Recent discoveries of a new type of quantum criticality arising from Yb-valence fluctuations in Yb-based metal in periodic crystal and quasicrystal have opened a new class of quantum critical phenomena in correlated electron systems. To clarify whether this new concept can be generalized to other rare-earth-based semimetal and insulator, we study SmS which exhibits golden-black phase transition under pressure. By constructing the model for SmS, we show that Coulomb repulsion between 4f and 5d orbitals at Sm drives first-order valence transition (FOVT) and semimetal-to-insulator transition (MIT) simultaneously, which explains the golden-black phase transition. We clarify the ground-state phase diagram for the FOVT and MIT by identifying the quantum critical point of the FOVT. We find that exciton condensates in both semimetal and insulator phases. Our result explains measured peak anomalies in the specific heat and compressibility in pressurized golden SmS and provides a cue to clarify recently-observed anomalies in black SmS.
The electronic structure changes of SmS surfaces under potassium (K) doping are elucidated using synchrotron-based core-level photoelectron spectroscopy and angle-resolved photoelectron spectroscopy (ARPES). The Sm core-level and ARPES spectra indicate that the Sm mean valence of the surface increased from the nearly divalent to trivalent states, with increasing K deposition. Carrier-induced valence transition (CIVT) from Sm$^{2+}$ to Sm$^{3+}$ exhibits a behavior opposite to that under conventional electron doping. Excess electrons are trapped by isolated excitons, which is inconsistent with …
The ZrSiS family of compounds hosts various exotic quantum phenomena due to the presence of both topological nonsymmorphic Dirac fermions and nodal-line fermions. In this material family, the LnSbTe (Ln= lanthanide) compounds are particularly interesting owing to the intrinsic magnetism from magnetic Ln which leads to new properties and quantum states. In this work, the authors focus on the previously unexplored compound SmSbTe. The studies reveal a rare combination of a few functional properties in this material, including antiferromagnetism with possible magnetic frustration, electron correl…
The phonon dispersion curve of SmS under pressure was studied by inelastic x-ray scattering around the pressure-induced valence transition. A significant softening of the longitudinal acoustic modes propagating along the [111] direction was observed spanning a wide $q$ region from ($\frac{2π}{3a},\frac{2π}{3a},\frac{2π}{3a}$) up to the zone boundary as SmS becomes metallic. The largest softening occurs at the zone boundary and stays stable up to the highest measured pressure of 80 kbar while a gradual hardening of the low $q$ modes simultaneously appears. This phonon spectrum indicates favorab…
We demonstrate theoretically that the golden phase of SmS ($g$-SmS), a correlated mixed-valent system, exhibits nontrivial surface states with diverse topology. It turns out that this material is an ideal playground to investigate different band topologies in different surface terminations. We have explored surface states on three different (001), (111), and (110) surface terminations. Topological signature in the (001) surface is not apparent due to a hidden Dirac cone inside the bulk-projected bands. In contrast, the (111) surface shows a clear gapless Dirac cone in the gap region, demonstra…
Motivated by the recent upsurge in research of three-dimensional topological semimetals (SMs), we theoretically study the RKKY interaction between magnetic impurities in node-line SMs with and without the chirality and obtain the analytical expressions. We find that unique toroidal Fermi surface (FS) in nodal-line SMs, distinctly different from the spheroid FS in the SMs with the point nodes, has significant influences on the RKKY interaction, leading to strong anisotropic oscillation and unique decay features. In the direction perpendicular to node-line plane, as usual, there is only one osci…
Golden SmS is a paramagnetic, mixed-valence system with a pseudogap. With increasing pressure across a critical pressure Pc, the system undergoes a discontinuous transition into a metallic, anti-ferromagnetically ordered state. By using a combination of thermodynamic, transport, and magnetic measurements, we show that the pseudogap results from the formation of a local bound state with spin singlet. We further argue that the transition Pc is regarded as a transition from an insulating electron-hole gas to a Kondo metal, i.e., from a spatially bound state to a Kondo virtually bound state betwee…
We have investigated temperature-dependent behaviors of electronic structure and resistivity in a mixed-valent golden phase of SmS, based on the dynamical mean-field theory band structure calculations. Upon cooling, the coherent Sm 4$f$ bands are formed to produce the hybridization induced pseudogap near the Fermi level, and accordingly the topology of Fermi surface is changed to exhibit a Lifshitz-like transition. The surface states emerging in the bulk gap region are found to be not topologically protected states but just typical Rashba spin-polarized states, indicating that SmS is not a top…
Topologically non-trivial electronic structures can give rise to a range of unusual physical phenomena, and the interplay of band topology with other effects such as electronic correlations and magnetism requires further exploration. The rare earth monopnictides $X$(Sb,Bi) ($X$ = lanthanide) are a large family of semimetals where these different effects may be tuned by the substitution of rare-earth elements. Here we observe anomalous behavior in the quantum oscillations of one member of this family, antiferromagnetic SmSb. The analysis of Shubnikov-de Haas (SdH) oscillations provides evidence…
We measured the thermal expansion of the valence fluctuating phase of SmS (golden SmS) to construct a pressure vs temperature phase diagram. The obtained phase diagram is characterized by three lines. One is a crossover line that divides the paramagnetic phase into two regions. The other two lines correspond to a second-order Neel transition and a first-order Neel transition. The crossover line appears to emerge from a tricritical point that separates the first-order Neel transition from the second-order one. We argue that a valence jump occurs at the border of antiferromagnetism.
