arXiv subjects

A. B. Vorontsov

Publications and source records attributed to A. B. Vorontsov.

At least 19 recordsLinked to original sources

arXiv2019

Phase Crystals

Superconductivity owes its properties to the phase of the electron pair condensate that breaks the $U(1)$ symmetry. In the most traditional ground state, the phase is uniform and rigid. The normal state can be unstable towards special inhomogeneous superconducting states: the Abrikosov vortex state, and the Fulde-Ferrell-Larkin-Ovchinnikov state. Here we show that the phase-uniform superconducting state can go into a fundamentally different and more ordered non-uniform ground state, that we denote as a phase crystal. The new state breaks translational invariance through formation of a spatially periodic modulation of the phase, manifested by unusual superflow patterns and circulating currents, that also break time-reversal symmetry. We list the general conditions needed for realization of phase crystals. Using microscopic theory we then derive an analytic expression for the superfluid density tensor for the case of a non-uniform environment in a semi-infinite superconductor. We demonstrate how the surface quasiparticle states enter the superfluid density and identify phase crystallization as the main player in several previous numerical observations in unconventional superconductors, and predict existence of a similar phenomenon in superconductor-ferromagnetic structures. This analytic approach provides a new unifying aspect for the exploration of boundary-induced quasiparticles and collective excitations in superconductors. More generally, we trace the origin of phase crystallization to non-local properties of the gradient energy, which implies existence of similar pattern-forming instabilities in many other contexts.

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arXiv2017

Spontaneously broken translational symmetry at edges of high-temperature superconductors: thermodynamics in magnetic field

We investigate equilibrium properties, including structure of the order parameter, superflow patterns, and thermodynamics of low-temperature surface phases of layered d_{x^2-y^2}-wave superconductors in magnetic field. At zero external magnetic field, time-reversal symmetry and continuous translational symmetry along the edge are broken spontaneously in a second order phase transition at a temperature $T^*\approx 0.18 T_c$, where $T_c$ is the superconducting transition temperature. At the phase transition there is a jump in the specific heat that scales with the ratio between the edge length $D$ and layer area ${\cal A}$ as $(Dξ_0/{\cal A})ΔC_d$, where $ΔC_d$ is the jump in the specific heat at the d-wave superconducting transition and $ξ_0$ is the superconducting coherence length. The phase with broken symmetry is characterized by a gauge invariant superfluid momentum ${\bf p}_s$ that forms a non-trivial planar vector field with a chain of sources and sinks along the edges with a period of approximately $12ξ_0$, and saddle point disclinations in the interior. To find out the relative importance of time-reversal and translational symmetry breaking we apply an external field that breaks time-reversal symmetry explicitly. We find that the phase transition into the state with the non-trivial ${\bf p}_s$ vector field keeps its main signatures, and is still of second order. In the external field, the saddle point disclinations are pushed towards the edges, and thereby a chain of edge motifs are formed, where each motif contains a source, a sink, and a saddle point. Due to a competing paramagnetic response at the edges, the phase transition temperature $T^*$ is slowly suppressed with increasing magnetic field strength, but the phase with broken symmetry survives into the mixed state.

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arXiv2014

Temperature Dependence of the Magnetic Penetration Depth and Nodal Gap Structure of UPt$_3$ from Small Angle Neutron Scattering

Spanning a broad range of physical systems, complex symmetry breaking is widely recognized as a hallmark of competing interactions. This is exemplified in superfluid $^3$He which has multiple thermodynamic phases with spin and orbital quantum numbers $S=1$ and $L=1$, that emerge on cooling from a nearly ferromagnetic Fermi liquid. The heavy fermion compound UPt$_3$ exhibits similar behavior clearly manifest in its multiple superconducting phases. However, consensus as to its order parameter symmetry has remained elusive. Our small angle neutron scattering measurements indicate a linear temperature dependence of the London penetration depth characteristic of nodal structure of the order parameter. Our theoretical analysis is consistent with assignment of its symmetry $L=3$ odd parity state for which one of the three thermodynamic phases in non-zero magnetic field is chiral.

