Interference-induced surface superconductivity: Enhancement by tuning the Debye energy

Chen L., Chen Y., Zhang W., Zhou S.

Recently a novel surface pair-density-wave (PDW) superconducting state has been discovered in Refs. Barkman et al. (2019) and Samoilenka et al. (2020), which may go through a distinct multiple phase transition (MPT) when the superconductivity fades away from bulk to the boundary (e.g. edges and corners). Based on the Bogoliubov-de Gennes equations for the attractive tight-binding Hubbard modal in a one-dimensional chain, we demonstrate that the surface PDW state has a non-gapless quasiparticle spectrum, which is contrary to the conventional surface superconducting state. Moreover, we find that the MPT is associated with a zero-bias fast oscillating pattern in the LDOS near the surface. Our findings provide a potential experimental clue to identify the surface PDW state. • For the first time, we found that the excitation spectra of recent discovered surface superconducting states in the attractive Hubbard model are non-gapless, contrary to the conventional gapless surface superconductivity under an external magnetic field between H c2 and H c3 . • We predicted a distinctive experimental clue for observing multiple phase transition of this novel surface superconducting states: zero-bias fast oscillations in the local density of states (LDOS).

Guzman E., Kargar F., Angeles F., Meidanshahi R.V., Grotjohn T., Hardy A., Muehle M., Wilson R.B., Goodnick S.M., Balandin A.A.

We report the results of the investigation of bulk and surface acoustic phonons in the undoped and boron-doped single-crystal diamond films using the Brillouin-Mandelstam light scattering spectroscopy. The evolution of the optical phonons in the same set of samples was monitored with Raman spectroscopy. It was found that the frequency and the group velocity of acoustic phonons decrease nonmonotonically with the increasing boron doping concentration, revealing pronounced phonon softening. The change in the velocity of the shear-horizontal and the high-frequency pseudo-longitudinal acoustic phonons in the degenerately doped diamond, as compared to that in the undoped diamond, was as large as ∼15% and ∼12%, respectively. As a result of boron doping, the velocity of the bulk longitudinal and transverse acoustic phonons decreased correspondingly. The frequency of the optical phonons was unaffected at low boron concentration but experienced a strong decrease at the high doping level. The density-functional-theory calculations of the phonon band structure for the pristine and highly doped samples confirm the phonon softening as a result of boron doping in diamond. The obtained results have important implications for thermal transport in heavily doped diamond, which is a promising material for ultra-wide-band-gap electronics.

Croitoru M.D., Shanenko A.A., Chen Y., Vagov A., Aguiar J.A.

In this work, we revisit the problem of superconductivity under the influence of boundary effects. By solving the Bogoliubov-de Gennes (BdG) equations for the tight-binding model, we demonstrate that the critical temperature of the nucleation of superconductivity near a sample surface can be considerably enhanced as compared to its bulk value. To bring to light this effect, we investigate different methods to solve numerically the BdG equations, including the continuous and Anderson approximations, and perform the calculations for a wide range of the system parameters. We obtain that all the self-consistent BdG eigenstates are delocalized and occupy the entire volume of the sample. Our results reveal that the enhancement of the surface critical temperature originates from the quantum interference of different BdG states contributing to the order parameter. We also find that the surface enhancement is the largest when the conduction band is symmetric with respect to the Fermi level, particularly, the half filling is an important proviso for the pronounced surface effect on the critical temperature. The approximate continuous model as well as the Anderson approximation do not capture the main feature of the surface effect. In addition, our study of this effect versus surface roughness reveals its fragile character.

Samoilenka A., Babaev E.

Bardeen-Cooper-Schrieffer (BCS) theory describes a superconducting transition as a single critical point where the gap function or, equivalently, the order parameter vanishes uniformly in the entire system. We demonstrate that in superconductors described by standard BCS models, the superconducting gap survives near the sample boundaries at higher temperatures than superconductivity in the bulk. Therefore, conventional superconductors have multiple critical points associated with separate phase transitions at the boundary and in the bulk. We show this by revising the Caroli-De Gennes-Matricon theory of a superconductor-vacuum boundary and finding inhomogeneous solutions of the BCS gap equation near the boundary, which asymptotically decay in the bulk. This is demonstrated for a BCS model of almost free fermions and for lattice fermions in a tight-binding approximation. The analytical results are confirmed by numerical solutions of the microscopic model. The existence of these boundary states can manifest itself as discrepancies between the critical temperatures observed in calorimetry and transport probes.

Szczęśniak R., Durajski A.P.

