Ordered Bose Glass of Vortices in Superconducting YBa2Cu3O7- Thin Films with a Periodic Pin Lattice Created by Focused Helium Ion Irradiation

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Citation: Backmeister, L.; Aichner, B.;

Karrer, M.; Wurster, K: Kleiner, R.;

Goldobin, E; Koelle, D.; Lang, W.

Ordered Bose Glass of Vortices in

Superconducting YBa2Cu3O7−δThin

Films with a Periodic Pin Lattice

Created by Focused Helium Ion

Irradiation. Nanomaterials 2022,12,

3491. https://doi.org/10.3390/

nano12193491

Academic Editor: M.V. Ramallo

Received: 14 September 2022

Accepted: 2 October 2022

Published: 6 October 2022

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4.0/).

nanomaterials

Article

Ordered Bose Glass of Vortices in Superconducting YBa2Cu3O7−δ

Thin Films with a Periodic Pin Lattice Created by Focused Helium

Ion Irradiation

Lucas Backmeister 1, Bernd Aichner 1, Max Karrer 2, Katja Wurster 2, Reinhold Kleiner 2, Edward Goldobin 2,

Dieter Koelle 2, Wolfgang Lang 1,*

1Faculty of Physics, University of Vienna, A-1090 Wien, Austria; lucas.backmeister@univie.ac.at (L.B.);

bernd.aichner@univie.ac.at (B.A.)

2Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, Universität Tübingen,

D-72076 Tübingen, Germany; max.karrer@uni-tuebingen.de (M.K.); katja.wurster@uni-tuebingen.de (K.W.);

kleiner@uni-tuebingen.de (R.K.); gold@uni-tuebingen.de (E.G.); koelle@uni-tuebingen.de (D.K.)

*Correspondence: wolfgang.lang@univie.ac.at

Abstract:

The defect-rich morphology of YBa

7−δ

(YBCO) thin ﬁlms leads to a glass-like arrange-

ment of Abrikosov vortices which causes the resistance to disappear in vanishing current densities. This

vortex glass consists of entangled vortex lines and is identiﬁed by a characteristic scaling of the voltage–

current isotherms. Randomly distributed columnar defects stratify the vortex lines and lead to a Bose

glass. Here, we report on the observation of an ordered Bose glass in a YBCO thin ﬁlm with a hexagonal

array of columnar defects with 30 nm spacings. The periodic pinning landscape was engineered by a

focused beam of 30 keV He+ions in a helium-ion microscope.

Keywords:

copper-oxide superconductors; vortex glass; ordered Bose glass; vortex matching; voltage–

current isotherms; helium-ion microscope

1. Introduction

The copper oxide high-temperature superconductors (HTS) are in the extreme type-II limit,

with a minor lower critical ﬁeld

Bc1

and a high upper critical ﬁeld

Bc2

. The large difference

in the critical ﬁelds spans a vast area in the phase diagram, the mixed state. The magnetic

ﬂux enters as Abrikosov vortices, quantized portions of ﬂux

Φ0=h/

, where

is the Planck

constant and

is the elementary charge. The mixed state in HTS exhibits qualitatively new

phenomenology [

] and is the predominant operating condition for most applications of these

materials. Therefore, it is of utmost importance under which experimental conditions zero

resistance, the hallmark of superconductivity, can be achieved. Moreover, the parameter space

for utilizing superconductivity is limited by the critical temperature

, the upper critical

ﬁeld

Bc2

, and the critical current density

. The latter can be enhanced by various pinning

mechanisms that block the dissipative motion of the vortices [

]. In HTS, the boundaries

of this simple picture are substantially blurred by strong thermodynamic ﬂuctuations of the

superconducting order parameter.

