Nikolai Kristoffel, Küllike Rägo
An estimation shows that the interband pairing channel between the valence band components of doped graphane can support a superconducting transition temperature (or a contribution into this expected event) of the order of 100 K at the coupling strength near 1 eV.
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We study the existence of intraband and interband pairing in the extended two band and three-band Hubbard model. It is shown that including interband pairing significantly increases the superconducting critical temperature in comparison with critical temperature of the intraband pairing. This increase allows for decrease of the nearest-neighbor interaction constant necessary for critical temperature in high temperature superconductors to the realistic values.
Interband pairing as the origin of the sublattice dichotomy in monolayer FeSe/SrTiO_3
单层FeSe/SrTiO_3中亚晶格二元性源于能带间配对，无论对称性打破发生在正常态还是配对态，均需能带间配对来解释超导机制。
Topological states of multiband superconductors with interband pairing
本文研究 D4h 对称两带超导体中带间配对对节点结构和边界态的影响，发现其可改变节点拓扑并导致零能态转变为螺旋边缘态。
The origin of interband electron pairing responsible for enhancing superconductivity and the factors controlling its strength were examined. We show that the interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during the electron-phonon interactions. Its strength is determined by the pair-state excitations around the Fermi surfaces that take place to form a superconducting state. Fermi surfaces favorable for the pairing were found and its implications were discussed.
Contrary to the usual assumption, the electron Bloch states in crystals with spin-orbit coupling do not always transform under symmetry operations in the same way as the pure spin-1/2 states. This has profound consequences for the symmetry properties and nodal structure of superconductors, especially for the interband gap functions. Focusing on tetragonal superconductors, we show that the interband pairing in the conventional (s-wave) channel can have features which are traditionally associated with unconventional pairing, such as triplet components and odd parity, and can produce line nodes i…
Interband pairing in two-band superconductors with spin-orbit and Zeeman couplings
研究通过泽曼磁场在两能带超导体中实现能带配对，发现无能隙的准粒子谱及异常热力学行为。
The discovery of high-$T_c$ superconductivity in the pnictides, materials with a Fermi surface determined by several bands, highlights the need to understand how superconductivity arises in multiband systems. In this effort, using symmetry considerations and mean-field approximations, we discuss how strong hybridization among orbitals may lead to both intra and interband pairing, and we present calculations of the spectral functions to guide the experimental search for this kind of state.
Ginzburg-Landau energy of multiband superconductors with interband pairing
本文从微观推导了含带间配对的多带超导体Ginzburg-Landau自由能泛函，发现带间配对项稳定低温下时间反演对称性破缺的超导态。
Based on an effective two-band model and using the fluctuation-exchange (FLEX) approach, we explore spin fluctuations and unconventional superconducting pairing in Fe-based layer superconductors. It is elaborated that one type of interband antiferromagnetic (AF) spin fluctuation stems from the interband Coulomb repulsion, while the other type of intraband AF spin fluctuation originates from the intraband Coulomb repulsion. Due to the Fermi-surface topology, a spin-singlet extended s-wave superconducting state is more favorable than the nodal $d_{XY}$-wave state if the interband AF spin fluctua…
We consider a model for superconductivity in a two-band superconductor, having an anisotropic electronic structure made of two partially overlapping bands with a first hole-like and a second electron-like fermi surface. In this pairing scenario, driven by the interplay between interband $V_{i,j}$ and intraband $V_{i,i}$ pairing terms, we have solved the two gap equations at the critical temperature $T = T_c$ and calculate $T_c$ and the chemical potential $μ$ as a function of the number of carriers $n$ for various values of pairing interactions, $V_{1,1}$, $V_{2,2}$, and $V_{1,2}$. The results …
We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in …
Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliub…
The newly discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that, in the limit where the pairing occurs within the interband channel, several surprising effects occur quite naturally and generally: different density-of-states on the two bands lead to several unusual properties, including a gap ratio which behaves inversely to the ratio of density-of-states; the weak-coupling limit of the Eliashberg and the BCS theory, commonly taken as equivalent, in fact predict qualitatively different dependence of the $Δ_…
Recent experimental findings show that the pairing interaction in hole-doped cuprates resides in the nodal (FS arcs) region accompanied by the separate antinodal pseudogap. A corresponding multiband model of cuprate superconductivity is developed. It is based on the electronic spectrum evolving with doping and extends authors earlier approaches. The leading pair-transfer interaction is supposed between the itinerant (mainly oxygen) band and a nodal defect (polaron) band created by doping. These components are overlapping. The defect subband created in the antinodal region of the momentum space…
