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This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates, distance between the processes in integral norms, and parameter estimation. The squared Bessel process is shown to be a phase transition of the CIR process and can be approximated by a sequence of CIR processes. Differences in stochastic stability are also highlighted, with the Bessel process displaying instability, while the CIR process remains ergodic and stable., Comment: 21 pages

EuAl$_4$ is proposed to host a topological Hall state. This material also undergoes four consecutive antiferromagnetic (AFM) transitions upon cooling below TN1 = 15.4 K in the presence of charge density wave (CDW) order that sets in below TCDW = 140 K. We use angle-resolved photoemission spectroscopy and density-functional-theory calculations to study how magnetic ordering affects the electronic properties in EuAl$_4$. We found changes in the band structure upon each of the four consecutive AFM transitions including band splitting, renormalizations, and appearance of new bands forming additional Fermi sheets. In addition we also found significant enhancement of the quasiparticles' lifetime due to suppression of spin flip scattering, similar to what was previously reported for ferromagnetic EuCd$_2$As$_2$. Surprisingly, we observe that most significant changes in electronic properties occur not at TN1, but instead at the AFM3 to AFM4 transition, which coincides with the largest drop in resistivity.

We perform angle-resolved photoemission spectroscopy (ARPES) measurements in conjunction with density functional theory (DFT) calculations to investigate the evolution of the electronic structure of CeBi upon a series of antiferromagnetic (AFM) transitions. We find evidence for a new AFM transition in addition to two previously known from transport studies. We demonstrate the development of an additional Dirac state in the (+-+-) ordered phase and a transformation of unconventional surface-state pairs in the (++--) ordered phase. This revises the phase diagram of this intriguing material, where there are now three distinct AFM states below TN in zero magnetic field instead of two as it was previously thought., Comment: 16 pages, 4 figures

The recent discovery of unconventional surface-state pairs, which give rise to Fermi arcs and spin textures, in antiferromagnetically ordered rare-earth monopnictides attracted the interest in these materials. We use angle-resolved photoemission spectroscopy (ARPES) measurements in conjunction with density functional theory (DFT) calculations to investigate the evolution of the electronic structure of GdBi and DyBi. We find that new surface states, including a Dirac cone, emerge in the AFM state. However, they are located along a direction in momentum space that is different than what was found in NdSb, NdBi, and CeBi. The observed changes in the electronic structure are consistent with the presence of AFM-II-A type order.

We use high-resolution angle resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) to investigate the electronic structure of the charge density wave (CDW) system LaSb$_2$. This compound is among an interesting group of materials that manifests both a CDW transition and lower temperature superconductivity. We find the DFT calculations to be in good agreement with our ARPES data. The Fermi surface of LaSb$_2$ consists of two small hole pockets close to $\Gamma$ and four larger pockets near the Brillouin zone (BZ) boundary. The overall features of the Fermi surface do not vary with temperature. A saddle point is present at -0.19 $eV$ below the Fermi level at $\Gamma$. Critical points in band structure have more pronounced effects on a materials properties when they are located closer to the Fermi level, making doped LaSb$_2$ compounds a potential interesting subject of future research. Multiple peaks are present in the generalized, electronic susceptibility calculations indicating the presence of possible nesting vectors. We were not able to detect any signatures of the CDW transition at 355 K, pointing to the subtle nature of this transition. This is unusual, given that such a high transition temperature is expected to be associated with the presence of a large CDW gap. This is confirmed through investigation of the Fermi surface and through analysis of momentum distribution curves (MDC). It is possible that changes are subtle and occur below current sensitivity of our measurements.