We present a real-space view of one-dimensional (1D) to three-dimensional (3D) topological materials with 13 representative samples selected from each class, including 1D trans-polyacetylene, two-dimensional (2D) graphene, and 3D topological insulators, Dirac semimetals, Weyl semimetals, and nodal-line semimetals. This review is not intended to present a complete up-to-date list of publications on topological materials, nor to provide a progress report on the theoretical concepts and experimental advances, but rather to focus on an analysis based on the valence-bond model to help the readers g…
We report the pressure-dependent optical reflectivity spectra of a strongly correlated insulator, samarium monosulfide (SmS), in the far- and middle-infrared regions to investigate the origin of the pressure-induced phase transition from the black phase to the golden phase. The energy gap becomes narrow with increasing pressure in the black phase. A valence transition from Sm2+ in the black phase to mainly Sm3+ in the golden phase accompanied by spectral change from insulator to metal were observed at the transition pressure of 0.65 GPa. The black-to-golden phase transition occurs when the ene…
Pressure induced isostructural insulator to metal transition for SmS is characterised by the presence of an intermediate valence state at higher pressure which cannot be captured by the density functional theory. As a direct outcome of including the charge and spin fluctuations incorporated in dynamical mean field theory, we see the emergence of insulating and metallic phases with increasing pressure as a function of changing valence. This is accompanied by significantly improved predictions of the equilibrium lattice constants and bulk moduli for all Sm-monochalcogenides verifying experiments…
SmS, a prototypical intermediate valence compound, has been studied by performing high-pressure nuclear magnetic resonance measurements on a $^{33}$S-enriched sample. The observation of an additional signal below 15-20 K above a nonmagnetic-magnetic transition pressure $P_{\rm c2} \approx 2$ GPa gives evidence of a magnetic transition. The absence of a Curie-term in the Knight shift near $P_{\rm c2}$ indicates that the localized character of $4f$ electrons is entirely screened and the mechanism of the magnetic ordering is not described within a simple localized model. Simultaneously, the line …
Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.
