BCS Theory Research Articles

Non-Hermitian topological Fermi superfluid near the p -wave unitary limit

We discuss theoretically the non-Hermitian superfluid phase transition in one-dimensional two-component Fermi gases near the $p$-wave Feshbach resonance accompanied by the two-body loss associated with dipolar relaxation. We point out that this system gives us an opportunity to explore the interplay among various nontrivial properties such as universal thermodynamics at divergent $p$-wave scattering lengths, the topological phase transition at vanishing chemical potential, and the non-Hermitian Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) transition, in a unified manner. In the BCS phase, the loss-induced superfluid-normal transition occurs when the exceptional point appears in the effective non-Hermitian Hamiltonian. In the BEC phase, the diffusive gapless mode can be regarded as a precursor of the instability of the superfluid state. Moreover, we show that the superfluid state is fragile against the two-body loss near the topological phase transition point.

Electrical conductivity and nuclear magnetic resonance relaxation rate of Eliashberg superconductors in the weak-coupling limit

Electrical conductivity is an important transport response in superconductors, enabling clear signatures of dynamical interactions to be observed. Of primary interest in this paper is to study characteristics of the electron-phonon interaction in weak-coupling Eliashberg theory (Eth), and to note the distinctions with Bardeen-Cooper-Schrieffer (BCS) theory. Recent analysis of weak-coupling Eth has shown that while there are modifications from the BCS results, certain dimensionless ratios are in agreement. Here we show that the conductivities in BCS theory and Eth fundamentally differ, with the latter having an imaginary gap component that damps a divergence. We focus on the dirty limit, and for both BCS theory and Eth we derive expressions for the low-frequency limit of the real conductivity. For Eth specifically, there are two limits to consider, depending on the relative size of the frequency and the imaginary part of the gap. In the case of identically zero frequency, we derive an analytical expression for the nuclear magnetic resonance relaxation rate. Our analysis of the conductivity complements the previous study of the Meissner response and provides a thorough understanding of weak-coupling Eth.

Ultracold Feshbach molecules in an orbital optical lattice

Quantum gas systems provide a unique experimental platform to study the crossover between Bose–Einstein condensed molecular pairs and Bardeen–Cooper–Schrieffer superfluidity. The few studies in optical lattices have so far focused on the case when only the lowest Bloch band is populated, thus excluding orbital degrees of freedom. Here we demonstrate the preparation of ultracold Feshbach molecules of fermionic atoms in the second Bloch band of an optical square lattice. We cover a wide range of interaction strengths, including the regime of unitarity in the middle of the crossover. Binding energies and band relaxation dynamics are measured by means of a method resembling mass spectrometry. We find that the longest lifetimes arise for strongly interacting Feshbach molecules at the onset of unitarity. In the case of strong confinement in a deep lattice potential, we observe bound dimers also for negative values of the scattering length, extending previous findings for molecules in the lowest band.

Superconductivity of K‐Intercalated Epitaxial Bilayer Graphene

AbstractGraphene‐based materials are among the most promising candidates for studying superconductivity arising from reduced dimensionality. Apart from doping by twisted stacking, superconductivity can also be achieved by metal‐intercalation of stacked graphene sheets, where the properties depend on the choice of the metal atoms and the number of graphene layers. Many different and even unconventional pairing mechanisms and symmetries are predicted in the literature for graphene monolayers and few‐layers. However, those theoretical predictions have yet to be verified experimentally. Here, it is shown that potassium‐intercalated epitaxial bilayer graphene is a superconductor with a critical temperature of Tc = 3.6 ± 0.1 K. By scanning‐tunneling microscopy and angle‐resolved photoelectron spectroscopy, the physical mechanisms are analyzed in great detail, using laboratory equipment. The data demonstrate that electron–phonon coupling is the driving force enabling superconductivity. Although the consideration of an s‐wave pairing symmetry is sufficient to explain the experimental data, evidence is found for the existence of multiple energy gaps. Furthermore, it is shown that low‐dimensional effects are most likely the cause of a gap ratio of 6.1 ± 0.2 that strongly exceeds the Bardeen‐Cooper‐Schrieffer (BCS) value of 3.52 for conventional superconductors. These results highlight the importance of reduced dimensionality yielding unusual superconducting properties of K‐intercalated epitaxial bilayer graphene.