The recent discovery of unconventional surface state pairs, which give rise to Fermi arcs and spin textures, in antiferromagnetically ordered NdBi raised the interest in rare-earth monopnictides. Several scenarios of antiferromagnetic order have been suggested to explain the origin of these states with some of them being consistent with the presence of non-trivial topologies. In this study, we use angle-resolved photoemission spectroscopy (ARPES) and density-functional-theory (DFT) calculations to investigate the electronic structure of NdSb. We found the presence of distinct domains that have different electronic structure at the surface. These domains correspond to different orientations of magnetic moments in the AFM state with respect to the surface. We demonstrated remarkable agreement between DFT calculations and ARPES that capture all essential changes in the band structure caused by transition to a magnetically ordered state.

We use high-resolution angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to study the electronic and magnetic properties of La2Ni7, an itinerant magnetic system with a series of three magnetic transition temperatures upon cooling, which end in a weak itinerant antiferromagnetic (wAFM) ground state. Our APRES data reveal several electron and hole pockets that have hexagonal symmetry near the $\Gamma$ point. We observe significant reconstruction of the band structure upon successive magnetic transitions at T1 = 61 K, T2 = 57 K and T3 = 42 K. The experimental data are in a reasonable agreement with DFT calculations, demonstrating their applicability to itinerant antiferromagnet systems. Our results detail the effects of magnetic ordering on the electronic structure in a Ni-based weak antiferromagnet., Comment: 17 pages, 4 figures

Since the discovery of topological insulators a lot of research effort has been devoted to magnetic topological materials, in which non-trivial spin properties can be controlled by magnetic fields, culminating in a wealth of fundamental phenomena and possible applications. The main focus was on ferromagnetic materials that can host Weyl fermions and therefore spin textured Fermi arcs. The recent discovery of Fermi arcs and new magnetic bands splitting in antiferromagnet (AFM) NdBi has opened up new avenues for exploration. Here we show that these uncharted effects are not restricted to this specific compound, but rather emerge in CeBi, NdBi, and NdSb when they undergo paramagnetic to AFM transition. Our data show that the Fermi arcs in NdSb have 2-fold symmetry, leading to strong anisotropy that may enhance effects of spin textures on transport properties. Our findings thus demonstrate that the RBi and RSb series are materials that host magnetic Fermi arcs and may be a potential platform for modern spintronics., Comment: 19 pages, five figures, supplemental information

Many complex magnetic structures in a high-symmetry lattice can arise from a superposition of well-defined magnetic wave vectors. These "multi-q" structures have garnered much attention because of interesting real-space spin textures such as skyrmions. However, the role multi-q structures play in the topology of electronic bands in momentum space has remained rather elusive. Here we show that the type-I anti-ferromagnetic 1q, 2q and 3q structures in an face-centered cubic sublattice with band inversion, such as NdBi, can induce unconventional surface state pairs inside the band-folding hybridization bulk gap. Our density functional theory calculations match well with the recent experimental observation of unconventional surface states with hole Fermi arc-like features and electron pockets below the Neel temperature. We further show that these multi-q structures have Dirac and Weyl nodes. Our work reveals the special role that band-folding from anti-ferromagnetism and multi-q structures can play in developing new types of surface states., Comment: 31 pages, 11 figures

The Fermi arcs are signatures of exotic states in solids because they defy conventional concept of Fermi surfaces as closed contours in momentum space. Fermi arcs were first discovered in cuprates, and caused by the pseudogap. Weyl semimetals provided another way to generate Fermi arcs by breaking either the time reversal symmetry (TRS) or inversion symmetry of a 3D Dirac semimetal, which can result in a Weyl semimetal with pairs of Weyl nodes that have opposite chirality. The bulk-boundary correspondence associated with the Chern number leads to the emergence of Fermi arcs on the boundary. Here, we present experimental evidence that pairs of magnetically split hole- and electron-like Fermi arcs emerge below the Neel temperature, in the antiferromagnetic (AFM) state of cubic NdBi due to a novel band splitting effect. Whereas TRS is broken by the AFM order, both inversion and nonsymmorphic TRS are preserved in the bulk, precluding the possibility of a Weyl semimetal. The observed magnetic splitting is highly unusual, as it creates bands of opposing curvature, that changes with temperature and follows the antiferromagnetic order parameter. This is completely different from previously reported cases of magnetic splittings such as traditional Zeeman and Rashba, where the curvature of the bands is preserved. Therefore, our finding represents a new Fermionic state created by new type of magnetic band splitting in the presence of a long-range AFM order that are not readily explained by existing theoretical ideas., Comment: 16 pages, 4 figures main text and 20 pages, 12 figures supplement