Recent experiments have set a new record for the transition temperature at which a material (hydrogen sulfide, H3S) becomes superconducting. Moreover, a pronounced isotope shift of T C in D3S is evidence of an existence of phonon-mediated pairing mechanism of superconductivity that is consistent with the well established Bardeen-Cooper-Schrieffer scenario. Herein, we reported a theoretical studies of the influence of the substitution of 32S atoms by the heavier isotopes 33S, 34S and 36S on the electronic properties, lattice dynamics and superconducting critical temperature of H3S. There are two equally fundamental results presented in this paper. The first one is an anomalous sulfur-derived superconducting isotope effect, which, if observed experimentally, will be subsequent argument that proves to the classical electron-phonon interaction. The second one is fact that critical temperature rise to extremely high value of 242 K for H336S at 155 GPa. This result brings us closer to the room temperature superconductivity.

Lanzillo N.A., Thomas J.B., Watson B., Washington M., Nayak S.K.

Significance Understanding the pressure response of the electrical properties of metals provides a fundamental way of manipulating material properties for potential device applications. In particular, the electrical resistivity of a metal, which is an intrinsic property determined primarily by the interaction strength between electrons and collective lattice vibrations (phonons), can be reduced when the metal is pressurized. In this article, we show that first-principles calculations of the resistivity, as well as experimental measurements using a solid media piston–cylinder apparatus, predict a significant reduction in the electrical resistivity of aluminum and copper when subject to high pressure due primarily to the reduction in the electron–phonon interaction strength. This study suggests innovative ways of controlling transport phenomena in metals.

Balandin A.A., Nika D.L.

Phonons – quanta of crystal lattice vibrations – reveal themselves in all electrical, thermal, and optical phenomena in materials. Nanostructures open exciting opportunities for tuning the phonon energy spectrum and related material properties for specific applications. The possibilities for controlled modification of the phonon interactions and transport – referred to as phonon engineering or phononics – increased even further with the advent of graphene and two-dimensional van der Waals materials. We describe methods for tuning the phonon spectrum and engineering the thermal properties of the low-dimensional materials via ribbon edges, grain boundaries, isotope composition, defect concentration, and atomic-plane orientation.

Chen Y., Croitoru M.D., Shanenko A.A., Peeters F.M.

It is well known that, in bulk, the solution of the Bogoliubov–de Gennes equations is the same whether or not the Hartree–Fock term is included. Here the Hartree–Fock potential is position independent and so gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. This is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position-dependent Hartree–Fock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubov–de Gennes equations with the Hartree–Fock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters.

Jérome D., Mazaud A., Ribault M., Bechgaard K.

Balandin A.A., Pokatilov E.P., Nika D.L.

Phonons, i.e., quanta of lattice vibrations, manifest themselves practically in all electrical, thermal, optical, and noise phenomena in semiconductors and other material systems. Reduction of the size of electronic devices below the acoustic phonon mean free path creates a new situation for the phonons propagation and interaction. From one side, it may complicate heat removal from the downscaled devices. From the other side, it opens up an opportunity for engineering phonon spectrum in nanostructured materials, and achieving enhanced operation of nanoscale devices. This chapter reviews the development of the nanoscale phonon engineering concept and discusses possible device applications. The focus of this review is on tuning the phonon spectrum in the acoustically mismatched nanoand heterostructures in order to change the ability of semiconductors to conduct heat or electric current. New approaches for the electron–phonon scattering rates suppression and improvement of the carrier mobility as well as for formation of the phonon stop-bands are discussed. The phonon engineering concept can be potentially as powerful as the band gap engineering, which led to some ground-breaking developments in the electronics.

Pokatilov E.P., Nika D.L., Balandin A.A.

We have theoretically studied acoustic phonon spectra and phonon propagation in rectangular nanowires embedded within elastically dissimilar materials. As example systems, we have considered GaN nanowires with AlN and plastic barrier layers. It has been established that the acoustically mismatched barriers dramatically influence the quantized phonon spectrum of the nanowires. The barriers with lower sound velocity compress the phonon energy spectrum and reduce the phonon group velocities in the nanowire. The barriers with higher sound velocity have an opposite effect. The physical origin of this effect is related to redistribution of the elastic deformations in the acoustically mismatched nanowires. In the case of the “acoustically slow” barriers, the elastic deformation waves are squeezed in the barrier layer. The effect predicted for the nanowires embedded with elastically dissimilar materials could be used for reengineering phonon spectrum in nanostructures.

Zhang Y., Jia J., Han T., Tang Z., Shen Q., Guo Y., Qiu Z.Q., Xue Q.

Using a low temperature growth method, we have prepared atomically flat Pb thin films over a wide range of film thickness on a Si-(111)-7 x 7 surface. The Pb film morphology and electronic structure are investigated in situ by scanning tunneling microscopy and angle-resolved photoemission spectroscopy. Well-defined and atomic-layer-resolved quantum-well states of the Pb films are used to determine the band structure and the electron-phonon coupling constant (lambda) of the films. We found an oscillatory behavior of lambda with an oscillation periodicity of two atomic layers. Almost all essential features in the Pb/Si(111) system, such as the growth mode, the oscillatory film stability, and the 9 monolayer envelope beating pattern, can be explained by our results in terms of the electron confinement in Pb films.