Superconductivity in Te-Deficient ZrTe2.

We present structural, electrical, and thermoelectric potential measurements on high-quality single crystals of ZrTe1.8 grown from isothermal chemical vapor transport. These measurements show that the Te-deficient ZrTe1.8, which forms the same structure as the nonsuperconducting ZrTe2, is superconducting below 3.2 K. The temperature dependence of the upper critical field (H c2) deviates from the behavior expected in conventional single-band superconductors, being best described by an electron-phonon two-gap superconducting model with strong intraband coupling. For the ZrTe1.8 single crystals, the Seebeck potential measurements suggest that the charge carriers are predominantly negative, in agreement with the ab initio calculations. Through first-principles calculations within DFT, we show that the slight reduction of Te occupancy in ZrTe2 unexpectedly gives origin to density of states peaks at the Fermi level due to the formation of localized Zr-d bands, possibly promoting electronic instabilities at the Fermi level and an increase at the critical temperature according to the standard BCS theory. These findings highlight that the Te deficiency promotes the electronic conditions for the stability of the superconducting ground state, suggesting that defects can fine-tune the electronic structure to support superconductivity.

Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb,Bi)2Sr2CuO6+δ

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but the superconductivity at high doping is often believed to be governed by conventional mean-field Bardeen–Cooper–Schrieffer theory1. However, it was shown that the superfluid density vanishes when the transition temperature goes to zero2,3, in contradiction to expectations from Bardeen–Cooper–Schrieffer theory. Our scanning tunnelling spectroscopy measurements in the overdoped regime of the (Pb,Bi)2Sr2CuO6+δ high-temperature superconductor show that this is due to the emergence of nanoscale superconducting puddles in a metallic matrix4,5. Our measurements further reveal that this puddling is driven by gap filling instead of gap closing. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.

Extreme enhancement of superconductivity in epitaxial aluminum near the monolayer limit.

BCS theory has been widely successful at describing elemental bulk superconductors. Yet, as the length scales of such superconductors approach the atomic limit, dimensionality as well as the environment of the superconductor can lead to drastically different and unpredictable superconducting behavior. Here, we report a threefold enhancement of the superconducting critical temperature and gap size in ultrathin epitaxial Al films on Si(111), when approaching the 2D limit, based on high-resolution scanning tunneling microscopy/spectroscopy (STM/STS) measurements. Using spatially resolved spectroscopy, we characterize the vortex structure in the presence of a strong Zeeman field and find evidence of a paramagnetic Meissner effect originating from odd-frequency pairing contributions. These results illustrate two notable influences of reduced dimensionality on a BCS superconductor and present a platform to study BCS superconductivity in large magnetic fields.

Enhancement of vortex liquid phase and reentrant behavior in NiBi3 single crystals

We investigate the vortex phase diagram of needle shaped high quality NiBi3 single crystals by transport measurements. The current is applied along the crystalline b-axis of this intermetallic quasi-1D BCS superconductor. The single crystals show a Ginzburg-Levanyuk (G i) parameter of about 10−7, larger by two orders of magnitude than G i in elemental low T c BCS superconductors. Vortex phase diagram, critical currents and pinning forces have been extracted from the experimental data. We observe (i) an enhancement of the vortex liquid phase, (ii) a reentrance of the liquid phase at low fields and (iii) an unusual magnetic field dependence of the pinning force. We suggest that these phenomena result from the interplay between pinning due to quenched disorder and the quasi-1D character of the material which could lead, for instance, to more complex pinning mechanisms at play.