High-quality single crystals of KCo$_2$As$_2$ with the body-centered tetragonal ThCr$_2$Si$_2$ structure were grown using KAs self flux. Structural, magnetic, thermal, and electrical transport were investigated. No clear evidence for any phase transitions was found in the temperature range 2 to 300 K. The in-plane electrical resistivity $\rho$ versus temperature $T$ is highly unusual, showing a $T^4$ behavior below 30 K and an anomalous positive curvature up to 300 K which is different from the linear behavior expected from the Bloch-Gr\"uneisen theory for electron scattering by acoustic phonons. This positive curvature has been previously observed in the in-plane resistivity of high-conductivity layered delafossites such as PdCoO$_2$ and PtCoO$_2$. The in-plane $\rho(T\to0) = 0.36~\mu\Omega$ cm of KCo$_2$As$_2$ is exceptionally small for this class of compounds. The material also exhibits a nearly linear magnetoresistance at low $T$ which attains a value of about 40% at $T=2$K and magnetic field $H= 80$ kOe. The magnetic susceptibility $\chi$ of KCo$_2$As$_2$ is isotropic and about an order of magnitude smaller than the values for the related compounds SrCo$_2$As$_2$ and BaCo$_2$As$_2$. The $\chi$ increases above 100 K which is found from our first-principles calculations to arise from a sharp peak in the electronic density of states just above the Fermi energy $E_{\rm F}$. Heat capacity $C_{\rm p}(T)$ data at low $T$ yield an electronic density of states $N(E_{\rm F})$ that is about 36% larger than predicted by the first-principles theory. The $C_{\rm p}(T)$ data near room temperature suggest the presence of excited optic vibration modes which may also be the source of the positive curvature in $\rho(T)$. Our results show that KCo$_2$As$_2$ provides a new avenue for investigating the physics of high-purity metals., Comment: 13 pages, 14 figures

Fermi surfaces, three-dimensional (3D) abstract interfaces that define the occupied energies of electrons in a solid, are important for characterizing and predicting the thermal, electrical, magnetic, and optical properties of crystalline metals and semiconductors [1]. Angle-resolved photoemission spectroscopy (ARPES) is the only technique directly probing the Fermi surface by measuring the Fermi momenta (kF) from energy and angular distribution of photoelectrons dislodged by monochromatic light [2]. Existing electron analyzers are able to determine a number of kF-vectors simultaneously, but current technical limitations prohibit a direct high-resolution 3D Fermi surface mapping. As a result, no such datasets exist, strongly limiting our knowledge about the Fermi surfaces and restricting a detailed comparison with the widely available nowadays calculated 3D Fermi surfaces. Here we show that using a simpler instrumentation, based on the Fourier electron optics combined with a retardation field of the detector, it is possible to perform 3D-mapping within a very short time interval and with very high resolution. We present the first detailed experimental 3D Fermi surface recorded in the full Brillouin zone along the kz-direction as well as other experimental results featuring multiple advantages of our technique. In combination with various light sources, including synchrotron radiation, our methodology and instrumentation offer new opportunities for high-resolution ARPES in the physical and life sciences., Comment: 14 pages, 4 figures