Matsumoto M., Heeb R.

Quasiparticle states around a single vortex in a $p_x\pm i p_y$-wave superconductor are studied on the basis of the Bogoliubov-de Gennes (BdG) theory, where both charge and current screenings are taken into account. Due to the violation of time reversal symmetry, there are two types of vortices which are distinguished by their winding orientations relative to the angular momentum of the chiral Cooper pair. The BdG solution shows that the charges of the two types of vortices are quite different, reflecting the rotating Cooper pair of the $p_x\pm i p_y$-wave paring state.

Tanaka K., Marsiglio F.

We test the Anderson prescription, a BCS formalism for describing superconductivity in inhomogeneous systems, and compare results with those obtained from the Bogoliubov--de Gennes formalism, using the attractive Hubbard model with surfaces and nonmagnetic impurities. The Anderson approach captures the essential features of the spatial variation of the gap parameter and electron density around a surface or an impurity over a wide range of parameters. It breaks down, however, in the strong-coupling regime for a weak impurity potential.

Hayashi N., Isoshima T., Ichioka M., Machida K.

Focusing on a quantum-limit behavior, we study a single vortex in a clean s-wave type-II superconductor by self-consistently solving the Bogoliubov-de Gennes equation. The discrete energy levels of the vortex bound states in the quantum limit is discussed. The vortex core radius shrinks monotonically up to an atomic-scale length on lowering the temperature T, and the shrinkage stops to saturate at a lower T. The pair potential, supercurrent, and local density of states around the vortex exhibit Friedel-like oscillations. The local density of states has particle-hole asymmetry induced by the vortex. These are potentially observed directly by STM.

Ding S., Bai Y., Bulekov A.A., Zhang W., Shanenko A.A., Chen Y.

Chen Y., Chen K., Zhu J., Shanenko A.A.

Chen Y., Zhu Q., Zhang M., Luo X., Shanenko A.A.

Recently, a surface superconductor-insulator transition has been predicted for a bulk superconductor in an electric field applied perpendicular to its surface. The related calculations were performed within a one-dimensional Hubbard model by numerically solving the Bogoliubov-de Gennes (BdG) equations without the Hartree-Fock (HF) interaction potential. The phase diagram of the surface superconducting, metallic, and insulating states was obtained as dependent on the electric field and temperature. This diagram was found to be in agreement with experimental results reported previously for (Li,Fe)OHFeSe thin flakes. In the present work, by taking into account the HF potential, we find that the latter acts as a kind of an extra electrostatic potential that enhances the electric-field effects on the surface states. The qualitative features of the phase diagram remain the same but the surface superconductor-insulator transition occurs at significantly lower electric fields, which supports prospects of its experimental observation in bulk samples.

Bai Y., Zhang L., Luo X., Shanenko A.A., Chen Y.

Nucleation of the pair condensate near surfaces above the upper critical magnetic field and the pair-condensate enhancement/suppression induced by changes in the electron-phonon interaction at interfaces are the most known examples of the surface superconductivity. Recently, another example has been reported when the surface enhancement of the critical superconducting temperature occurs due to quantum interference. In this case the pair states spread over the entire volume of the system while exhibiting the constructive interference near the surface. In the present work we investigate how an applied electric field impacts the interference-induced surface superconductivity. The study is based on a numerical solution of the self-consistent Bogoliubov-de Gennes equations for a one-dimensional attractive Hubbard model. Our results demonstrate that the surface superconducting characteristics, especially the surface critical temperature, are sensitive to the applied electric field and can be tailored by changing its magnitude.

Yin L., Bai Y., Zhang M., Shanenko A.A., Chen Y.

It is well known that the electric field can induce phase transitions between superconducting, metallic and insulating states in thin-film materials due to its control of the charge carrier density. Since a similar effect on the charge carriers can also be expected for surfaces of bulk samples, here, we investigate the transformation of the surface states in a superconductor under an applied screened electric field. Our study is performed by numerically solving the self-consistent Bogoliubov--de Gennes equations for the one-dimensional attractive Hubbard model. It is found that the surface insulating regime occurs at sufficiently large (but still experimentally accessible) electric fields. Our calculations yield the phase diagram of the surface superconducting, metallic, and insulating states for a wide range of temperatures and applied fields. Our results are in qualitative agreement with the phase diagram obtained with the transport measurements for (Li, Fe)OHFeSe thin flakes [Ma et al., Sci. Bull. 64, 653 (2019); Yin et al., ACS Nano 14, 7513 (2020)].

de Bragança R.H., Croitoru M.D., Shanenko A.A., Aguiar J.A.