arXiv subjects

Konstantin B. Efetov

Publications and source records attributed to Konstantin B. Efetov.

At least 19 recordsLinked to original sources

arXiv2021

Slowly decaying real-time oscillations in instanton crystal

Instanton crystal is a fascinating phase which is encountered when the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in the form of a chain of alternating instantons and anti-instantons. We present the results of the investigation of the real-time correlation functions of the order parameter in the instanton crystal phase. In order to obtain the correlation functions in real-time, we formulate an original method of analytic continuation from imaginary times, which is easily adapted into an efficient numerical scheme for the computations. The resulting correlation functions exhibit non-trivial slowly decaying oscillations in real-time, which is reminiscent of prethermal time crystals.

cond-mat.str-el↗

arXiv2020

Phase transition into Instanton Crystal

We propose a class of models exhibiting instanton crystal phase. In this phase, the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in a form of a chain of alternating instantons and antiinstantons. The resulting characteristic feature of this state is that the average of the order parameter over the imaginary time vanishes. In order to study the model in a broad region of parameters of the model quantitatively, and prove the existence of the instanton crystal phase, we develop an efficient numerical scheme, suitable for the exact treatment of the proposed models. In a certain limit, results demonstrating the existence of the instanton crystal phase are obtained also analytically. The numerical study of the model shows that there is a phase transition between the instanton crystal and the state with the imaginary-time-independent order parameter.

cond-mat.str-el↗

arXiv2020

Supersymmetry method for interacting chaotic and disordered systems: the SYK model

The nonlinear supermatrix $σ$-model is widely used to understand the physics of Anderson localization and the level statistics in noninteracting disordered electron systems. In contrast to the general belief that the supersymmetry method applies only to systems of noninteracting particles, we adopt this approach to the disorder averaging in the interacting models. In particular, we apply supersymmetry to study the Sachdev-Ye-Kitaev (SYK) model, where the disorder averaging has so far been performed only within the replica approach. We use a slightly modified, time-reversal invariant version of the SYK model and perform calculations in real-time. As a demonstration of how the supersymmetry method works, we derive saddle point equations. In the semiclassical limit, we show that the results are in agreement with those found using the replica technique. We also develop the formally exact superbosonized representation of the SYK model. In the latter, the supersymmetric theory of original fermions and their superpartner bosons is reformulated as a model of unconstrained collective excitations. We argue that the supersymmetry description of the model paves the way for precise calculations in SYK-like models used in condensed matter, gravity, and high energy physics.

cond-mat.str-el↗

arXiv2019

Thermodynamic Quantum Time Crystals

Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now. Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and thermodynamically stable, results of a more careful study of the problem seemed to indicate that quantum time crystals could be realized only in systems out of equilibrium. Here we show that, in contrast to the general belief, thermodynamically stable macroscopic quantum time crystals can exist. The order parameter of this new state of matter is periodic in both real and imaginary time but its average over the phase of the oscillations equals zero. At the same time, correlation functions characterizing physical quantities oscillate periodically in time without any decay. An alternative interpretation of the results is based on a concept of an operator order parameter. Calculations are performed for a rather general microscopic model that may in particular be suitable for describing the pseudogap state in superconducting cuprates.

cond-mat.str-el↗

arXiv2019

Order parameter in electron systems: its fluctuations and oscillations

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.

cond-mat.str-el↗

arXiv2019

Mean-field thermodynamic quantum time-space crystal: spontaneous breaking of time-translation symmetry in a macroscopic fermion system

A model demonstrating existence of a thermodynamically stable quantum time-space crystal has been proposed and studied. This state is characterized by an order parameter periodic in both real and imaginary times. The average of the order parameter over phases of the oscillations vanishes but correlation functions of two or more order parameters show non-decaying oscillations. An alternative interpretation of the results is based on a concept of an operator order parameter introduced for this purpose. The model studied here has been suggested previously, in particular, for describing the pseudogap state in superconducting cuprates. Although many properties of the time-space crystal considered here are close to those of a well known DDW state, static magnetic moments oscillating at $ ( π,π) $ do not exist. Instead, $δ$-peaks at finite energies are predicted in the cross-section of inelastic spin-polarized neutron scattering.