We report on the low-energy electronic structure of Tantalum ditelluride (1$T'$-TaTe$_2$), one of the charge density wave (CDW) materials from the group V transition metal dichalcogenides using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT). We find that the Fermi surface topology of TaTe$_2$ is quite complicated compared to its isovalent compounds such as TaS$_2$, TaSe$_2$, and isostructural compound NbTe$_2$. More importantly, we discover that the surface electronic structure of 1$T'$-TaTe$_2$ has more resemblance to the 2$H$-TaTe$_2$, while the bulk electronic structure has more resemblance to the hypothetical 1$T$-TaTe$_2$. These experimental observations are thoroughly compared with our DFT calculations performed on 1$T$-, 2$H$- and 2$H$ (monolayer)/1$T$- TaTe$_2$. We further notice that the Fermi surface topology is temperature independent up to 180 K, confirming that the 2$H$ phase on the surface is stable up to 180 K and the CDW order is not due to the Fermi surface nesting., Comment: 5 figures, 22 pages, Accepted for publication in JPCC

Most recent observation of topological Fermi arcs on the surface of manyfold degenerate B20 systems, CoSi and RhSi, have attracted enormous research interests. Although an another isostructural system, FeSi, has been predicted to show bulk chiral fermions, it is yet to be clear theoretically and as well experimentally that whether FeSi possesses the topological surface Fermi arcs associated with the exotic chiral fermions in vicinity of the Fermi level. In this contribution, using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), we present the low-energy electronic structure of FeSi. We further report the surface state calculations to provide insights into the surface band structure of FeSi near the Fermi level. Unlike in CoSi or RhSi, FeSi has no topological Fermi arcs near the Fermi level as confirmed both from ARPES and surface state calculations. Further, the ARPES data show spin-orbit coupling (SOC) band splitting of 40 meV, which is in good agreement with bulk band structure calculations. We noticed an anomalous temperature dependent resistivity in FeSi which can be understood through the electron-phonon interactions as we find a Debye energy of 80 meV from the ARPES data., Comment: 9 pages, 7 figures

Topological superconductors should be able to provide essential ingredients for quantum computing, but are very challenging to realize. Spin-orbit interaction in iron-based superconductors opens the energy gap between the $p$-states of pnictogen and $d$-states of iron very close to the Fermi level, and such $p$-states have been recently experimentally detected. Density functional theory predicts existence of topological surface states within this gap in FeTe$_{1-x}$Se$_x$ making it an attractive candidate material. Here we use synchrotron-based angle-resolved photoemission spectroscopy and band structure calculations to demonstrate that FeTe$_{1-x}$Se$_x$ (x=0.45) is a superconducting 3D Dirac semimetal hosting type-I and type-II Dirac points and that its electronic structure remains topologically trivial. We show that the inverted band gap in FeTe$_{1-x}$Se$_x$ can possibly be realized by further increase of Te content, but strong correlations reduce it to a sub-meV size, making the experimental detection of this gap and corresponding topological surface states very challenging, not to mention exact matching with the Fermi level. On the other hand, the $p-d$ and $d-d$ interactions are responsible for the formation of extremely flat band at the Fermi level pointing to its intimate relation with the mechanism of high-T$_c$ superconductivity in IBS., Comment: 10 pages, 5 figures, 28 references

Using angle resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations we studied the low-energy electronic structure of bulk ZrTe$_2$. ARPES studies on ZrTe$_2$ demonstrate free charge carriers at the Fermi level, which is further confirmed by the DFT calculations. An equal number of hole and electron carrier density estimated from the ARPES data, points ZrTe$_2$ to a semimetal. The DFT calculations further suggest a band inversion between Te $p$ and Zr $d$ states at the $\Gamma$ point, hinting at the non-trivial band topology in ZrTe$_2$. Thus, our studies for the first time unambiguously demonstrate that ZrTe$_2$ is a topological semimetal. Also, a comparative band structure study is done on ZrSe$_2$ which shows a semiconducting nature of the electronic structure with an indirect band gap of 0.9 eV between $\Gamma (A) $ and $M (L)$ high symmetry points. In the below we show that the metal-chalcogen bond-length plays a critical role in the electronic phase transition from semiconductor to a topological semimetal ingoing from ZrSe$_2$ to ZrTe$_2$., Comment: 10 pages, 7 figures