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arXiv2013

Superconducting gap with sign reversal between hole pockets in heavily hole-doped Ba1-xKxFe2As2

To gain insight into the unconventional superconductivity of Fe-pnictides with no electron pockets, we measure the thermal conductivity $κ$ and penetration depth $λ$ in the heavily hole-doped regime of Ba$_{1-x}$K$_x$Fe$_2$As$_2$. The residual thermal conductivity $(κ/T)_{T \rightarrow 0\,{\rm K}}$ and $T$-dependence of $λ$ consistently indicate the fully gapped superconductivity at $x=0.76$ and the (line) nodal superconductivity at higher hole concentrations. The magnitudes of $\fracκ{T}\cdot T_c|_{T \rightarrow 0\,{\rm K}}$ and $\frac{dλ}{d(T/T_c)}$ at low temperatures, both of which are determined by the properties of the low-energy excitations, exhibit a highly unusual non-monotonic x-dependence. These results indicate a dramatic change of the nodal characteristics in a narrow doping range, suggesting a doping crossover of the gap function between the s-wave states with and without sign reversal between $Γ$-centered hole pockets.

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arXiv2013

Field-angle-resolved anisotropy in superconducting CeCoIn5 using realistic Fermi surfaces

We compute the field-angle-resolved specific heat and thermal conductivity using realistic model band structure for the heavy-fermion superconductor CeCoIn5 to identify the gap structure and location of nodes. We use a two-band tight-binding parametrization of the band dispersion as input for the self-consistent calculations in the quasiclassical formulation of the superconductivity. Systematic analysis shows that modest in-plane anisotropy in the density of states and Fermi velocity in tetragonal crystals significantly affects the fourfold oscillations in thermal quantities, when the magnetic field is rotated in the basal plane. The Fermi surface anisotropy substantially shifts the location of the lines in the H-T plane, where the oscillations change sign compared to quasicylindrical model calculations. In particular, at high fields, the anisotropy and sign reversal are found even for isotropic gaps. Our findings imply that a simultaneous analysis of the specific heat and thermal conductivity, with an emphasis on the low energy sector, is needed to restrict potential pairing scenarios in multiband superconductors. We discuss the impact of our results on recent measurements of the Ce-115 family, namely CeTIn5 with T=Co,Rh,Ir.

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arXiv2011

Nodal gap structure of BaFe_2(As_{1-x}P_x)_2 from angle-resolved thermal conductivity in a magnetic field

The structure of the superconducting order parameter in the iron-pnictide superconductor BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$ ($T_c=31$\,K) with line nodes is studied by the angle-resolved thermal conductivity measurements in a magnetic field rotated within the basal plane. We find that the thermal conductivity displays distinct fourfold oscillations with minima when the field is directed at $\pm45^\circ$ with respect to the tetragonal a-axis. We discuss possible gap structures that can account for the data, and conclude that the observed results are most consistent with the closed nodal loops located at the flat parts of the electron Fermi surface with high Fermi velocity.

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arXiv2011

$^{75}$As NMR of Ba(Fe$_{0.93}$Co$_{0.07}$)$_{2}$As$_{2}$ in High Magnetic Field

The superconducting state of an optimally doped single crystal of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$ was investigated by $^{75}$As NMR in high magnetic fields from 6.4 T to 28 T. It was found that the Knight shift is least affected by vortex supercurrents in high magnetic fields, $H>11$ T, revealing slow, possibly higher order than linear, increase with temperature at $T \lesssim 0.5 \, T_c$, with $T_c \approx 23 \, K$. This is consistent with the extended s-wave state with $A_{1g}$ symmetry but the precise details of the gap structure are harder to resolve. Measurements of the NMR spin-spin relaxation time, $T_2$, indicate a strong indirect exchange interaction at all temperatures. Below the superconducting transition temperature vortex dynamics lead to an anomalous dip in $T_2$ at the vortex freezing transition from which we obtain the vortex phase diagram up to $H = 28$ T.