Quench-drive spectroscopy and high-harmonic generation in BCS superconductors

In pump-probe spectroscopies, THz pulses are used to quench a system, which is subsequently probed by either a THz or optical pulse. In contrast, third-harmonic generation experiments employ a single multicycle driving pulse and measure the induced third harmonic. In this work, we analyze a spectroscopy setup where both a quench and a drive are applied and two-dimensional spectra as a function of time and quench-drive delay are recorded. We calculate the time evolution of the nonlinear current generated in the superconductor within an Anderson-pseudospin framework and characterize all experimental signatures using a quasiequilibrium approach. We analyze the superconducting response in Fourier space with respect to both the frequencies corresponding to the real time and the quench-drive delay time. In particular, we show the presence of a transient modulation of higher harmonics, induced by a wave mixing process of the drive with the quench pulse, which probes both quasiparticle and collective excitations of the superconducting condensate.

Superconducting properties and gap structure of the topological superconductor candidate Ti3Sb

We present a study of the superconducting properties of the candidate topological superconductor Ti_(3)Sb. Electrical transport measurements show zero resistance with a T_(c,onset) of ~ 5.9 K with a transition width {\Delta}T_c~ 0.6 K. The superconducting phase boundaries as derived from magneto-transport and magnetic susceptibility measurements agree well. We estimate an upper critical field Bc2(0)~4.5 T. A Ginzburg-Landau (GL) analysis yields values of the coherence length and penetration depth of {\zeta} = 6.2 nm and {\lambda} = 340 nm, respectively, and a GL parameter ~ 55, indicating extreme type-II behavior. Furthermore, we observed a step height in the specific heat ({\Delta}C_e)/({\gamma}T_c )~1.61, a value larger than the Bardeen-Cooper-Schrieffer (BCS) value of 1.43, suggesting modest coupling. Measurements of the temperature dependence of the London penetration depth via the tunnel-diode oscillator (TDO) technique down to ~ 450 mK show a full superconducting gap, consistent with a conventional s-wave gap structure.

Variational approach to quantum spin liquid in a Rydberg atom simulator

Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid (QSL) on a kagome lattice. Evidence of QSL has been obtained experimentally by directly measuring non-local string order. In this paper, we report a Bardeen–Cooper–Schrieffer (BCS)-type variational wave function study of the spin liquid state in this model. This wave function is motivated by mapping the Rydberg blockade model to a lattice gauge theory, where the local gauge conservations replace the role of constraints from the Rydberg blockade. We determine the variational parameter from the experimental measurement of the Rydberg atom population. Then we compare the predictions of this deterministic wave function with the experimental measurements of non-local string order. Combining the measurements on both open and closed strings, we extract the fluctuations only associated with the closed-loop as an indicator of the topological order. The prediction from our wave function agrees reasonably well with the experimental data, with only one fitting parameter determined by measurement of Rydberg atom population. Our variational wave function provides a simple and intuitive picture of the QSL in this system that can be generalized to similar spin liquid phases in other lattice geometry.

Enhancement of superconductivity at a quantum critical point in (Ca x Sr1−x )3Rh4Sn13

We report microscopic studies by muon spin spectroscopy of the superconducting properties as a function of chemical and hydrostatic pressure in the cubic ternary intermetallic (Ca x Sr1−x )3Rh4Sn13 compounds. We find evidence of a quantum critical point at a critical pressure p c in the superconducting phase, where the superfluid density increases by a factor of two and the superconducting pairing strength displays a pronounced maximum. The enhancement of superconductivity is related to the structural phase transition at p c , which is accompanied by profound changes of the Fermi surface associated to the suppression of a charge density wave (CDW). The quantum critical point separates a superconducting phase coexisting with CDW from a pure superconducting phase, while in both phases superconductivity has a strong-coupling phonon-mediated BCS-like s-wave character. Together with the related isoelectronic compound (Ca x Sr1−x )3Ir4Sn13, this system shows that conventional BCS superconductors in the presence of competing orders may display behaviour and characteristics of unconventional superconductors.