cond-mat.str-el↗

arXiv2018

Charge and current orders in the spin-fermion model with overlapping hot spots

Experiments carried over the last years on the underdoped cuprates have revealed a variety of symmetry-breaking phenomena in the pseudogap state. Charge-density waves, breaking of $C_{4}$ rotational symmetry as well as time-reversal symmetry breaking have all been observed in several cuprate families. In this regard, theoretical models where multiple non-superconducting orders emerge are of particular interest. We consider the recently introduced (Phys. Rev. B 93, 085131 (2016)) spin-fermion model with overlapping 'hot spots' on the Fermi surface. Focusing on the particle-hole instabilities we obtain a rich phase diagram with the chemical potential relative to the dispersion at $(0,π);\;(π,0)$ and the Fermi surface curvature in the antinodal regions being the control parameters. We find evidence for d-wave Pomeranchuk instability, d-form factor charge density waves as well as commensurate and incommensurate staggered bond current phases similar to the d-density wave state. The current orders are found to be promoted by the curvature. Considering the appropriate parameter range for the hole-doped cuprates, we discuss the relation of our results to the pseudogap state and incommensurate magnetic phases of the cuprates.

cond-mat.str-el↗

arXiv2017

s+is superconductivity with incipient bands: doping dependence and STM signatures

Motivated by the recent observations of small Fermi energies and comparatively large superconducting gaps, present also on bands not crossing the Fermi energy (incipient bands) in iron-based superconductors, we analyse the doping evolution of superconductivity in a four-band model across the Lifshitz transition including BCS-BEC crossover effects on the shallow bands. Similar to the BCS case we find that with hole doping the phase difference between superconducting order parameters of the hole bands changes from $0$ to $π$ through an intermediate $s+is$ state breaking time-reversal symmetry. The transition however occurs in the region where electron bands are incipient and chemical potential renormalization in the superconducting state leads to a significant broadening of the $s+is$ region. We further present the qualitative features of the $s+is$ state that can be observed in scanning tunnelling microscopy (STM) experiments also taking incipient bands into account.

cond-mat.supr-con↗

arXiv2017

Superbosonization in disorder and chaos: The role of anomalies

Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The derivation is essentially based on the supersymmetric generalization of the Itzikson-Zuber integral in the presence of anomalies in the Berezinian and shows how an integral over supervectors is eventually reduced to an integral over commuting variables. The approach is tested by calculating both one and two point correlation functions in a class of random matrix models. It is argued that the approach is capable of producing nonperturbative results in various systems with disorder, including physics of many-body localization, and other situations hosting localization phenomena.

cond-mat.dis-nn↗

arXiv2017

Amplitude Higgs mode and admittance in superconductors with a moving condensate

We consider the amplitude (Higgs) mode in a superconductor with a condensate flow (supercurrent). We demonstrate that, in this case, the amplitude mode corresponding to oscillations $δ|Δ|_Ω \exp(i Ωt)$ of the superconducting gap is excited by an external ac electric field $\mathbf{E}_Ω \exp(i Ωt)$ already in the first order in $|\mathbf{E}_Ω|$, so that ${δ|Δ|_Ω \propto (\mathbf{v}_{0} \mathbf{E}_Ω)}$, where $\mathbf{v}_{0}$ is the velocity of the condensate. The frequency dependence $δ|Δ|_Ω$ has a resonance shape with a maximum at ${Ω= 2 Δ}$. In contrast to the standard situation without the condensate flow, the oscillations of the amplitude $δ|Δ(t)|$ contribute to the admittance $Y_Ω$. We provide a formula for admittance of a superconductor with a supercurrent. The predicted effect opens new ways of experimental investigation of the amplitude mode in superconductors and materials with superconductivity competing with other states.

cond-mat.supr-con↗

arXiv2016

Excess current in ferromagnet-superconductor structures with fully polarized triplet component

We study the $I$-$V$ characteristics of S$_{\text{T}}$/n/N contacts, where S$_{\text{T}}$ is a BCS superconductor S with a built-in exchange field $h$, n represents a normal metal wire, and N---a normal metal reservoir. The superconductor S$_{\text{T}}$ is separated from the n-wire by a spin filter which allows the passage of electrons with a certain spin direction so that only fully polarized triplet Cooper pairs penetrate into the n-wire. We show that both the subgap conductance $σ_{\text{sg}}$ and the excess current $I_{\text{exc}}$, which occur in conventional S/n/N contacts due to Andreev reflection (AR), exist also in the considered system. In our case, they are caused by unconventional AR that is not accompanied by spin flip. The excess current $I_{\text{exc}}$ exists only if $h$ exceeds a certain magnitude $h_{\text{c}}$. At ${h < h_{\text{c}}}$ the excess current is converted into a deficit current $I_\text{def}$. The dependencies of the differential conductance and the current $I_{\text{exc}}$ are presented as a function of voltage and $h$.