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arXiv2011

Specific heat jump at superconducting transition in the presence of Spin-Density-Wave in iron-pnictides

We analyze the magnitude of the specific heat jump ΔC at the superconducting transition temperature T_c in the situation when superconductivity develops in the pre-existing antiferromagnetic phase. We show that ΔC/T_c differs from the BCS value and is peaked at the tri-critical point where this coexistence phase first emerges. Deeper in the magnetic phase, the onset of coexistence, T_c, drops and ΔC/T_c decreases, roughly as ΔC/T_c \propto T^2_c at intermediate T_c and exponentially at the lowest T_c, in agreement with the observed behavior of ΔC/T_c in iron-based superconductors.

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arXiv2011

Effect of annealing on the specific heat of Ba(Fe1-xCox)2As2

We report on the effect of annealing on the temperature and field dependencies of the low temperature specific heat of the electron-doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ for under-(x = 0.045), optimal- (x = 0.08) and over-doped (x = 0.105 and 0.14) regimes. We observed that annealing significantly improves some superconducting characteristics in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$. It considerably increases $T_{c}$, decreases $γ_{0}$ in the superconducting state and suppresses the Schottky-like contribution at very low temperatures. The improved sample quality allows for a better identification of the superconducting gap structure of these materials. We examine the effects of doping and annealing within a self-consistent framework for an extended s-wave pairing scenario. At optimal doping our data indicates the sample is fully gapped, while for both under and overdoped samples significant low-energy excitations possibly consistent with a nodal structure remain. The difference of sample quality offers a natural explanation for the variation in low temperature power laws observed by many techniques.

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arXiv2010

Calorimetric Evidence for Nodes in the Overdoped Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$

We present low-temperature specific heat of the electron-doped Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$, which does not show any indication of an upturn down to 400 mK, the lowest measuring temperature. The lack of a Schottky-like feature at low temperatures or in magnetic fields up to 9 Tesla enables us to identify enhanced low-temperature quasiparticle excitations and to study anisotropy in the linear term of the specific heat. Our results can not be explained by a single or multiple isotropic superconducting gap, but are consistent with multi-gap superconductivity with nodes on at least one Fermi surface sheet.

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arXiv2010

Nodes vs. minima in the energy gap of iron-pnictides from field-induced anisotropy

We develop the formalism for computing the oscillations of the specific heat and thermal transport under rotated magnetic field in multiband superconductors with anisotropic gap and apply it to iron-pnictides. We show that these oscillations change sign at low temperatures and fields, which strongly influences the conclusions about the gap structure based on experiment. We find that recent measurements of the specific heat oscillations indicate that the iron-based superconductors possess an anisotropic gap with deep minima or nodes close to the line connecting electron and hole pockets. We make predictions for the behavior of the thermal conductivity that will help distinguish between these cases.

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arXiv2010

Superconductivity and spin-density-waves in multi-band metals

We present a detailed description of two-band quasi-2D metals with s-wave superconducting (SC) and antiferromagnetic spin-density wave (SDW) correlations. We present a general approach and use it to investigate the influence of the difference between the shapes and the areas of the two Fermi surfaces on the phase diagram. In particular, we determine the conditions for the co-existence of SC and SDW orders at different temperatures and dopings. We argue that a conventional s-wave SC order co-exists with SDW order only at very low $T$ and in a very tiny range of parameters. An extended s-wave superconductivity, for which SC gap changes sign between the two bands, co-exists with antiferromagnetic SDW over a much wider range of parameters and temperatures, but even for this SC order the regions of SDW and SC can still be separated by a first order transition. We show that the co-existence range becomes larger if SDW order is incommensurate. We apply our results to iron-based pnictide materials, in some of which co-existence of SDW and SC orders has been detected.

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arXiv2010

London penetration depth in Ba(Fe$_{1-x}$T$_x$)$_2$As$_2$ (T=Co, Ni) superconductors irradiated with heavy ions

Irradiation with Pb ions was used to study the effect of disorder on the in-plane London penetration depth, $λ(T)$, in single crystals of Ba(Fe$_{1-x}$T$_x$)$_2$As$_2$ (T=Co, Ni). An increase of the irradiation dose results in a monotonic decrease of the superconducting transition temperature, $T_c$, without affecting much the transition width. In both Co and Ni doped systems we find a power-law behavior, $Δλ(T) \propto T^n$, with the exponent $n$ systematically decreasing with the increase of disorder. This observation, supported by the theoretical analysis, conclusively points to a nodeless $s^\pm$ state with pairbreaking impurity scattering (interband) with strength being intermediate between Born and unitary limits.