The application of pressure to elemental bismuth reduces its conduction-valence band overlap, and results in a semimetal-semiconductor (SMSC) transition around 25 kbar. This transition is nominally of the topological "Lifshitz" Fermi surface variety, but there are open questions about the role of interactions at low charge densities. Using a novel pressure cell with optical access, we have performed an extensive study of bismuth's infrared conductivity under pressure. In contrast to the expected pure band behavior we find signatures of enhanced interaction effects, including strongly coupled c…
The magnetic spectral response of black-phase mixed-valence Sm0.83Y0.17S has been measured by inelastic neutron scattering on a single crystal. Two magnetic peaks are observed in the energy range of the Sm2+ spin-orbit transition (25-40 meV). Both of them exhibit significant dispersion along the three main symmetry directions, reminiscent of the spin-orbit exciton branch found in pure divalent SmS. The results can be reproduced by a simple phenomenological model accounting for the existence of sizeable Sm-Sm exchange interactions, and a microscopic mechanism is proposed on the basis of the "lo…
We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and $2π$-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and $2π$-flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate paramet…
We present a systematic investigation of the magnetoresponses of the Weyl points (WPs) with a topological charge of n = 2, 3 and 4, and with both linear and quadratic energy tilt. The linear tilt always tends to squeeze the Landau levels (LLs) of both conduction and valence bands of all the WPs, and eventually leads to LL collapse in the type-II phase. However, the quadratic energy tilt has more complex influences on the LLs of the unconventional WPs. For charge-n (n = 2, 4) WP, the influence of the quadratic tilt on the LLs of conduction and valence bands are opposite, i.e. if the LLs of cond…
The phase diagram of the filled skutterudite CeOs$_4$Sb$_{12}$ has been mapped in fields $H$ of up to 60 T and temperatures $T$ down to 0.5 K using resistivity, magnetostriction, and MHz conductivity. The valence transition separating the semimetallic, low-$H$, low-$T$, $\cal{L}$ phase from the metallic high-$H$, high-$T$ $\cal{H}$ phase exhibits a very unusual, wedge-shaped phase boundary, with a non-monotonic gradient alternating between positive and negative. This is quite different from the text-book "elliptical" phase boundary usually followed by valence transitions. Analysis of Shubnikov…
In this paper we discuss the N$\acute{e}$el and Kekul$\acute{e}$ valence bond solids quantum criticality in graphene Dirac semimetal. Considering the quartic four-fermion interaction $g(\barψ_iΓ_{ij}ψ_j)^2$ that contains spin,valley, and sublattice degrees of freedom in the continuum field theory, we find the microscopic symmetry is spontaneously broken when the coupling $g$ is greater than a critical value $g_c$. The symmetry breaking gaps out the fermion and leads to semimetal-insulator transition. All possible quartic fermion-bilinear interactions give rise to the uniform critical coupling,…
We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half-filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a dire…
We act on the suggestion that an excitonic insulator state might separate---at very low temperatures---a semimetal from a semiconductor and ask for the nature of these transitions. Based on the analysis of electron-hole pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb attraction between both species, a continuous crossover between a BCS-like transition of Cooper-type pairs and a Bose-Einstein condensation of preformed tightly-bound excitons might be achieved in a solid-state system. The precursor of this crossover in the normal state might cause the transport anom…
We report a new family of ternary 111 hexagonal LnAuSb (Ln = La-Nd, Sm) compounds that, with a 19 valence electron count, has one extra electron compared to all other known LnAuZ compound. The "19th" electron is accommodated by Au-Au bonding between the layers; this Au-Au interaction drives the phases to crystallize in the YPtAs-type structure rather than the more common LiGaGe-type. This is critical, as the YPtAs structure type has the symmetry-allowed band crossing necessary for the formation of Dirac semimetals. Band structure, density of stats, and crystal orbital calculations confirm this…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combin…
Transition metal chalcogenide Ta$_2$NiSe$_5$, a promising material for the excitonic insulator, is investigated on the basis of the quasi-one-dimensional three-chain Hubbard model with two conduction ($c$) bands and one valence ($f$) band. In the semimetallic case where only one of two $c$ bands and the $f$ band cross the Fermi level, the transition from the $c$-$f$ compensated semimetal to the uniform excitonic insulator takes place at low temperature as the same as in the semiconducting case. On the other hand, when another $c$ band also crosses the Fermi level, the system shows three types …
