领域：学术论文 · 自然科学

When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital1 . The hallmark of one-dimensional physics is a breaking up of the elementary electron into its separate degrees of freedom2 . The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago3 . Here we report observation of the separation of the orbital degree of freedom (orbiton) using resonant inelastic X-ray scattering on the one-dimensional Mott  insulator Sr2CuO3. We resolve an orbiton separating itself from spinons and propagating through the lattice as a distinct quasiparticle with a substantial dispersion in energy over momentum, of about 0.2 electronvolts, over nearly one Brillouin zone. 
It was pointed out in the 1970s that in a solid not only the charge and spin of electrons can become ordered—leading to magnetism—but also the electrons’ orbital degree of freedom1 . This observation sparked a field that has gone on to produce a number of important results. Although a physical electron combines spin, charge and orbital, theoretically an electron can be considered a bound state of the three independent, fundamental quasi-particles: a spinon, carrying the electron’s spin; a holon (or chargon), carrying its charge; and an orbiton, carrying its orbital degree of freedom. 
A remarkable and fundamental property of one-dimensional (1D) systems is that electronic excitations break up into deconfined spinons and holons. This was predicted decades ago (ref. 2 and references therein) and confirmed in the mid 1990s by angle-resolved photoemission spectroscopy experiments3–5. The spin–charge separation is an example of particle fractionalization, a phenomenon in which the 
quantum numbers of quasi-particles are not multiples of those of the elementary particle, but fractions. This effect is one of the most unusual manifestations of collective quantum physics of interacting particles and is a profound concept that has found its way into a number of theories, for example that describing high-temperature 
superconductivity in copper oxides6,7. 
To search for the further fractionalization of the electron, we consider the excitation of a copper orbital degree of freedom in the antiferromagnetic spin-chain compound Sr2CuO3. The spin–orbital separation process that we are looking for is analogous to the spin–charge separation mechanism (Fig. 1b). The latter occurs, for instance, when an electron is annihilated, removing a single spin and leaving behind a hole in the antiferromagnetic chain. This hole can start to propagate freely only after exciting one spinon (a domain wall in the  antiferromagnetic chain). Subsequently, the spinon can delocalize and separate itself completely from the holon. When instead of creating a hole, as typically is done in a photoemission experiment, an electron is excited from one copper 3d orbital to another, the phenomenon of spin–orbital separation can in principle occur (Fig. 1a). The orbiton created in this manner may also deconfine after exciting a spinon, thus splitting the electron into its orbital and spin degrees of freedom8 . 
Here we use high-resolution resonant inelastic X-ray scattering (RIXS) to search experimentally for spin–orbital separation in the quasi-1D copper oxide Sr2CuO3 (for material details, see Supplementary Information, section 1). We observe deconfinement of the spinon and orbiton during orbital excitation from the ground-state copper 3d orbital to an excited copper 3d xy or xz orbital (Fig. 1c–e). For simplicity, we will from henceforth use the so-called ‘hole’ language: although nominally there are nine electrons in the 3d orbitals of the Cu21 ion in Sr2CuO3, by using the ‘electron–hole’ transformation we can map the problem onto an effective system with one particle occupying a single 3d orbital (Supplementary Information, section 2). 
We measure an orbiton dispersion that is almost as large as the dispersion of the two-spinon continuum at low energies. As for spin–charge separation3–5, the orbiton dispersion has periodicity p (see Fig. 1c and see discussion below), which indicates the presence of an orbiton liberated from the spinon. 
We measured the orbital excitations of Sr2CuO3 using RIXS at the L3 edge of the copper ion. RIXS is a second-order scattering technique and can excite transitions between the copper 3d states of different symmetry (orbital excitations), owing to the involvement of two subsequent electric dipole transitions9,10 (Supplementary Information, section 3). With the unique capability of RIXS also to probe spin excitations11–13 and to vary the photon momentum transfer, the dispersion of orbital and spin excitations can be mapped out across the first Brillouin zone11–16. The experiments were carried out at the ADRESS beamline of the Swiss Light Source at the Paul Scherrer Institut17,18. 
For fixed momentum transfer, q, along the chains, peaks in the RIXS spectrum at constant energy transfer reveal the presence of charge-neutral elementary excitations and are visible in the RIXS intensity map of Sr2CuO3 across the copper L3 edge in Fig. 2a. The spectrum for which the incident energy was precisely tuned to the resonance maximum of the absorption spectrum is shown in Fig. 2b. In both plots, the excitations of the spin, orbital and charge degrees of freedom are indicated. The momentum dependence and, in particular, the dispersion of the spin and orbital excitations (Fig. 1c and Supplementary Fig. 2a) are indicative of their collective nature. 