We derive the effective action for superconducting fluctuations in a four-band model for pnictides, discussing the emergence of a single critical mode out of a dominant interband pairing mechanism. We then apply our model to calculate the paraconductivity in two-dimensional and layered three-dimensional systems, and compare our results with recent resistivity measurements in SmFeAsOF
We investigate pairing mechanism in multiband superconductors. To put our feet on firm ground, unbiased renormalization group analysis is carried out for iron-based superconductors. It is quite remarkable that, after integrating out quantum fluctuations, the renormalization-group flows agree exceedingly well with a mean-field Hamiltonian where interband pair hopping plays an essential role. Through interband pair hopping, electrons can overcome the repulsive interaction between them and form resonating Cooper pairs between different bands. Unlike the conventional superconductors, the pairing m…
Interband-Pairing-Boosted Supercurrent Diode Effect in Multiband Superconductors
该研究提出带间配对可显著增强多带超导体约瑟夫森结中的超电流二极管效应，预测FeSe/STO可实现高达30%的效率，并可作为探测配对对称性的有力工具。
The effects of spin independent hybridization potential and spin orbit coupling on two band superconductor with equal time s-wave inter band pairing order parameter is investigated theoretically. To study symmetry classes in two band superconductors the Gorkov equations are solved analytically. By defining spin singlet and spin triplet s wave order parameter due to two band degree of freedom the symmetry classes of Cooper pair are studied. For spin singlet case it is shown that spin independent hybridization generates Cooper pair belongs to even frequency spin singlet even momentum even band p…
Recently, it has been proposed that a mechanism for the appearance of non-equilibrium superconductivity in a resonantly driven semiconductor with repulsive interband interactions exists.~\cite{Goldstein_PRB15} The underlying microscopic model relies on the appearance of a specific fermionic dissipation mechanism and the careful simultaneous tailoring of the electronic dispersion relation and electron-electron interactions. We, instead, show that the phenomenon is rather general and does not need a special fine tuning of parameters. By considering a pair of bands with locally the same sign of c…
Symmetry-Enforced Pair-Density Wave and Chiral Interband Superconductivity in Strongly Correlated Kagome Systems
研究Kagome晶格扩展t-J模型，发现对称性强制布洛赫波函数的子晶格结构导致非常规配对态，在p型范霍夫奇点处出现配对密度波态，在m'型范霍夫奇点处手性带间态稳定。
We study a four-band model for the iron oxypnictides, in which the superconducting properties are assumed to be determined by the interband coupling between hole-like and electron-like Fermi sheets. We show that reasonable parameters can account for the angle-resolved photoemission spectra showing multiple gaps in Ba$_{1-x}$K$_x$Fe$_2$As$_2$, and for the temperature dependence of the superfluid density. At the same time, the zero-temperature value of the superfluid density shows a conventional scaling with the number of carriers.
The possible strong electron-phonon coupling and the pairing within the full width of the electron band and not only in a narrow sheet near the Fermi surface are taken into account. It is found that the effect of pairing of electrons belonging to different bands is crucial to the appearance of high Tc in some two-band materials. The existence of another set of the two-band high temperature materials with transition temperature Tc, not yielding Tc in cuprates, is predicted.
We show that in two-band $s$-wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband $s$-wave interactions, in sharp contrast to single-band $s$-wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: (I) BCS pairing in both b…
Decoupled interband pairing in a bilayer iron-based superconductor evidenced by ultrahigh-resolution ARPES
研究通过ARPES揭示双层铁基超导体中弱耦合多能带超导态，发现双层能带间配对抑制机制，为工程新型超导性提供新思路。
Gap structure in noncentrosymmetric superconductors with spin-orbit band splitting is studied using a microscopic model of pairing mediated by phonons and/or spin fluctuations. The general form of pairing interaction in the band representation is derived, which includes both the intraband and interband pairing terms. In the case of isotropic interaction (in particular, for a BCS-contact interaction), the interband pairing terms vanish identically at any magnitude of the band splitting. The effects of pairing interaction anisotropy are analyzed in detail for a metal of cubic symmetry with stron…
We have investigated the effect of unconventional pairing mechanism in MgB2 using a two-band model within the framework of Bogoliubov-Valatin formalism. The approach incorporates the intra- band s-wave interaction in the s- and p-bands, as well as interband s-wave interaction between them. The analysis assumes the pairing interaction matrix comprises of attractive electron-phonon, charge fluctuation and repulsive electron-electron (Coulomb) interactions to account for superconductivity in MgB2. The model is used to estimate the transition temperature and isotope effect exponent as well as to e…