We report experimental and theoretical evidence that GaGeTe is a basic $Z_2$ topological semimetal with three types of charge carriers: bulk-originated electrons and holes as well as surface state electrons. This electronic situation is qualitatively similar to the primer 3D topological insulator Bi2Se3, but important differences account for an unprecedented transport scenario in GaGeTe. High-resolution angle-resolved photoemission spectroscopy combined with advanced band structure calculations show a small indirect energy gap caused by a peculiar band inversion in the \textit{T}-point of the Brillouin zone in GaGeTe. An energy overlap of the valence and conduction bands brings both electron- and hole-like carriers to the Fermi level, while the momentum gap between the corresponding dispersions remains finite. We argue that peculiarities of the electronic spectrum of GaGeTe have a fundamental importance for the physics of topological matter and may boost the material's application potential.

Nematicity plays an important role in the physics of iron-based superconductors (IBS). Its microscopic origin and in particular its importance for the mechanism of high-temperature superconductivity itself are highly debated. A crucial knowledge in this regard is the degree to which the nematic order influences the electronic structure of these materials. Earlier angle-resolved photoemission spectroscopy (ARPES) studies found that the effect is dramatic in three families of IBS including 11, 111 and 122 compounds: energy splitting reaches 70 meV and Fermi surface becomes noticeably distorted. More recent experiments, however, reported significantly lower energy scale in 11 and 111 families, thus questioning the degree and universality of the impact of nematicity on the electronic structure of IBS. Here we revisit the electronic structure of undoped parent BaFe2As2 (122 family). Our systematic ARPES study including the detailed temperature and photon energy dependencies points to the significantly smaller energy scale also in this family of materials, thus establishing the universal scale of this phenomenon in IBS. Our results form a necessary quantitative basis for theories of high-temperature superconductivity focused on the nematicity., Comment: 14 pages 4 figures

The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBS) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken $C_4$ rotational symmetry. One of the few stoichiometric IBS, lithium iron arsenide, superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, using angle-resolved photoemission, that even superconducting state in LiFeAs is also a nematic one. We observe spontaneous breaking of the rotational symmetry in the gap amplitude on all Fermi surfaces, as well as unidirectional distortion of the Fermi pockets. Remarkably, these deformations disappear above superconducting $T_c$. Our results demonstrate the realization of a novel phenomenon of superconductivity-induced nematicity in IBS, emphasizing the intimate relation between them. We suggest a theoretical explanation based on the emergence of a secondary instability inside the superconducting state, which leads to the nematic order and s-d mixing in the gap function.

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) we study the electronic structure of layered BaZnBi$_2$. Our experimental results show no evidence of Dirac states in BaZnBi$_2$ originated either from the bulk or the surface. The calculated band structure without spin-orbit interaction shows several linear dispersive band crossing points throughout the Brillouin zone. However, as soon as the spin-orbit interaction is turned on, the band crossing points are significantly gapped out. The experimental observations are in good agreement with our DFT calculations. These observations suggest that the Dirac fermions in BaZnBi$_2$ are trivial and massive. We also observe experimentally that the electronic structure of BaZnBi$_2$ comprises of several linear dispersive bands in the vicinity of Fermi level dispersing to a wider range of binding energy., Comment: 7 pages, 4 figures

We present a systematic angle-resolved photoemission spectroscopy study of the superconducting gap in FeSe. The gap function is determined in a full Brillouin zone including all Fermi surfaces and kz-dependence. We find significant anisotropy of the superconducting gap in all momentum directions. While the in-plane anisotropy can be explained by both, nematicity-induced pairing anisotropy and orbital-selective pairing, the kz-anisotropy requires additional refinement of theoretical approaches., Comment: Main text: 6 pages, 4 figures; Supplemental Material: 2 pages, 1 figure