In particular, the question of whether one can observe a genuine zero-resistance state at a

ﬁnite temperature or only at zero temperature has raised much interest. Following the ﬂux-

creep theory of Anderson and Kim [

], or the thermally-assisted ﬂux-ﬂow model (TAFF) [

one has to conclude that the resistance remains ﬁnite, even when the current density

j→

Indeed, voltage–current (

) isotherms in the mixed state of many HTS reveal an ohmic

behavior down to the lowest experimentally accessible voltages at temperatures not too far

Nanomaterials 2022,12, 3491. https://doi.org/10.3390/nano12193491 https://www.mdpi.com/journal/nanomaterials

arXiv:2210.03156v1 [cond-mat.supr-con] 6 Oct 2022

Nanomaterials 2022,12, 3491 2 of 11

below

. This observation is attributed to TAFF. Numerical simulations reveal a rich variety of

different dynamic phases when a vortex ensemble is driven over a background of correlated or

random pinning defects [7].

The minuscule coherence lengths in HTS and the importance of intrinsic randomly dis-

tributed defects have triggered theoretical proposals of a thermodynamic equilibrium phase

with a glass-like arrangement of vortices. Different theories have been proposed for randomly

distributed pinning defects, depending on their dimensionality: the vortex-glass (VG) model

for point-like defects [

] and the Bose-glass (BG) model for columnar defects penetrating the

entire sample thickness [10,11].

The VG model has been conﬁrmed by scaling of DC-current

isotherms in a variety

of HTS, among them YBa

7−δ

(YBCO) in the shape of optimally doped thin ﬁlms [

oxygen-deﬁcient ﬁlms [

], ultrathin ﬁlms [

], and single crystals [

]. In addition, in the

highly anisotropic compound Bi

CaCu

(BSCCO-2212), an agreement with the VG theory

was found in single crystals [

] and thin ﬁlms [

]. A transition from

3 to

2 VG

scaling was reported in oxygen-depleted YBCO ﬁlms [

]. In addition, phase-resolved AC

impedance measurements have provided another route to estimate the dynamic VG parameter

zVG [19].

The above considerations relate to defects in HTS that are not correlated along the crystal-

lographic

axis. In contrast, columnar defects (CDs) change the underlying physics, leading

to a Bose glass [

]. For instance, irradiation with swift heavy ions produces cylindrical

channels of amorphous material that act as

-axis correlated pinning sites and evoke a BG

behavior [

]. The fact that planar defects oriented parallel to the

axis are ubiquitous in thin

YBCO ﬁlms can lead to inconsistent observations of VG [

] or BG [

] behavior, depending

on the details of the material’s morphology. Moreover, earlier investigations of engineered

nanoinclusions of different dimensionality have reported a crossover between VG and BG

behavior [23]. For example, the latter was found for disordered BaZrO3nanorods in YBCO.

The transitions between these various vortex phases, governed by temperature, magnetic

ﬁeld, and disorder, are long-standing issues. One aspect of the problem is that in earlier

experiments, no periodic engineered pinning sites were available with spacings smaller than the

London penetration depth and pronounced vortex pinning effects down to low temperatures.

Recent advances in nanopatterning of HTS by masked or focused light-ion irradiation [

–

] allow for the engineering of CDs with a periodic arrangement [

–

]. Using YBCO thin

ﬁlms with an unprecedented dense hexagonal lattice of CDs, created by focused He

-ion-beam

irradiation, allows us to observe a novel kind of glassy vortex correlations, which we will call

an ordered Bose glass (OBG). This paper explores the OBG phase by measuring the

isotherms

at various temperatures and magnetic ﬁelds.

2. Theoretical Background

Both vortex and Bose glasses form below a magnetic-ﬁeld-dependent glass temperature

Tg(B)<Tc

that marks a bifurcation between two essentially different domains of voltage–

current (

) isotherms. While at

T>Tg(B)

ohmic characteristics prevail down to vanishing

, the zero-resistance state emerges at

T<Tg(B)

already at ﬁnite

. More importantly, the

theories predict a critical scaling of several physical parameters at the continuous second-order

phase transition between vortex or Bose glass and vortex liquid. In a VG, the central parameter

is the glass correlation length

ξVG ∝|T−Tg|−ν

, which is determined by the size of glassy

islands and of ﬂuctuating vortex liquid droplets above and below

Tg(B)

. The lifetime of these

ﬂuctuations is τ∝ξz

VG ∝|T−Tg|−νz.

