Superconducting Ground State Research Articles

Real and imaginary energy gaps: a comparison between single excitation Superradiance and Superconductivity and robustness to disorder

A comparison between the single particle spectrum of the discrete Bardeen-Cooper-Schrieffer (BCS) model, used for small superconducting grains, and the spectrum of a paradigmatic model of Single Excitation Superradiance (SES) is presented. They are both characterized by an equally spaced energy spectrum (Picket Fence) where all the levels are coupled between each other by a constant coupling which is real for the BCS model and purely imaginary for the SES model. While the former corresponds to the discrete BCS-model describing the coupling of Cooper pairs in momentum space and it induces a Superconductive regime, the latter describes the coupling of single particle energy levels to a common decay channel and it induces a Superradiant transition. We show that the transition to a Superradiant regime can be connected to the emergence of an imaginary energy gap, similarly to the transition to a Superconductive regime where a real energy gap emerges. Despite their different physical origin, it is possible to show that both the Superradiant and the Superconducting gaps have the same magnitude in the large gap limit. Nevertheless, some differences appear: while the critical coupling at which the Superradiant gap appears is independent of the system size $N$, for the Superconductivity gap it scales as $(\ln N)^{-1}$. The presence of a gap in the imaginary energy axis between the Superradiant and the Subradiant states shares many similarities with the "standard" gap on the real energy axis: the superradiant state is protected against disorder from the imaginary gap as well as the superconducting ground state is protected by the real energy gap. Moreover we connect the origin of the gapped phase to the long-range nature of the coupling between the energy levels.

Superconductivity in monocrystalline YNiSi3 and LuNiSi3

We report the discovery of bulk superconductivity in the ternary intermetallics ${\mathrm{YNiSi}}_{3}$ and ${\mathrm{LuNiSi}}_{3}$. High-quality single crystals were grown via the Sn-flux method and studied using magnetization, specific-heat, and resistivity measurements at low temperatures. The critical temperatures obtained from these different techniques are in very good agreement and yield ${T}_{\mathrm{c}}=1.36(3)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{c}}=1.61(2)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ for ${\mathrm{YNiSi}}_{3}$ and ${\mathrm{LuNiSi}}_{3}$, respectively. Magnetization measurements indicate that both compounds are among the rare cases where type-I superconductivity occurs in a ternary intermetallic, however, the jump in the specific heat at the transition is lower than the value expected from BCS theory ($\mathrm{\ensuremath{\Delta}}{C}_{\mathrm{el}}/{\ensuremath{\gamma}}_{\mathrm{n}}{T}_{\mathrm{c}}=1.43$) in both materials and is equal to 1.14(9) and 0.71(5) for the Y and Lu compounds, respectively. Resistivity measurements exhibit sharp transitions but with critical fields ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}}(0)$ ($\ensuremath{\approx}0.05\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ for ${\mathrm{YNiSi}}_{3}$ and $\ensuremath{\approx}0.08\phantom{\rule{0.28em}{0ex}}\mathrm{T}$ for ${\mathrm{LuNiSi}}_{3}$) considerably higher than those obtained from the magnetization and specific heat ($\ensuremath{\approx}0.01\phantom{\rule{0.28em}{0ex}}\mathrm{T}$). First-principles density functional theory calculated electronic structure shows that these compounds have highly anisotropic and complex Fermi surfaces with one electronic and two holelike branches. One hole branch and the electron branch have a large cylindrical topology connecting the first Brillouin-zone boundaries, the former being built up by the hybridization of Y(Lu) $d$, Ni $d$, and Si $p$ states, and the latter being built up by Ni $d$ and Si $p$ states. The calculated phononic structures indicate that the coupling of the Y(Lu), Ni $d$, and Si $p$ electrons in the low-lying optical phonon branches is responsible for the formation of Cooper pairs and the observed superconducting state. Therefore, these compounds can be classified as anisotropic three-dimensional metals with multiband superconducting ground states in the weak-coupling regime.

Quantum Monte Carlo study of the dominating pairing symmetry in doped honeycomb lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11774019, 11504067, 11574032, and 11734002), the National Key Research and Development Program of China (Grant No. 2016YFA0300304), and the Fundamental Research Funds for the Central Universities, China (Grant No. HIT.NSRIF.2019057).