We reveal an ultrafast purely electronic phase transition in \TNS, which is a plausible excitonic insulator, after excited by an ultrafast infrared laser pulse. Specifically, the order parameter of the strong electron-hole binding shrinks with enhancing the pump pulse, and above a critical pump fluence, a photo-excited semimetallic state is experimentally identified with the absence of ultrafast structural transition. In addition, the bare valence and conduction bands and also the effective exciton binding energy in \TNS~are determined. These findings and detailed analysis suggest a bare noneq…
In electronic topological Dirac semimetals the conduction and valence bands touch at discrete points in the Brillouin zone and form Dirac cones. They are robust against spin-orbit interaction (SOI) and protected by crystal symmetries. They can be driven to different topological phases by breaking the symmetries. In the low-temperature quantum magnetic systems the magnon dispersions have similar band structures as the electron dispersions, but with positive definite energies. In these magnetic systems SOI manifests in the form of the Dzyaloshinskii-Moriya interaction (DMI). In this Communicatio…
Eu2Ir2O7, a candidate Weyl semimetal, shows an insulator-to-metal transition as a function of Bi substitution at the Eu site. In this work, we investigate the (Eu_1-xBi_x)2Ir2O7 series via Hard X-ray Photoemission Spectroscopy (HAXPES), where substitution of larger Bi3+ for Eu3+ is reported to result in an anomalous lattice contraction (20 %) for low Bi doping (3.5 %). Using HAXPES, we confirm that all the cations retain their nominal valence state throughout the series. The asymmetric nature of Bi core-level spectra for compositions in the metallic region indicates that Bi contributes to the …
The antiferromagnet and semimetal EuCd$_2$As$_2$ has recently attracted a lot of attention due to a wealth of topological phases arising from the interplay of topology and magnetism. In particular, the presence of a single pair of Weyl points is predicted for a ferromagnetic configuration of Eu spins along the $c$-axis in EuCd$_2$As$_2$. In the search for such phases, we investigate here the effects of hydrostatic pressure in EuCd$_2$As$_2$. For that, we present specific heat, transport and $μ$SR measurements under hydrostatic pressure up to $\sim\,2.5\,$GPa, combined with {\it ab initio} dens…
Fermion-induced quantum critical points (FIQCPs) were recently discovered at the putatively first-order transitions between two-dimensional (2D) Dirac semimetals and the Kekule valence bond solids on the honeycomb lattice by sign-free quantum Monte Carlo simulations [Nature Communications 8, 314, (2017)]. Here, we investigate possible FIQCP in 3D topological Weyl semimetals at a $Z_3$ symmetry-breaking transition that is putatively first-order according to the Landau criterion. We construct a lattice model featuring 3D double-Weyl fermions (monopole charges $\pm$2) and we show that $Z_3$ nodal…
The excitonic insulator Ta$_2$NiSe$_5$ experiences a first-order structural transition under pressure from rippled to flat layer-structure at Ps = 3 GPa, which drives the system from an almost zero-gap semiconductor to a semimetal. The pressure-induced semimetal, with lowering temperature, experiences a transition to another semimetal with a partial-gap of 0.1-0.2 eV, accompanied with a monoclinic distortion analogous to that occurs at the excitonic transition below Ps. We argue that the partial-gap originates primarily from a symmetry-allowed hybridization of Ta-conduction and Ni-valence band…
Time-resolved ARPES gives access to the band structure and ultrafast dynamics of excited electronic states in solids. The orbital character of the bands close to the Fermi level is essential to understand the origin of several exotic phenomena in quantum materials. By performing polarization dependent time- and angle-resolved photoemission spectroscopy and by analyzing the chirality of the photoelectron yield for two different crystal orientations, we identify the orbital character of bands below and above the chemical potential for the Dirac semimetal BaNiS2. Our results illustrate how the co…
Nodal line semimetals (NLSM) exhibit interesting quantum oscillation characteristics when acted upon by a strong magnetic field. We study the combined effect of strong direct (dc) and alternating (ac) magnetic field, perpendicular to the nodal plane in an untilted NLSM in order to probe the behavior of the low lying Landau level (LL) states that can periodically become gapless for suitably chosen field parameters. The oscillatory field variation, as opposed to a steady one, has interesting impact on the quantum oscillation phenomena with the Landau tubes crossing the Fermi surface extremally t…
A clean noninteracting parabolic semimetal is characterized by quadratic band touching between the conduction and the valence bands at isolated diabolic points in the Brillouin zone and describes a fermionic quantum critical system with dynamic exponent z=2. We consider the stability of such a semimetal against electronic interaction and quenched disorder using a perturbative renormalization group analysis for two and three spatial dimensions. For the noninteracting problem infinitesimally weak disorder leads to an Anderson insulator and a diffusive metal respectively in two and three dimensio…
