricky open problem. Through an ``optimized perturbative'' approach that uses excitons with a flexible hole mass as a basis, we show that for zero exciton wave vector, the heavy-light hole mass difference does not split the $(2\times4)$ exciton degeneracy in zinc-blende-like semiconductors, the hole m…
We report on the first experimental determination of the coherence length of excitons in semiconductors using the combination of spatially resolved photoluminescence with phonon sideband spectroscopy. The coherence length of excitons in ZnSe quantum wells is determined to be 300 ~ 400 nm, about 25 ~ 30 times the exciton de Broglie wavelength. With increasing exciton kinetic energy, the coherence length decreases slowly. The discrepancy between the coherence lengths measured and calculated by only considering the acoustic phonon scattering suggests an important influence of static disorder.
Spin exchange between a single-electron charged quantum dot and itinerant electrons leads to an emergence of Kondo correlations. When the quantum dot is driven resonantly by weak laser light, the resulting emission spectrum allows for a direct probe of these correlations. In the opposite limit of vanishing exchange interaction and strong laser drive, the quantum dot exhibits coherent oscillations between the single-spin and optically excited states. Here, we show that the interplay between strong exchange and non-perturbative laser coupling leads to the formation of a new nonequilibrium quantu…
The underscreened Kondo lattice consisting of a single twofold degenerate conduction band and a CEF split 4f-electron quasi-quartet has non-conventional quasiparticle dispersions obtained from the constrained mean-field theory. An additional genuinely heavy band is found in the main hybridization band gap of the upper and lower hybridzed bands whose heavy effective mass is controlled by the CEF splitting. Its presence should profoundly influence the dynamical optical and magnetic response functions. In the former, the onset of the optical conductivity is not the main hybridisation energy but t…
Excitonic insulators conduct neither electrons nor holes but bound electron-hole pairs, excitons. Unfortunately, it is not possible to inject and detect the electron and hole currents independently within a single semiconducting layer. However, interlayer excitonic insulators provide a spatial separation of electrons and holes enabling exciton current measurements. The problem is that the spatial separation weakens electron-hole pairing and may lead to interlayer exciton disassociation. Here we develop an explicitly solvable model to determine an interlayer separation that is strong enough to …
Excitons in two-dimensional semiconductors provide a novel platform for fundamental studies of many-body interactions. In particular, dipolar interactions between spatially indirect excitons may give rise to strongly correlated phases of matter that so far have been out of reach of experiments. Here, we show that excitonic few-body systems in atomically thin transition-metal dichalcogenides undergo a crossover from a Tonks-Girardeau to a charge-density-wave regime. To this end, we take into account realistic system parameters and predict the effective exciton-exciton interaction potential. We …
We present a detailed investigation of the temperature and depth dependence of the magnetic properties of 3D topological Kondo insulator SmB6 , in particular near its surface. We find that local magnetic field fluctuations detected in the bulk are suppressed rapidly with decreasing depths, disappearing almost completely at the surface. We attribute the magnetic excitations to spin excitons in bulk SmB6 , which produce local magnetic fields of about ~1.8 mT fluctuating on a time scale of ~60 ns. We find that the excitonic fluctuations are suppressed when approaching the surface on a length scal…
Observation of quasi-steady dark excitons and gap phase in a doped semiconductor
Institute for Advanced Studies, Wuhan University（武汉大学高等研究院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）
We present Floquet-Keldysh non-equilibrium dynamical mean field calculations (DMFT) with an iterative perturbative solver (IPT) for high pump-power induced Stark states yielding a closing gap within semiconductor bulk and nano-cavities. Our model predicts unusual broadening of bands in systems like ZnO random lasers. This can be explained as an exciton-polariton coupling within the single crystalline pillar meeting the Mie resonance condition. Extraordinary enhancement of the lifetime of electronic states within the gap can lead to stable lasing modes and gain narrowing.