We study the low-energy electronic structure of three-dimensional Dirac semimetal, Cd$_3$(As$_{1-x}$P$_x$)$_2$ [$x$ = 0 and 0.34(3)], by employing the angle-resolved photoemission spectroscopy (ARPES). We observe that the bulk Dirac states in Cd$_3$(As$_{0.66}$P$_{0.34}$)$_2$ are gapped out with an energy of 0.23 eV, contrary to the parent Cd$_3$As$_2$ in which the gapless Dirac states have been observed. Thus, our results confirm the earlier predicted topological phase transition in Cd$_3$As$_2$ with perturbation. We further notice that the critical P substitution concentration, at which the two Dirac points that are spread along the $c$-axis in Cd$_3$As$_2$ form a single Dirac point at $\Gamma$, is much lower [x$_c$(P)$<$ 0.34(3)] than the predicted value of x$_c$(P)=0.9. Therefore, our results suggest that the nontrivial band topology of Cd$_3$As$_2$ is remarkably sensitive to the P substitution and can only survive over a narrow substitution range, i.e., 0 $\leq$ x (P) $<$ 0.34(3)., Comment: 3 figures, 5 pages

The asymptotic behavior, as $T\to\infty$, of some functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,dW_T(s)$, $t\ge0$ is studied. Here $\xi_T(t)$ is the solution to the time-inhomogeneous It\^{o} stochastic differential equation \[d\xi_T(t)=a_T\bigl(t,\xi_T(t)\bigr)\,dt+dW_T(t),\quad t\ge0, \xi_T(0)=x_0,\] $T>0$ is a parameter, $a_T(t,x),x\in\mathbb{R}$ are measurable functions, $|a_T(t,x)|\leq C_T$ for all $x\in\mathbb{R}$ and $t\ge0$, $W_T(t)$ are standard Wiener processes, $F_T(x),x\in\mathbb{R}$ are continuous functions, $g_T(x),x\in\mathbb{R}$ are measurable locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_T(t)$ is established under nonregular dependence of $a_T(t,x)$ and $g_T(x)$ on the parameter $T$., Comment: Published at http://dx.doi.org/10.15559/17-VMSTA83 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/). arXiv admin note: text overlap with arXiv:1607.03661

The nonmagnetic compounds showing extremely large magnetoresistance are attracting a great deal of research interests due to their potential applications in the field of spintronics. PtBi$_2$ is one of such interesting compounds showing large linear magnetoresistance (MR) in its both the hexagonal and pyrite crystal structure. We use angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT) calculations to understand the mechanism of liner MR observed in the hexagonal PtBi$_2$. Our results uncover for the first time linear dispersive surface Dirac states at the $\bar{\Gamma}$-point, crossing Fermi level with node at a binding energy of $\approx$ 900 meV, in addition to the previously reported Dirac states at the $\bar{M}$-point in the same compound. We further notice from our dichroic measurements that these surface states show an asymmetric spectral intensity when measured with left and right circularly polarized light, hinting at a substantial spin polarization of the bands. Following these observations, we suggest that the linear dispersive Dirac states at the $\bar{\Gamma}$ and $\bar{M}$-points are likely to play a crucial role for the linear field dependent magnetoresistance recorded in this compound.

We present ARPES data taken from the structurally simplest representative of iron-based superconductors, FeSe, in a wide temperature range. Apart from the variations related to the nematic transition, we detect very pronounced shifts of the dispersions on the scale of hundreds of kelvins. Remarkably, upon warming the sample up, the band structure has a tendency to relax to the one predicted by conventional band structure calculations, right opposite to what is intuitively expected. Our findings shed light on the origin of the dominant interaction shaping the electronic states responsible for high-temperature superconductivity in iron-based materials., Comment: 8 pages, 4 figures, PDF only