We perform a systematic determinant quantum Monte Carlo (DQMC) study of the dominating pairing symmetry in a doped honeycomb lattice. The Hubbard model is simulated over a full range of filling levels for both weak and strong interactions. For weak couplings, the d-wave state dominates. The effective susceptibility as a function of filling shows a peak, and its position moves toward half filling as the temperature is increased, from which the optimal filling of the superconducting ground state is estimated. Although the sign problem becomes severe for strong couplings, the simulations access the lowest temperature at which the DQMC method generates reliable results. As the coupling is strengthened, the d-wave state is enhanced in the high-filling region. Our systematic DQMC results provide new insights into the superconducting pairing symmetry in the doped honeycomb lattice.

Probing the superconducting ground state of ZrIrSi: A muon spin rotation and relaxation study

The superconducting ground state of newly reported ZrIrSi is probed by means of $\mu$SR technique along with resistivity measurement. The occurrence of superconductivity at $T_\mathrm{C}$ = 1.7 K is confirmed by resistivity measurement. ZF-$\mu$SR study revealed that below $T_\mathrm{C}$, there is no spontaneous magnetic field in the superconducting state, indicates TRS is preserved in case of ZrIrSi. From TF-$\mu$SR measurement, we have estimated the superfluid density as a function of temperature, which is described by an isotropic $s-$wave model with a superconducting gap $2\Delta(0)/k_\mathrm{B}T_\mathrm{C}$ = 5.1, indicates the presence of strong spin-orbit coupling. {\it Ab-initio} electronic structure calculation indicates that there are four bands passing through the Fermi level, forming four Fermi surface pockets. We find that the low-energy bands are dominated by the $4d$-orbitals of transition metal Zr, with substantially lesser weight from the $5d$-orbitals of the Ir-atoms.

Surface Pair-Density-Wave Superconducting and Superfluid States.

Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demonstrate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead, the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair-density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state.

Energy-dependent spatial texturing of charge order in 1T−CuxTiSe2

Scanning tunneling microscopy unveils an unprecedented energy-dependent patchwork of charge density wave (CDW) regions in 1$T$-Cu${}_{x}$TiSe${}_{2}$. This Cu-induced patterning is echoing a large CDW gap opening below the Fermi level. It suggests a possible coexistence of the CDW and superconducting ground states, as the two quantum condensates involve different energy ranges in the electronic band structure of Cu${}_{x}$TiSe${}_{2}$. Finally, the well-developed CDW order in Cu-doped metallic Cu${}_{x}$TiSe${}_{2}$ rules out a solely excitonic CDW formation mechanism in this system.

Type-I superconductivity in the noncentrosymmetric superconductor BeAu

The noncentrosymmetric superconductor AuBe have been investigated using the magnetization, resistivity, specific heat, and muon-spin relaxation/rotation measurements. AuBe crystallizes in the cubic FeSi-type B20 structure with superconducting transition temperature observed at $T_{c}$ = 3.2 $\pm$ 0.1 K. The low-temperature specific heat data, $C_{el}$(T), indicate a weakly-coupled fully gapped BCS superconductivity with an isotropic energy gap 2$\Delta(0)/k_{B}T_{c}$ = 3.76, which is close to the BCS value of 3.52. Interestingly, type-I superconductivity is inferred from the $\mu$SR measurements, which is in contrast with the earlier reports of type-II superconductivity in AuBe. The Ginzburg-Landau parameter is $\kappa_{GL}$ = 0.4 $<$ 1/$\sqrt{2}$. The transverse-field $\mu$SR data transformed in the maximum entropy spectra depicting the internal magnetic field probability distribution, P(H), also confirms the absence of the mixed state in AuBe. The thermodynamic critical field, $H_{c}$, calculated to be around 259 Oe. The zero-field $\mu$SR results indicate that time-reversal symmetry is preserved and supports a spin-singlet pairing in the superconducting ground state.

Spin-Triplet p-Wave Superconductivity Revealed under High Pressure in UBe_{13}.