The Raman response in a superconductor is a powerful probe to investigate the symmetry of the superconducting gap. Here we show that in a multiband superconductor it also offers the unique opportunity to establish if the driving pairing interaction has an intraband or interband character. In the model with one hole and one electron band the full gauge-invariant Raman response, obtained by accounting for the fluctuations of both the density and superconducting phase degrees of freedom, is always dominated by the Leggett mode, regardless its nature. However, while in the case of intra-band domin…
Considering model Hamiltonians that respect the symmetry properties of the pnictides, it is argued that pairing interactions that couple electrons at different orbitals with an orbital-dependent pairing strength inevitably lead to interband pairing matrix elements, at least in some regions of the Brillouin zone. Such interband pairing has not been considered of relevance in multiorbital systems in previous investigations. It is also observed that if, instead, a purely intraband pairing interaction is postulated, this requires that the pairing operator has the form $Δ^+(k)=f(k) \sum_α d^+_{k,α,…
Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a general mechanism for spin-triplet superconductivity in multi-band systems, where a non-retarded pairing interaction between conduction electrons is produced by their electronic repulsion to a third-electron undergoing a virtual interband transition. Our theory is analytically controlled by an interband hybridization parameter, and explicitly demonstrated in doped band insulators…
We point out that essentially all multi-band superconductors have an odd-frequency pairing component, as follows from a general symmetry analysis of even- and odd-frequency pairing states. We show that odd-frequency superconducting pairing requires only a finite band hybridization, or scattering, and non-identical intraband order parameters, of which only one band needs to be superconducting. Under these conditions odd-frequency odd-interband pairing is always present. From a symmetry analysis we establish a complete reciprocity between parity in band-index and frequency.
Eliashberg Theory and Superfluid Stiffness of Band-Off-Diagonal Pairing in Twisted Graphene
本文在Eliashberg理论框架下研究扭曲石墨烯中带间非对角配对的频率混合、谱权重增强及超流刚度，揭示带间结构可显著降低刚度饱和温度尺度，为解释最新超流刚度测量提供理论依据。
Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
本文研究了量子几何对多带系统中奇频超导配对迈斯纳响应的影响，发现奇频配对的反磁性响应主要来源于其不同带间的相互作用，而同带相互作用则表现为顺磁性，从而揭示了量子几何对奇频超导稳定性的作用。
Tunable Superconductivity Mediated by Heavy-Electron Plasmons: Band-Structure and Quantum-Geometric Engineering
研究重电子等离子体介导的可调谐超导性，通过随机相位近似和Eliashberg理论计算最小金属模型最优临界温度，发现适度声子吸引可提升临界温度，还考虑绝缘系统，提出相关平台，确立平带系统在超导性中可作可调谐配对介质的新角色。
Superconducting mechanism mediated by interband exchange Coulomb repulsion is examined in an extended two-band Hubbard models with a wide band crossing the Fermi level and coexisting with a narrower band located at moderately lower energy. We apply newly developed path-integral renormalization group method to reliably calculate pairing correlations. The correlation shows marked enhancement at moderate amplitudes of the exchange Coulomb repulsion taken smaller than the on-site repulsion for the narrower band. The pairing symmetry is s-wave while it has unconventional phases with the opposite si…
We consider the minimal two-band model for the Fe-based superconductors with a phenomenological pairing interaction which mimics short-range antiferromagnetic (AFM) fluctuations. Two superconducting (SC) gap solutions are found to exist with the model: sign-changing s-wave gap ($\pm$s-wave) and double d-wave gap states. Both solutions hold the approximate relation $Δ_{h} ^{max} N_h \approx Δ_{e} ^{max} N_e$, a generic feature of two band model with a dominant interband pairing interaction. We carried out the calculations of the SC properties of the both SC states such as the density of states,…
Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$ have raised intensive debates as to its exact gap structure of either sign-reversal ($s^{+-}$) or sign-preserving ($s^{++}$) pairing. Here we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between $s^{+-}$ and $s^{++}$ pairing states, which include the intragap impurity resonance and a significant energy-depend…
A "negative" route to pair density wave order
本研究提出通过强耦合多带超导体中的带间配对机制，实现稳健的配对密度波有序。
Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings
该研究理论探究带近邻自旋轨道耦合的魔角扭曲双层石墨烯，发现其可产生拓扑平带与谷极化，且能通过费米面嵌套实现与谷失衡共存的非常规谷间带间超导，为非常规超导实现提供新路径。
We estimate the contribution of the long-wavelength el-TO-ph interaction and discuss the effect it has on electron pairing in doped polar systems like SrTiO3 and PbTe. The analytical and numerical results presented in the study indicate that the el-TO-ph interaction tends to contribute little to the total strength of electron-phonon coupling in these and related materials. To explain this fact we consider possible reasons why the effect of the polar long-wavelength transverse optical phonons on the coupling constant "lambda" is far less than one might suppose.