Triplet proximity effects in superconductor/ferromagnet hybrid structures exhibiting intrinsic spin–orbit coupling

The conventional spin–singlets with momentum zero can be transformed into spin-polarized triplet states with non-zero momentum at the superconductor/ferromagnet interface by an inhomogeneous magnetic exchange field. While the decaying spectrum of triplet pairs in ferromagnetic metals has received significant attention, less is known about the decay of these pairs in ferromagnets with intrinsic spin–orbit coupling (SOC) present at the superconductor/ferromagnet interface. We have performed simulations to study the triplet proximity effects in hybrid structures composed of a BCS superconductor and ferromagnet with intrinsic spin orbit coupling (SOC) in the diffusive limit where the quasiclassical boundary conditions have been modified to incorporate the effect of SO coupling in Usadel equations and the self-consistent equation. We laid emphasis on the modification of the density of states inside the ferromagnet near the Fermi energy. The generated short ranged triplets (SRTs) present themselves in the form of zero energy gap in the density of states (DOS) even in the presence of comparatively larger values of the exchange field oriented either in plane or out of plane of the hybrid structure and the Long ranged triplets (LRTs) present themselves in the form of zero energy peak in the DOS for feasible magnitude and orientation of the exchange field. Understanding and modeling these observations is important as it is difficult to model such hybrid structures experimentally. Where earlier research has focused on the scenario of substantial spin orbit coupling in the ballistic threshold/clean limit, in this paper we provide conclusions that are applicable to the diffusive transport/dirty limit regime. Also, the findings reveal that the SO coupling generates a distinct imprint in the DOS, which exhibits extremely nonmonotonic behavior with magnetization orientations.

Ni-Intercalation-Induced Topological Nodal Line States and Superconductivity in NiTe

Based on symmetry analyses and first-principles calculations, we report the predictions of topological fermions and superconductivity in Ni-intercalated transition metal chalcogenide NiTe. The self-intercalation of Ni introduces nonsymmorphic symmetry operations, protecting a pair of Dirac points and three intersecting Dirac nodal lines near Fermi energy level (EF), which generate spin-textured surface states across EF. Moreover, the Ni-intercalation strongly enhances electron–phonon coupling in NiTe and makes it an anisotropic Bardeen–Cooper–Schrieffer superconductor with a full superconducting gap and a critical temperature Tc ∼1.5 K. The coexistence of topological surface states and superconductivity implies that NiTe is a potential material platform for exploring topological superconductivity.

Momentum space entanglement of interacting fermions

Momentum space entanglement entropy probes quantum correlations in interacting fermionic phases. It is very sensitive to interactions, obeying volume-law scaling in general, while vanishing in the Fermi gas. We show that the R\'enyi entropy in momentum space has a systematic expansion in terms of the phase space volume of the partition, which holds at all orders in perturbation theory. This permits, for example, the controlled computation of the entropy of thin shells near the Fermi wavevector in isotropic Fermi liquids and BCS superconductors. In the Fermi liquid, the thin shell entropy is a universal function of the quasiparticle residue. In the superconductor, it reflects the formation of Cooper pairs. Momentum space R\'enyi entropies are accessible in cold atomic and molecular gas experiments through a time-of-flight generalization of previously implemented measurement protocols.

Electronic structure of NdNiO[formula omitted] superconductor from ab initio density-functional-theory calculations

Understanding high-temperature superconductivity is nowadays a challenge in the area of quantum materials and presents major unsolved problems. The recent discovery of superconductivity in infinite-layer nickelates has provided a new platform for studying unconventional superconductivity. Although the nickelates are analogous to the cuprates high-temperature superconductors, many theoretical analyses indicate that the nickelates do not precisely mirror the cuprates. For instance, hybridization between Ni 3dx2−y2 and O 2p is weak, which presents a high contrast to the hybridization between Cu 3d and O 2p in the cuprates. The similarities and differences between the nickelates and the cuprates provide great opportunities to reveal the origin of high-temperature superconductivity. In this study, with the employment of first-principles density-functional-theory calculations, we determine and analyze the electronic structure of the undoped infinite-layer nickelate NdNiO2. By performing phonon calculations and estimating the strength of the electron–phonon coupling, we find that this latter is weak, which indicates that the conventional BCS theory alone cannot explain the observed superconductivity in this material. Consequently, other still-unknown mechanisms may be at play. Moreover, we show from electronic band calculations that another conduction band crosses the Fermi level in addition to the Ni 3dx2−y2 band. This non-Ni conduction electron band is mainly composed of three orbitals: Nd 5d3z2−r2, Nd 5dxy, and another s-like orbital that does not belong to any specific atom. This interstitial s-like orbital is located around the (0,0,0.5) site. The rare-earth orbital Nd 5d3z2−r2 mixes with Ni 3dx2−y2 at the Fermi level, which causes some holes from the Nd 5d band to be (self-) doped into the Ni 3dx2−y2 orbitals.