To unravel the nature of the superconducting symmetry of the enigmatic 5f heavy-fermion UBe_{13}, the pressure dependence of the upper critical field and of the normal state are studied up to 10GPa. Remarkably, the pressure evolution of the anomalous H_{c2}(T,P) over the entire pressure range up to 5.9GPa can be successfully explained by the gradual admixture of a field-pressure-induced E_{u} component in an A_{1u} spin-triplet ground state. This result provides strong evidence for parallel-spin pairing in UBe_{13}, which is also supported by the recently observed fully gapped excitation spectrum at ambient pressure. Moreover, we have also found a novel non-Fermi-liquid behavior of the resistivity, ρ(T)∼T^{n} (n≲1), which disappears with the collapse of the negative magnetoresistance behavior and the existence of a superconducting ground state around P=6 GPa, suggesting a close interplay between Kondo scattering and superconductivity.

Superconducting and normal state properties of the noncentrosymmetric superconductor NbOs2 investigated by muon spin relaxation and rotation

Noncentrosymmetric superconductors with $\alpha$-manganese structure has attracted much attention recently, after the discovery of time-reversal symmetry breaking in all the members of Re$_{6}$X (X = Ti, Hf, Zr) family. Similar to Re$_{6}$X, NbOs$_{2}$ also adopts $\alpha$-$Mn$ structure and found to be superconducting with critical temperature $T_{c}$ $\approx$ 2.7 K. The results of the resistivity, magnetization, specific heat and muon-spin relaxation/rotation measurements show that NbOs$_{2}$ is a weakly coupled type-II superconductor. Interestingly, the zero-field muon experiments indicate that the time-reversal symmetry is preserved in the superconducting state. The low-temperature transverse-field muon measurements and the specific heat data evidence a conventional isotropic fully gapped superconductivity. However, the calculated electronic properties in this material show that the NbOs$_{2}$ is positioned close to the band of unconventionality of the Uemura plot, indicating that NbOs$_{2}$ potentially borders an unconventional superconducting ground state.

Colloquium : Anomalous metals: Failed superconductors

The observation of metallic ground states in a variety of two-dimensional electronic systems poses a fundamental challenge for the theory of electron fluids. Here, we analyze evidence for the existence of a regime, which we call the "anomalous metal regime," in diverse 2D superconducting systems driven through a quantum superconductor to metal transition (QSMT) by tuning physical parameters such as the magnetic field, the gate voltage in the case of systems with a MOSFET geometry, or the degree of disorder. The principal phenomenological observation is that in the anomalous metal, as a function of decreasing temperature, the resistivity first drops as if the system were approaching a superconducting ground state, but then saturates at low temperatures to a value that can be orders of magnitude smaller than the Drude value. The anomalous metal also shows a giant positive magneto-resistance. Thus, it behaves as if it were a "failed superconductor." This behavior is observed in a broad range of parameters. We moreover exhibit, by theoretical solution of a model of superconducting grains embedded in a metallic matrix, that as a matter of principle such anomalous metallic behavior can occur in the neighborhood of a QSMT. However, we also argue that the robustness and ubiquitous nature of the observed phenomena are difficult to reconcile with any existing theoretical treatment, and speculate about the character of a more fundamental theoretical framework.

Spin switch effect in multiply connected superconductor-ferromagnet hybrid geometry

We consider a superconducting spin valve in multiply connected superconductor-ferromagnet hybrid geometry such as a superconducting ring enclosed a ferromagnetic metal, in the framework of linearized Usadel equations. We simplify our model by considering the presence of the exchange field in the superconducting ring which allows us to manipulate magnetization orientations in parallel or antiparallel configurations by switching the weaker exchange field. In such geometry the superconducting ground state is activated to higher orbital states characterized by the nonvanishing vorticity parameters L which will be the energetically favorable superconducting state in some ranges of the proximity superconductor-ferromagnet region. The competing effects caused by the exchange interactions and the orbital effect, are analyzed through the nonmonotonic dependence of the superconducting critical temperature Tc on the radius df of the ferromagnetic core. The analytic Tc(df) formula is obtained within the single mode approach and the analysis of the spin switch effect is given.

Mixed type I and type II superconductivity due to intrinsic electronic inhomogeneities in the type II Dirac semimetal PdTe2

The type II Dirac semimetal PdTe is unique in the family of topological parent materials because it displays a superconducting ground state below 1.7 K. Despite wide speculation on the possibility of an unconventional topological superconducting phase, tunneling and heat capacity measurements revealed that the superconducting phase of PdTe follows predictions of the microscopic theory of Bardeen, Cooper and Schrieffer for conventional superconductors. The superconducting phase in PdTe is further interesting because it also displays properties that are characteristic of type-I superconductors and are generally unexpected for binary compounds. Here, from scanning tunneling spectroscopic measurements we show that the surface of PdTe displays intrinsic electronic inhomogeneities in the normal state which leads to a mixed type I and type II superconducting behaviour along with a spatial distribution of critical fields in the superconducting state. Understanding of the origin of such inhomogeneities may be important for understanding the topological properties of PdTe in the normal state.