Nonequilibrium conditions offer novel routes to superconductivity that are not available at equilibrium. For example, by engineering nonequilibrium electronic populations, pairing may develop between electrons in different energy bands. A concrete proposal has been made to photo-induce superconductivity in a semiconductor, where pairing occurs between electrons in the conduction and valence bands, even for repulsive interactions. Here, we calculate the superfluid density for such a nonequilibrium paired state, and find it to be positive for repulsive interactions and interband pairing. The pos…
Superconductivity from interband coupling to ferroelectric quantum critical fluctuations in two dimensions
研究二维系统在铁电量子临界点附近，通过带间“斯塔克”耦合产生的有效双声子相互作用，发现临界温度相比BCS理论显著增强，并揭示了不同带隙区间的增强机制。
The isotope effects for Fe based superconductors are considered by including the phonon and magnetic fluctuations within the two band Eliashberg theory. We show that the recently observed inverse isotope effects of Fe, $α_{Fe} \approx -0.18 \pm 0.03 $,\cite{Shirage0903.3515} as well as the large positive isotope exponent ($α\approx 0.35$) can naturally arise for the magnetically induced sign revered s-wave pairing state within reasonable parameter range. Either experimental report can not be discarded from the present analysis based on the parameter values they require. The inverse and positiv…
We consider the origin of the anomalous Hall effect in a general model of a clean two-band chiral superconductor. Within the Kubo formalism we derive an analytic expression for the high-frequency ac Hall conductivity valid close to the critical temperature. This expression involves two distinct gauge-invariant time-reversal-odd bilinear (TROB) functions involving the pairing potential and its Hermitian conjugate. We argue that the existence of at least one of these TROBs generically implies a nonzero ac Hall conductivity. The TROBs allow us to clarify the roles of intra- and interband pairing,…
In the framework of four-band model of superconductivity in iron arsenides proposed by Barzykin and Gor'kov we analyze the gap ratios on hole - like and electron - like Fermi - surface cylinders. It is shown that experimentally observed (ARPES) gap ratios can be obtained only within rather strict limits on the values of pairing coupling constants. The difference of T_c values in 1111 and 122 systems is reasonably explained by the relative values of partial densities of states. The multiple bands electronic structure of these systems leads to a significant enhancement of effective pairing coupl…
Phase stiffness in flat-band superconductors with nodal pairing
本文研究了具有节点配对的平板带超导体中相刚度的二次温度依赖性，并探讨了杂质对超导性的影响。
The model of two (s and p) channel superconductivity known to be necessary to explain the superconductivity in MgB2 has been applied to the Al1-xMgxB2 diborides by tuning x from MgB2 to AlMgB4. The evolution of the interband coupling parameter (probing the strength of the interchannel pairing due to quantum interference effects) and the two gaps in the s and p channel as a function of x have been calculated. While in MgB2 the quantum interference effects give an amplification of Tc by a factor of 1.5 in comparison with the dominant intra s band single channel pairing, in AlMgB4 the amplificati…
The properties of the phonon-induced interaction between electrons are studied using the local density approximation (LDA). Restricting the electron momenta to the Fermi surface we find generally that this interaction has a pronounced peak for large momentum transfers and that the interband contributions between bonding and antibonding band are of the same magnitude as the intraband ones. Results are given for various symmetry averages of this interaction over the Fermi surface. In particular, we find that the dimensionless coupling constant in the d-wave channel $λ^d$, relevant for supercondu…
We study the nonequilibrium dynamics of multiband BCS superconductors subjected to ultrashort pump pulses. Using density-matrix theory, the time evolution of the Bogoliubov quasiparticle densities and the superconducting order parameters are computed as a function of pump pulse frequency, duration, and intensity. Focusing on two-band superconductors, we consider two different model systems. The first one, relevant for iron-based superconductors, describes two-band superconductors with a repulsive interband interaction $V_{12}$ which is much larger than the intraband pairing terms. The second m…
We report a low-temperature specific heat study of high-quality single crystals of the heavily hole doped superconductor Ca$_{0.32}$Na$_{0.68}$Fe$_2$As$_2$. This compound exhibits bulk superconductivity with a transition temperature $T_c \approx 34$\,K, which is evident from the magnetization, transport, and specific heat measurements. The zero field data manifests a significant electronic specific heat in the normal state with a Sommerfeld coefficient $γ\approx 53$ mJ/mol K$^{2}$. Using a multi-band Eliashberg analysis, we demonstrate that the dependence of the zero field specific heat in the…