Topological nodal-line semimetals (TNLSMs) are materials whose conduction and valence bands cross each other, meeting a topologically-protected closed loop rather than discrete points in the Brillouin zone (BZ). The anticipated properties for TNLSMs include drumhead-like nearly flat surface states, unique Landau energy levels, special collective modes, long-range Coulomb interactions, or the possibility of realizing high-temperature superconductivity. Recently, SrAs3 has been theoretically proposed and then experimentally confirmed to be a TNLSM. Here, we report high-pressure experiments on Sr…
We calculate the critical temperature below which an excitonic insulator exists at the pressure-induced semiconductor-semimetal transition. Our approach is based on an effective-mass model for valence and conduction band electrons interacting via a statically screened Coulomb potential. Assuming pressure to control the energy gap, we derive, in the spirit of a BEC-BCS crossover scenario, a set of equations which determines, as a function of the energy gap (pressure), the chemical potentials for the two bands, the screening wave number, and the critical temperature. We (i) show that in leading …
In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and $Z_3$-ordered phases (e.g. Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first-order. From large-$N$ renormalization group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nature Communications 8, 314 (2017)] occur when $N$ (the number of flavors of four-component Dirac fermions) is larger than a critical value $N_c$. Remarkably, …
Topological semimetals are systems in which the conduction and the valence bands cross each other and this crossing is protected by topological constraints. These materials provide an intriguing test of fundamental theory and their exceptional physical properties promise a wide range of possible applications. Here we report a study of the thermoelectric power (S) for a single crystal of ZrSiS that is believed to be a topological nodal-line semimetal. We detect multiple quantum oscillations in the magnetic field dependence of S that are still visible at temperature as high as T = 100 K. Two of …
CeOs$_4$Sb$_{12}$, a member of the skutterudite family, has an unusual semimetallic low-temperature $\cal{L}$-phase that inhabits a wedge-like area of the field $H$ - temperature $T$ phase diagram. We have conducted measurements of electrical transport and megahertz conductivity on CeOs$_4$Sb$_{12}$ single crystals under pressures of up to 3 GPa and in high magnetic fields of up to 41 T to investigate the influence of pressure on the different $H$-$T$ phase boundaries. While the high-temperature valence transition between the metallic $\cal{H}$-phase and the $\cal{L}$-phase is shifted to highe…
Bose condensation has shaped our understanding of macroscopic quantum phenomena, having been realized in superconductors, atomic gases, and liquid helium. Excitons are bosons that have been predicted to condense into either a superfluid or an insulating electronic crystal. Using the recently developed momentum-resolved electron energy-loss spectroscopy (M-EELS), we study electronic collective modes in the transition metal dichalcogenide semimetal, 1T-TiSe$_2$. Near the phase transition temperature, T$_c$ = 190 K, the energy of the electronic mode falls to zero at nonzero momentum, indicating d…
We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral …
Unconstrained compact lattice QED$_{2+1}$ coupled to phonons: Gauss sectors, orthogonal semimetal, and deconfined criticality
Institut für Theoretische Physik und Astrophysik, Universität Würzburg（维尔茨堡大学理论物理与天体物理研究所）；Würzburg-Dresden Cluster of Excellence ctd.qmat（维尔茨堡-德累斯顿卓越集群ctd.qmat）
We compute the effects of electronic interactions on gapless spin-3/2 excitations that in a noninteracting system emerge at a bi-quadratic touching of Kramers degenerate valence and conduction bands, known as Luttinger semimetal. This model can describe the low-energy physics of HgTe, gray-Sn, 227 pyrochlore iridates and half-Heuslers. For the sake of concreteness we only consider the short-range components of the Coulomb interaction. By combining mean-field analysis with a renormalization group (RG) calculation, we construct multiple cuts of the global phase diagram of interacting spin-3/2 fe…
A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group (RG) analysis we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermi…
We study the zero-temperature phase diagrams of Majorana-Hubbard models with SO($N$) symmetry on two-dimensional honeycomb and $π$-flux square lattices, using mean-field and renormalization group approaches. The models can be understood as real counterparts of the SU($N$) Hubbard-Heisenberg models, and may be realized in Abrikosov vortex phases of topological superconductors, or in fractionalized phases of strongly-frustrated spin-orbital magnets. In the weakly-interacting limit, the models feature stable and fully symmetric Majorana semimetal phases. Increasing the interaction strength beyond…
Coulomb interactions famously drive three dimensional quadratic band crossing semimetals into a non-Fermi liquid phase of matter. In a previous work, Phys. Rev. B 95, 205106 (2017), the effect of disorder on this non-Fermi liquid phase was investigated, assuming that the bandstructure was isotropic, assuming that the conduction and valence bands had the same band mass, and assuming that the disorder preserved exact time-reversal symmetry and statistical isotropy. It was shown that the non-Fermi liquid fixed point is unstable to disorder, and that a runaway flow to strong disorder occurs. In th…