cond-mat.supr-con↗

arXiv2016

Cross-over from retro to specular Andreev reflections in bilayer graphene

Ongoing experimental progress in the preparation of ultra-clean graphene/superconductor (SC) interfaces enabled the recent observation of specular interband Andreev reflections (AR) at bilayer graphene (BLG)/NbSe$_{2}$ van der Waals interfaces [Nature Physics 12, (2016)]. Motivated by this experiment we theoretically study the differential conductance across a BLG/SC interface at the continuous transition from high to ultra-low Fermi energies $E_{F}$ in BLG. Using the Bogoliubov-deGennes equations and the Blonder-Tinkham-Klapwijk formalism we derive analytical expressions for the differential conductance across the BLG/SC interface. We find a characteristic signature of the cross-over from intra-band retro- (high $E_{F}$) to inter-band specular (low $E_{F}$) ARs, that manifests itself in a strongly suppressed interfacial conductance when the excitation energy $|\varepsilon |=|E_{F}|<Δ$ (the SC gap). The sharpness of these conductance dips is strongly dependent on the size of the potential step at the BLG/SC interface $U_{0}$.

cond-mat.mes-hall↗

arXiv2016

Spin-fermion model with overlapping hot spots and charge modulation in cuprates

We study particle-hole instabilities in the framework of the spin-fermion (SF) model. In contrast to previous studies, we assume that adjacent hot spots can overlap due to a shallow dispersion of the electron spectrum in the antinodal region. In addition, we take into account effects of a remnant low energy and momentum Coulomb interaction. We demonstrate that at sufficiently small values $|\varepsilon (π,0)-E_{F}|\lesssim Γ$, where $E_{F}$ is the Fermi energy, $\varepsilon \left( π,0\right) $ is the energy in the middle of the Brillouin zone edge, and $Γ$ is a characteristic energy of the fermion-fermion interaction due to the antiferromagnetic fluctuations, the leading particle-hole instability is a d-form factor Fermi surface deformation (Pomeranchuk instability) rather than the charge modulation along the Brillouin zone diagonals predicted within the standard SF model previously. At lower temperatures, we find that the deformed Fermi surface is further unstable to formation of a d-form factor charge density wave (CDW) with a wave vector along the Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnant Coulomb interaction enhances the d-form factor symmetry of the CDW. These findings can explain the robustness of this order in the cuprates. The approximations made in the paper are justified by a small parameter that allows one an Eliashberg-like treatment. Comparison with experiments suggests that in many cuprate compounds the prerequisites for the proposed scenario are indeed fulfilled and the results obtained may explain important features of the charge modulations observed recently.

cond-mat.str-el↗

arXiv2016

Overlapping hot spots and charge modulation in cuprates

Particle-hole instabilities are studied within a two dimensional model of fermions interacting with antiferromagnetic spin fluctuations (spin-fermion model). In contrast to previous works, we assume that neighboring hot spots overlap due to a shallow dispersion of the electron spectrum in the antinodal region and include in the consideration effects of a remnant low energy and momentum Coulomb interaction. It turns out that this modification of the model drastically changes the behavior of the system. The leading particle-hole instability at not very weak fermion-fermion interaction is no longer a charge density wave with a modulation along the diagonals of the Brillouin zone predicted previously but a Pomeranchuk-type deformation of the Fermi surface breaking the C$_{4}$ symmetry of the system. This order does not prevent from further phase transitions at lower temperatures. We show that, depending on parameters of the interaction, either d-wave superconductivity or charge density wave with modulations along the bonds of the $CuO$ lattice is possible. The low momentum remnant Coulomb interaction enhances the d-form factor of the charge density wave. Comparison with experimental data allows us to conclude that in many cuprate compounds the conditions for the proposed scenario are indeed fulfilled. Our results may explain important features of the charge modulations observed recently.

cond-mat.str-el↗

arXiv2015

Chirality and spin transformation of triplet Cooper pairs upon interaction with singlet condensate