Nanomaterials 2022,12, 3491 3 of 11

The theoretical predictions can be experimentally veriﬁed by measuring

isotherms

near the VG transition and by comparing the data to the relation

I∝ξD−2−z

VG F± IξD−1

VG Φ0

kBT!, (1)

where

F±

are two universal, yet unknown, characteristic functions of a speciﬁc VG system

above (

F+

) and below (

F−

)

Tg(B)

, respectively,

is the dimensionality of the vortex ensemble,

and

is the Boltzmann constant. By appropriately scaling a set of

isotherms according to

(V/I)|1−T/Tg|νVG(D−2−zVG)=F±[(I/T)|1−T/Tg|νVG(1−D)], (2)

collected at various temperatures and at ﬁxed

, all curves collapse onto the two universal

F±

branches. The scaling is achieved by a proper choice of the parameters

νVG

, and

zVG

. The

bifurcation line right at Tgnot only separates the branches F±but also obeys a power law.

(V/I)|T=Tg∝I(zVG +2−D)/(D−1). (3)

Note that the BG theory predicts a similar scaling of the

isotherms that can be cast into

the same Equation (2). Since a BG requires 3D correlations, the respective critical exponents of

a 3D-VG can be transformed to those of a BG by [21]

νBG =2νVG

3and zBG =3zVG +1

2. (4)

The VG and BG theories were developed for randomly arranged point and columnar

defects, respectively. A new and unique situation arises when the CDs are periodically arranged.

In an external magnetic ﬁeld, applied parallel to the CDs, one or more magnetic ﬂux quanta

penetrate the CDs. The resulting magnetic commensurability (matching) ﬁelds are

Bm=m2Φ0

√3a2, (5)

where

is a rational number, and

denotes the lattice constant of a hexagonal CD lattice. At

the matching ﬁelds

, when each CD can be ﬁlled on average by

ﬂux quanta, a signiﬁcant

change in the vortex dynamics can be expected. The most prominent effects are observed when

is a natural number. At these matching ﬁelds, we observe the ordered Bose glass phase

discussed below.

Tuning the magnetic ﬁeld allows one to switch the vortex ensemble between VG and OBG.

However, in the case of YBCO thin ﬁlms with their strong intrinsic pinning by twin boundaries

and screw dislocations, the VG, the BG, and the OBG are competing phases of increasingly

frustrated disorder. At lower temperatures, the VG might evolve into a Bragg glass [

], where

vortex dislocations are absent, and quasi-long-range translational order is preserved. Similarly,

with vanishing disorder and at low temperatures, the OBG can transform into a vortex Mott

insulator [

], where the vortices condense in a commensurate arrangement with the CDs. Both

Bragg glass and vortex Mott insulator differ from VG, BG, and OBG as they melt through a

ﬁrst-order transition.

3. Materials and Methods

3.1. Sample Preparation

Thin YBCO ﬁlms were epitaxially grown on (LaAlO

)

0.3

(Sr

AlTaO

)

0.7

(LSAT) substrates

by pulsed laser deposition (PLD). The thickness of the ﬁlm

t= (

26.0

2.4

)

nm used in this

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摘要：

Citation:Backmeister,L.;Aichner,B.;Karrer,M.;Wurster,K:Kleiner,R.;Goldobin,E;Koelle,D.;Lang,W.OrderedBoseGlassofVorticesinSuperconductingYBa2Cu3O7dThinFilmswithaPeriodicPinLatticeCreatedbyFocusedHeliumIonIrradiation.Nanomaterials2022,12,3491.https://doi.org/10.3390/nano12193491AcademicEditor:M.V.Ram...

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Ordered Bose Glass of Vortices in Superconducting YBa2Cu3O7- Thin Films with a Periodic Pin Lattice Created by Focused Helium Ion Irradiation

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