For energy transfers of up to ,0.8 eV purely magnetic excitations are present, but the spectrum between ,1.5 and ,3.5 eV corresponds to excitations from the copper ground state to orbitals of symmetry (Fig. 1d, e). These peaks correspond toorbital excitations (called also d–d excitations), and not, for example, to charge transfer excitations, the intensity of which is non-zero for energies up to ,6 eV but here for the case of L-edge RIXS is at least an order of magnitude lower10. The orbital assignment of these excitations was unambiguously verified by comparing their energy with ab initio quantum chemistry cluster calculations19 (Supplementary Information, section 5, for detailed results). 
Zooming into the ‘magnetic’ part of Fig. 1c, between 0 and 0.8 eV in energy transfer, reveals strongly dispersing spin excitations. At the lower boundary the dispersion has period p, and at the continuum (upper boundary) it has period 2p (Fig. 3a). These RIXS data agree very well with recent inelastic neutron scattering studies on Sr2CuO3 (ref. 20). The simultaneous presence in the spectrum of a lower edge with period p and an upper one with period 2p indicates directly that in the spin chain the magnetic excitations with spin 1 break up and fractionalize into two-spinon (and higher-order) excitations that make up a continuum20, with each spinon having spin 1/2. These spectra confirm that RIXS for magnetic excitations probes the well-known 
spin dynamical structure factor as theoretically predicted11–13, in agreement with recent studies on TiOCl (ref. 21). The excellent statistics ofthe data further allow for a direct comparison of the RIXS line shapes with the exact two- and four-spinon dynamical structure factor of the spin-1/2 Heisenberg chain. In Fig. 3b, we show the fits for three selected momentum transfer values using the exact two- and four-spinon dynamical structure factor, S(q, v) (where q and v stand for the momentum and energy of the created excitation, respectively) in the representation of ref. 22. The obtained exchange coupling is in very good agreement with the value obtained from inelastic neutron scattering data20. 
Having unambiguously identified the fractionalized spinon excitations in the low-energy sector, we now concentrate on the orbital excitations spectrum in Fig. 4. We find that these are strongly momentum dependent and have a novel, distinct dispersion. This proves that the orbital excitations observed here are of collective nature. The xz excitation has the largest dispersion, of ,0.2 eV, and has a spectrum containing two peculiar components: a lower branch dispersing with periodicity p and, above that, an incoherent spectrum with a double-oval shape. This spectrum is strikingly similar to seemingly unrelated angle-resolved photoemission spectra of 1D copper oxides, which evidence spin–charge separation (see, for example, fig. 3 of ref. 3). This is an indication that the observed orbital dispersion is related to an analogous separation of degrees of freedom. 
To test this conjecture, we derived a microscopic model that describes the spin–orbital interactions in Sr2CuO3 (Methods). The low-energy Kugel’–Khomskii Hamiltonian for this was obtained8,23 from the charge transfer model of Sr2CuO3 in ref. 24. The crucial part of the Hamiltonian, responsible for the xz orbital propagation, 
where J and JO are respectively the spin and orbital exchange constants, both of which are fixed by the charge transfer model24; EO is the xz orbital on-site energy; c z js and cjs are operators that respectively annihilate and create particles in xz orbital with spin s; Sj is the spin of the particle in x2 2 y 2 orbital; 1 2 nj counts the number of particles in xz orbital; and ‘h.c.’ denotes Hermitian conjugate. The first term in the Hamiltonian describes the propagation of orbital excitations through the lattice. The second term represents the usual Heisenberg interaction between spins, which vanishes on bonds where an orbital excitation is present (Methods
To quantify the spectral weights within the orbiton–spinon continuum, we have calculated for the JO–J Hamiltonian the orbital excitation Green’s function by exactly diagonalizing the Hamiltonian on 28 lattice sites (as in the spin–charge separation studies3 , finite-size effects are negligible (they are estimated at ,0.01 eV)). From this, we calculate the RIXS spectrum following ref. 13, that is, by expressing the RIXS amplitude as a product of the single-ion local RIXS effective operator and the orbital excitation Green’s function (Methods). 
We find excellent agreement between theory and experiment (Fig. 4): both the sine-like xz orbiton dispersion and the xz spinon– orbiton continuum (the ‘double-oval’ incoherent spectrum), which are the hallmarks of spin–orbital separation, are present in the theory. The calculations also show that, in contrast to the xz orbital, the xy orbital has a small dispersion and that the excitations of both the orbital and the yz orbital are dispersionless, as is observed experimentally. This is an independent merit of the model because no fitting of dispersions to experimental data is involved. 
The large orbiton dispersion observed in this study is the key feature that distinguishes Sr2CuO3 from other systems with orbital excitations27–29, and relies on the 1D character of Sr2CuO3. In a system of higher dimensionality, orbitons interact with magnetic excitations, which tend to slow them down and thus reduce their dispersion. In one dimension, orbitons can avoid these renormalization effects by means of spin–orbital separation

翻译考点：
考点1. "two-spinon continuum"推荐翻译成"双自旋子连续谱"。
考点2. "Brillouin zone"推荐翻译成"布里渊区"，不可译为“布里墟区”。
考点3：“an orbiton liberated from the spinon”中liberated推荐译为“脱离”、“分离”或“摆脱”，不可译为“解放”