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arXiv2010

Vortex state in d-wave superconductors with strong paramagnetism: transport and specific heat anisotropy

We analyse the combined effect of orbital and Pauli depairing on the superconducting state, and apply the results to the heavy fermion CeCoIn$_5$. We find that: a) standard extrapolation based on the slope of $H_{c2}(T)$ in the vicinity of the transition temperature to T=0 does not always give accurate values of the orbital upper critical field; b) critical value of the Maki parameter, $α$, that determines onset of the first order transition depends on the Fermi surface shape and the symmetry of the gap, and is $α^*\approx 3$ for CeCoIn$_5$; c) the anisotropy of the thermodynamic and transport coefficients in the low-temperature, low-field part of the phase diagram is essentially insensitive to the Zeeman field and can be used to determine the nodal directions in Pauli-limited superconductors. The latter result confirms the finding of the $d_{x^2-y^2}$ order parameter CeCoIn$_5$.

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arXiv2009

Coexistence between superconducting and spin density wave states in iron-based superconductors: Ginzburg-Landau analysis

We consider the interplay between superconducting (SC) and commensurate spin-density-wave (SDW) orders in iron-pnictides by analyzing a multiple order Ginzburg-Landau free energy. We are particularly interested in whether the doping-induced transition between the two states is first order, or the two pure phases are separated by an intermediate phase with coexisting SC and SDW orders. For perfect nesting, the two orders do not coexist, because SDW order, which comes first, gaps the full Fermi surface leaving no space for SC to develop. When nesting is not perfect due to either ellipticity of electron bands or doping-induced difference in chemical potentials for holes and electrons, SDW order still leaves modified Fermi surfaces for not too strong SDW magnetism and the SC order may develop. We show that the two orders coexist only when certain relations between ellipticity and doping are met. In particular, in a compensated metal, ellipticity alone is not sufficient for coexistence of the two orders.

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arXiv2009

Reduced effect of impurities on the universal pairing scale in the cuprates

We consider the effect of non-magnetic impurities on the onset temperature $T^*$ for the $d-$wave pairing in spin-fluctuation scenario for the cuprates. We analyze intermediate coupling regime when the magnetic correlation length $ξ/a >1$ and the dimensionless coupling $u$ is O(1). In the clean limit, $T^* \approx 0.02 v_f/a$ in this parameter range, and weakly depends on $ξ$ and $u$. We found numerically that this universal pairing scale is also quite robust with respect to impurities: the scattering rate $Γ_{cr}$ needed to bring $T^*$ down to zero is about 4 times larger than in weak coupling, in good quantitative agreement with experiments. We provide analytical reasoning for this result.

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arXiv2009

Momentum dependence and nodes of the superconducting gap in iron-pnictides

We discuss the structure of the superconducting gap in iron pnictides. In the itinerant electron picture, gaps with or without nodes have the extended s-wave (s+) symmetry and emerge within the same pairing mechanism, determined by the interplay between intra-pocket repulsion and inter-band pair hopping. If the pair hopping is stronger, the system develops an s+ gap without nodes. In the opposite case the superconductivity is governed by of the momentum-dependent part of the pair-hopping, and an s+ gap shows nodes on electron Fermi surfaces. We argue that the gap without/with nodes emerges in systems with a stronger/weaker tendency towards a spin-density-wave order.

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arXiv2009

Broken translational and time-reversal symmetry in superconducting films

We demonstrate that films of unconventional (d-wave) superconductor at temperatures $T\lesssim 0.43 T_c$ can exhibit unusual superconducting phases. The new ground states beside the broken gauge and the point group symmetries can spontaneously break (i) continuous translational symmetry and form periodic order parameter structures in the plane of the film, or (ii) time-reversal symmetry and develop supercurrent flowing along the film. These states are result of the strong transverse inhomogeniety present in films with thickness of several coherence lengths. We show a natural similarity between formation of these states and the Fulde-Ferrell-Larkin-Ovchinnikov state.

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