We show that the fully polarized triplet s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current $I_{\text{J}}$ in a multiterminal Josephson contact of the S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ type with "magnetic" superconductors S$_{\text{m}}$ that generate fully polarized triplet components. The superconductors S$_{\text{m}}$ are attached to magnetic insulators (filters) which let to pass electrons with a fixed spin direction only. The filter axes are assumed to be oriented antiparallel to each other. The Josephson current is zero in two-terminal Josephson junction, i.e., in S/n/S$_{\text{m}}$ or in S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ contact. But in the three-terminal Josephson junction, with another S superconductor attached to the normal wire, the finite current $I_{\text{J}}$ appears flowing from the S~superconductor to S$_{\text{m}}$ superconductors. The currents through the right (left) superconductors S$_{\text{m}}$ are opposite in sign, ${I_{\text{R}} \equiv I_{\text{J}} = I_{\text{c}} \sin (χ_{\text{R}} + χ_{\text{L}} - 2 χ) = - I_{\text{L}}}$, where $χ_{\text{L/R}}$ and $χ$ are the phases of superconductors S$_{\text{m}}$, S$_{\text{m}}^{\prime}$, and S, respectively. We discuss possibilities of experimental observation of the effect.

cond-mat.supr-con↗

arXiv2015

Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics

We consider two types of magnetic Josephson junctions~(JJ). They are formed by two singlet superconductors~S and magnetic layers between them so that the JJ is a heterostructure of the S$_{\text{m}}$/n/S$_{\text{m}}$ type, where~S$_{\text{m}}$ includes two magnetic layers with non-collinear magnetization vectors. One layer is represented by a weak ferromagnet and another one---the spin filter---is either conducting strong ferromagnet (nematic or N\nobreakdash-type JJ) or magnetic tunnel barrier with spin-dependent transparency (magnetic or M\nobreakdash-type JJ). Due to spin filtering only fully polarized triplet component penetrates the normal n~wire and provides the Josephson coupling between the superconductors~S. Although both filters let to pass triplet Cooper pairs with total spin~$\mathbf{S}$ parallel to the filter axes, the behavior of nematic and magnetic JJs is completely different. Whereas in the nematic case the charge and spin currents,~$I_{\text{Q}}$ and~$I_{\text{sp}}$, do not depend on mutual orientation of the filter axes, both currents vanish in magnetic~JJ in case of antiparallel filter axes, and change sign under reversing the filter direction. The obtained expressions for~$I_{\text{Q}}$ and~$I_{\text{sp}}$ show clearly a duality between the superconducting phase~$φ$ and the angle~$α$ between the exchange fields in the weak magnetic layers.

cond-mat.supr-con↗

arXiv2015

Pairing gaps near ferromagnetic quantum critical points

We address the quantum-critical behavior of a two-dimensional itinerant ferromagnetic systems described by a spin-fermion model in which fermions interact with close to critical bosonic modes. We consider Heisenberg ferromagnets, Ising ferromagnets, and the Ising nematic transition. Mean-field theory close to the quantum critical point predicts a superconducting gap with spin-triplet symmetry for the ferromagnetic systems and a singlet gap for the nematic scenario. Studying fluctuations in this ordered phase using a nonlinear sigma model, we find that these fluctuations are not suppressed by any small parameter. As a result, we find that a superconducting quasi-long-range order is still possible in the Ising-like models but long-range order is destroyed in Heisenberg ferromagnets.

cond-mat.str-el↗

arXiv2015

Hidden Order as a Source of Interface Superconductivity

Interfacial superconductivity is observed in a variety of heterostructures composed of different materials including superconducting and nonsuperconducting (at appropriate doping and temperatures) cuprates and iron-based pnictides. The origin of this superconductivity remains in many cases unclear. Here, we propose a general mechanism of interfacial superconductivity for systems with competing order parameters. We assume that parameters characterizing the material allow formation of another order like charge- or spin-density wave competing and prevailing superconductivity in the bulk (hidden superconductivity). Diffusive electron scattering on the interface results in a suppression of this order and releasing the superconductivity. Our theory is based on the use of Ginzburg--Landau equations applicable to a broad class of systems. We demonstrate that the local superconductivity appears in the vicinity of the interface and the spatial dependence of the superconducting order parameter~$Δ(x)$ is described by the Gross--Pitaevskii equation. Solving this equation we obtain quantized values of temperature and doping levels at which~$Δ(x)$ appears. Remarkably, the local superconductivity shows up even in the case when the rival order is only slightly suppressed and may arise also on the surface of the sample (surface superconductivity).

cond-mat.supr-con↗