Visualization of defect-induced interband proximity effect at the nanoscale
本研究通过纳米尺度可视化缺陷诱导的能带近邻效应，揭示了如何通过局部调控能带耦合强度来改变超导序参数，为多能带超导体的量子效应研究提供了新途径。
We study superconductivity in the Hubbard model on various quasi-one-dimensional lattices with coexisting wide and narrow bands originating from multiple sites within a unit cell, where each site corresponds to a single orbital. The systems studied are the 2-leg and 3-leg ladders, the diamond chain, and the criss-cross ladder. These one-dimensional lattices are weakly coupled to form two-dimensional (quasi-one-dimensional) ones, and the fluctuation exchange approximation is adopted to study spin-fluctuation-mediated superconductivity. When one of the bands is perfectly flat, and the Fermi leve…
We show, based on microscopic models, that fermionic band insulators with multiple bands and strong interband attraction are generically unstable towards nonzero momentum Cooper pairing leading to a pair density wave (PDW) superfluid state. Our first model considers a band insulating state of fermionic atoms in a three-dimensional cubic optical lattice. We show that this insulator is unstable towards an incommensurate PDW in the vicinity of a Feshbach resonance. Our second model is a two-band tight binding model relevant to electrons in solids; we show that the insulating state of this model h…
Since their discovery, it has been suggested that pairing in pnictides can be mediated by spin fluctuations between hole and electron bands. In this view, multiband superconductivity would substantially differ from other systems like MgB2, where pairing is predominantly intraband. Indeed, interband-dominated pairing leads to the coexistence of bonding and antibonding superconducting channels. Here we show that this has profound consequences on the nature of the low-energy superconducting collective modes. In particular, the so-called Leggett mode for phase fluctuations is absent in the usual t…
Quantum geometric superfluid weight in multiband superconductors: A microscopic interpretation
本研究从微观过程出发，解析多带超导体中量子几何诱导的超流权重，识别出两类带间贡献，并数值展示负SW现象，为配对密度波序提供新见解。
Starting with the generic Ginzburg-Landau expansion from a microscopic $N$-band model, we focus on the case of a 3-band model which was suggested to be relevant to describe some iron-based superconductors. This can lead to the so-called $s+is$ superconducting state that breaks time-reversal symmetry due to the competition between different pairing channels. Of particular interest in that context, is the case of an interband dominated pairing with repulsion between different bands. For that case we consider in detail the relevant reduced two-component Ginzburg-Landau theory. We provide detailed…
We study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly-interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozières-Schmitt-Rink…
Anomalous impurity effect in the heavy-fermion superconductor CeCu2Si2
针对重费米子超导体CeCu₂Si₂常压下杂质效应的实验矛盾，通过带内带间杂质散射理论分析，揭示无节点s±波配对下Tc抑制的非单调变化，解决矛盾并支撑该配对图景，理论可推广至其他窄带超导体系。
We study the role of impurities in a two-band superconductor, and elucidate the nature of the recently predicted transition from s_{+-} state to s_{++} state induced by interband impurity scattering. Using a Ginzburg-Landau theory, derived from microscopic equations, we demonstrate that close to T_c this transition is necessarily a direct one, but deeper in the superconducting state an intermediate complex state appears. This state has a distinct order parameter, which breaks the time-reversal symmetry, and is separated from the s_{+-} and s_{++} states by phase transitions. Based on our resul…
Based on experimental data on the newly synthesized iron-based superconductors and the relevant band structure calculations, we propose a minimal two-band BCS-type Hamiltonian with the interband Hubbard interaction included. We illustrate that this two-band model is able to capture the essential features of unconventional superconductivity and spin density wave (SDW) ordering in this family of materials. It is found that bound electron-hole pairs can be condensed to reveal the SDW ordering for zero and very small doping, while the superconducting ordering emerges at small finite doping, whose …
The electron band around $M$ point in (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ compound -- completely lifted above the Fermi level for $x > 0.7$ and hence has no Fermi Surface (FS) -- can still form an isotropic s-wave gap ($Δ_e$) and it is the main pairing resource generating an s-wave gap ($Δ_h$) with an opposite sign on the hole pocket around $Γ$ point. The electron band developing the SC order parameter $Δ_e$ but having no FS displays a {\it shadow gap} feature which will be easily detected by various experimental probes such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling…
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