Superconducting properties of the noncentrosymmetric superconductor LaPtGe

We report superconducting properties of noncentrosymmetric superconductor LaPtGe which crystallizes in noncentrosymmetric $ \alpha $-ThSi$ _{2} $ structure. The magnetization, resistivity and specific heat measurements confirm that LaPtGe is a type-II bulk superconductor with a transition temperature T$ _{c} $ = 3.05 $ \pm $ 0.05 K. Muon-spin relaxation/rotation measurements confirms that time reversal preserved in the superconducting ground state.

Uniaxial pressure control of competing orders in a high-temperature superconductor.

Cuprates exhibit antiferromagnetic, charge density wave (CDW), and high-temperature superconducting ground states that can be tuned by means of doping and external magnetic fields. However, disorder generated by these tuning methods complicates the interpretation of such experiments. Here, we report a high-resolution inelastic x-ray scattering study of the high-temperature superconductor YBa2Cu3O6.67 under uniaxial stress, and we show that a three-dimensional long-range-ordered CDW state can be induced through pressure along the a axis, in the absence of magnetic fields. A pronounced softening of an optical phonon mode is associated with the CDW transition. The amplitude of the CDW is suppressed below the superconducting transition temperature, indicating competition with superconductivity. The results provide insights into the normal-state properties of cuprates and illustrate the potential of uniaxial-pressure control of competing orders in quantum materials.

Parity transitions in the superconducting ground state of hybrid InSb\u2013Al Coulomb islands

The number of electrons in small metallic or semiconducting islands is quantised. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting–semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS, and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e., compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes.

Smeared d‐Wave Anisotropy in a Monolayer Organic Superconductor

AbstractAn epitaxially grown monolayer of organic superconductor, (BETS)2GaCl4, on Ag(111) forms islands of uniform and mixed stacking of 2D stripes. A d‐wave superconducting gap of magnitude 2Δ = 14 meV is ubiquitously measured even though orientation directions of the molecular chains are altered in the inhomogeneous islands. Mixing of intrastripes antinodal states is manifested by smeared anisotropy of the low energy quasiparticle as well as features of multigaps in their density of states. Despite proximal convolution, the pronounced coherence peaks indicate well preserved superconducting state. The interplay between structural parameters and electronic properties makes single layer (BETS)2GaCl4 a unique playground to test the effect of confinement and symmetry variation on the superconducting ground state.

Atomic-scale tailoring of spin susceptibility via non-magnetic spin-orbit impurities

Following the discovery of topological insulators, there has been a renewed interest in superconducting systems that have strong spin-orbit (SO) coupling. Here we address the fundamental question of how the spin properties of a otherwise spin-singlet superconducting ground state evolve with increasing SO impurity density. We have mapped out the Zeeman critical field phase diagram of superconducting Al films that were deposited over random Pb cluster arrays of varying density. These phase diagrams give a direct measure of the Fermi liquid spin renormalization, as well as the spin orbit scattering rate. We find that the spin renormalization is a linear function of the average Pb cluster -to- cluster separation and that this dependency can be used to tune the spin susceptibility of the Al over a surprisingly wide range from 0.8χ0 to 4.0χ0, where χ0 is the non-interacting Pauli susceptibility.

Hidden charge-conjugation, parity, and time-reversal symmetries and massive Goldstone (Higgs) modes in superconductors