Flow equation and fermion gap in the holographic superconductors

We reconsider the fermion spectral function in the presence of the Cooper pair condensation and identified the interaction type of complex scalar and fermion, which gives consistent results with the expected s-wave superconductor for the first time. We derive the matrix Riccati equation, which allows the precise calculation of the fermion spectral function. Apart from the gap structure, we studied the effect of the chemical potential and the density and compared it with the BCS theory. We found that two theories give similar results in small chemical potential but very different ones in the high-density case, which we attribute to the correlation effect.

Band structure, superconductivity, and polytypism in AuSn4

The orthorhombic compound AuSn4 is compositionally similar to the Dirac node arc semimetal PtSn$_4$. AuSn$_4$ is, contrary to PtSn$_4$, superconducting with a critical temperature of T$_c$ = 2.35 K. Recent measurements present indications for quasi two-dimensional superconducting behavior in AuSn$_4$. Here we present measurements of the superconducting density of states and the band structure of AuSn$_4$ through Scanning Tunneling Microscopy (STM) and Angular Resolved Photoemission Spectroscopy (ARPES). The superconducting gap values in different portions of the Fermi surface are spread around {\Delta}0 = 0.4 meV, which is close to but somewhat larger than $\Delta =$ 1.76kBT$_c$ expected from BCS theory. We observe superconducting features in the tunneling conductance at the surface up to temperatures about 20% larger than bulk Tc. The band structure calculated with Density Functional Theory (DFT) follows well the results of ARPES. The crystal structure presents two possible stackings of Sn layers, giving two nearly degenerate polytypes. This makes AuSn$_4$ a rather unique case with a three dimensional electronic band structure but properties ressembling those of low dimensional layered compounds.

Electron–phonon interactions and superconductivity of β -Nb2N thin films

Niobium nitride (NbN) has attracted scientific interest due to its diverse physical properties and a variety of structural phases. The structure and superconductivity of the cubic δ-NbN phase are well established, but its hexagonal phases are not explored hitherto. In the present work, we report a simple synthesis route and a detailed study of hexagonal β-Nb2N thin films. Thermal annealing of sputtered grown α-NbN leads to a single phase β-Nb2N at 973 K as confirmed by x-ray diffraction and absorption spectroscopy. The electrical transport measurements revealed a dominance of electron–phonon interactions with a superconducting transition around 4.74 K and an upper critical field [HC2(0)] of 3.99 T. The estimated HC2(0) is well below the calculated Pauli limit, and the Maki parameter value (α < 1) indicates that HC2(0) is dominated by an orbital pair breaking effect. Finally, the obtained value of electron–phonon coupling constant (λ) is in excellent agreement with a weak coupling Bardeen–Cooper–Schrieffer value of conventional superconducting materials.

Nonequilibrium noise as a probe of pair-tunneling transport in the BCS-BEC crossover.

The detection of elementary carriers in transport phenomena is one of the most important keys to understand nontrivial properties of strongly correlated quantum matter. Here, we propose a method to identify the tunneling current carrier in strongly interacting fermions from nonequilibrium noise in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate crossover. The noise-to-current ratio, the Fano factor, can be a crucial probe for the current carrier. Bringing strongly correlated fermions into contact with a dilute reservoir produces a tunneling current in between. The associated Fano factor increases from one to two as the interaction becomes stronger, reflecting the fact that the dominant conduction channel changes from the quasiparticle tunneling to the pair tunneling.