A massive Goldstone (MG) mode, often referred to as a Higgs amplitude mode, is a collective excitation that arises in a system involving spontaneous breaking of a continuous symmetry, along with a gapless Nambu-Goldstone mode. It has been known in the previous studies that a pure amplitude MG mode emerges in superconductors if the dispersion of fermions exhibits the particle-hole (p-h) symmetry. However, clear understanding of the relation between the symmetry of the Hamiltonian and the MG modes has not been reached. Here we reveal the fundamental connection between the discrete symmetry of the Hamiltonian and the emergence of pure amplitude MG modes. To this end, we introduce nontrivial charge-conjugation ($\mathcal C$), parity ($\mathcal P$), and time-reversal ($\mathcal T$) operations that involve the swapping of pairs of wave vectors symmetrical with respect to the Fermi surface. The product of $\mathcal{CPT}$ (or its permutations) represents an exact symmetry analogous to the CPT theorem in the relativistic field theory. It is shown that a fermionic Hamiltonian with a p-h symmetric dispersion exhibits the discrete symmetries under $\mathcal C$, $\mathcal P$, $\mathcal T$, and $\mathcal{CPT}$. We find that in the superconducting ground state, $\mathcal T$ and $\mathcal P$ are spontaneously broken simultaneously with the U(1) symmetry. Moreover, we rigorously show that amplitude and phase fluctuations of the gap function are uncoupled due to the unbroken $\mathcal C$. In the normal phase, the MG and NG modes become degenerate, and they have opposite parity under $\mathcal T$. Therefore, we conclude that the lifting of the degeneracy in the superconducting phase and the resulting emergence of the pure amplitude MG mode can be identified as a consequence of the the spontaneous breaking of $\mathcal T$ symmetry but not of $\mathcal P$ or U(1).

Unconventional superconductivity in the cage-type compound Sc5Rh6Sn18

We have examined the superconducting ground state properties of the caged type compound Sc$_5$Rh$_6$Sn$_{18}$ using magnetization, heat capacity, and muon-spin relaxation or rotation ($\mu$SR) measurements. Magnetization measurements indicate type-II superconductivity with an upper critical field $\mu_0H_{c2}(0)$ = 7.24 T. The zero-field cooled and field cooled susceptibility measurements unveil an onset of diamagnetic signal below $T_{\bf c}$ = 4.4 K. The interpretation of the heat capacity results below $T_{\bf c}$ using the $\alpha-$BCS model unveils the value of $\alpha$ = 2.65, which gives the dimensionless ratio 2$\Delta(0)/k_B T_{\bf c}$ = 5.3, intimating that Sc$_5$Rh$_6$Sn$_{18}$ is a strong-coupling BCS superconductor. The zero-field $\mu$SR measurements in the longitudinal geometry exhibit a signature of a spontaneous appearance of the internal magnetic field below the superconducting transition temperature, indicating that the superconducting state is characterized by the broken time-reversal symmetry (TRS). We have compared the results of broken TRS in Sc$_5$Rh$_6$Sn$_{18}$ with that observed in R$_5$Rh$_6$Sn$_{18}$ (R = Lu and Y).

Doping evolution of spin fluctuations and their peculiar suppression at low temperatures in Ca(Fe1−xCox)2As2

Results of inelastic neutron scattering measurements are reported for two annealed compositions of ${\mathrm{Ca}(\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{)}_{2}{\mathrm{As}}_{2},x=0.026$ and 0.030, which possess stripe-type antiferromagnetically ordered and superconducting ground states, respectively. In the AFM ground state, well-defined and gapped spin waves are observed for $x=0.026$, similar to the parent ${\mathrm{CaFe}}_{2}{\mathrm{As}}_{2}$ compound. We conclude that the well-defined spin waves are likely to be present for all $x$ corresponding to the AFM state. This behavior is in contrast to the smooth evolution to overdamped spin dynamics observed in ${\mathrm{Ba}(\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{)}_{2}{\mathrm{As}}_{2}$, wherein the crossover corresponds to microscopically coexisting AFM order and SC at low temperature. The smooth evolution is likely absent in ${\mathrm{Ca}(\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{)}_{2}{\mathrm{As}}_{2}$ due to the mutual exclusion of AFM ordered and SC states. Overdamped spin dynamics characterize paramagnetism of the $x=0.030$ sample and high-temperature $x=0.026$ sample. A sizable loss of magnetic intensity is observed over a wide energy range upon cooling the $x=0.030$ sample, at temperatures just above and within the superconducting phase. This phenomenon is unique amongst the iron-based superconductors and is consistent with a temperature-dependent reduction in the fluctuating moment. One possible scenario ascribes this loss of moment to a sensitivity to the $c$-axis lattice parameter in proximity to the nonmagnetic collapsed tetragonal phase and another scenario ascribes the loss to a formation of a pseudogap.