The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

1.
P. W.
Anderson
,
B. I.
Halperin
, and
C. M.
Varma
, “
Anomalous low-temperature thermal properties of glasses and spin glasses
,”
Philos. Mag.
25
,
1
9
(
1972
).
2.
W. A.
Phillips
, “
Two-level states in glasses
,”
Rep. Prog. Phys.
50
,
1657
1708
(
1987
).
3.
M. A.
Ramos
and
U.
Buchenau
, “
Low-temperature thermal conductivity of glasses within the soft-potential model
,”
Phys. Rev. B
55
,
5749
5754
(
1997
).
4.
R. C.
Zeller
and
R. O.
Pohl
, “
Thermal conductivity and specific heat of noncrystalline solids
,”
Phys. Rev. B
4
,
2029
2041
(
1971
).
5.
V.
Lubchenko
and
P. G.
Wolynes
, “
The origin of the boson peak and thermal conductivity plateau in low-temperature glasses
,”
Proc. Natl. Acad. Sci. U. S. A.
100
,
1515
1518
(
2003
).
6.
Tunneling Systems in Amorphous and Crystalline Solids
, edited by
P.
Esquinazi
(
Springer
,
Berlin, Heidelberg
,
1998
).
7.
U.
Buchenau
,
G.
D’Angelo
,
G.
Carini
,
X.
Liu
, and
M. A.
Ramos
, “
Sound absorption in glasses
,”
Rev. Phys.
9
,
100078
(
2022
).
8.
V.
Lubchenko
and
P. G.
Wolynes
, “
Intrinsic quantum excitations of low temperature glasses
,”
Phys. Rev. Lett.
87
,
195901
(
2001
).
9.
A. J.
Leggett
and
D. C.
Vural
, “‘
Tunneling two-level systems’ model of the low-temperature properties of glasses: Are ‘smoking-gun’ tests possible?
,”
J. Phys. Chem. B
117
,
12966
12971
(
2013
).
10.
A. L.
Burin
and
Y.
Kagan
, “
On the nature of the universal properties of amorphous solids
,”
Phys. Lett. A
215
,
191
196
(
1996
).
11.
D.
Zhou
and
A. J.
Leggett
, “
Random nonlinear infinite-level-system model for amorphous solid phonon echo and saturation phenomena
,” arXiv:1510.05538 (
2015
).
12.
D.
Zhou
, “
Universal ratio of TTLS-phonon coupling constants in low-temperature amorphous solids
,”
J. Phys.: Condens. Matter
32
,
055704
(
2019
).
13.
H. M.
Carruzzo
and
C. C.
Yu
, “
Why phonon scattering in glasses is universally small at low temperatures
,”
Phys. Rev. Lett.
124
,
075902
(
2020
).
14.
H. M.
Carruzzo
,
A.
Bilmes
,
J.
Lisenfeld
,
Z.
Yu
,
B.
Wang
,
Z.
Wan
,
J. R.
Schmidt
, and
C. C.
Yu
, “
Distribution of two-level system couplings to strain and electric fields in glasses at low temperatures
,”
Phys. Rev. B
104
,
134203
(
2021
).
15.
C.
Artiaco
,
F.
Balducci
, and
A.
Scardicchio
, “
Signatures of many-body localization in the dynamics of two-level systems in glasses
,”
Phys. Rev. B
103
,
214205
(
2021
).
16.
V.
Lubchenko
and
P. G.
Wolynes
, “
The microscopic quantum theory of low temperature amorphous solids
,” in
Advances in Chemical Physics
, edited by
S. A.
Rice
(
John Wiley & Sons
,
Hoboken, NJ
,
2008
), pp.
95
206
.
17.
A.
Heuer
and
R. J.
Silbey
, “
Microscopic description of tunneling systems in a structural model glass
,”
Phys. Rev. Lett.
70
,
3911
3914
(
1993
).
18.
F.
Demichelis
,
G.
Viliani
, and
G.
Ruocco
, “
Properties of the double well potential and relaxation processes in a model glass
,”
PhysChemComm
2
,
20
23
(
1999
).
19.
J.
Reinisch
and
A.
Heuer
, “
How cooperative are the dynamics in tunneling systems? A computer study for an atomic model glass
,”
J. Low Temp. Phys.
137
,
267
287
(
2004
).
20.
T.
Damart
and
D.
Rodney
, “
Atomistic study of two-level systems in amorphous silica
,”
Phys. Rev. B
97
,
014201
(
2018
).
21.
D.
Khomenko
,
C.
Scalliet
,
L.
Berthier
,
D. R.
Reichman
, and
F.
Zamponi
, “
Depletion of two-level systems in ultrastable computer-generated glasses
,”
Phys. Rev. Lett.
124
,
225901
(
2020
).
22.
A.
Kumar
,
I.
Procaccia
, and
M.
Singh
, “
Density of quasi-localized modes in athermal glasses
,”
Europhys. Lett.
135
,
66001
(
2021
).
23.
C.
Müller
,
J. H.
Cole
, and
J.
Lisenfeld
, “
Towards understanding two-level-systems in amorphous solids: Insights from quantum circuits
,”
Rep. Prog. Phys.
82
,
124501
(
2019
).
24.
R.
Birney
,
J.
Steinlechner
,
Z.
Tornasi
,
S.
MacFoy
,
D.
Vine
,
A. S.
Bell
,
D.
Gibson
,
J.
Hough
,
S.
Rowan
,
P.
Sortais
,
S.
Sproules
,
S.
Tait
,
I. W.
Martin
, and
S.
Reid
, “
Amorphous silicon with extremely low absorption: Beating thermal noise in gravitational astronomy
,”
Phys. Rev. Lett.
121
,
191101
(
2018
).
25.
J.
Steinlechner
,
I. W.
Martin
,
A. S.
Bell
,
J.
Hough
,
M.
Fletcher
,
P. G.
Murray
,
R.
Robie
,
S.
Rowan
, and
R.
Schnabel
, “
Silicon-based optical mirror coatings for ultrahigh precision metrology and sensing
,”
Phys. Rev. Lett.
120
,
263602
(
2018
).
26.
A. Q.
Tool
, “
Relation between inelastic deformability and thermal expansion of glass in its annealing range
,”
J. Am. Ceram. Soc.
29
,
240
253
(
1946
).
27.
D. R.
Queen
,
X.
Liu
,
J.
Karel
,
T. H.
Metcalf
, and
F.
Hellman
, “
Excess specific heat in evaporated amorphous silicon
,”
Phys. Rev. Lett.
110
,
135901
(
2013
).
28.
T.
Pérez-Castañeda
,
C.
Rodríguez-Tinoco
,
J.
Rodríguez-Viejo
, and
M. A.
Ramos
, “
Suppression of tunneling two-level systems in ultrastable glasses of indomethacin
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
11275
11280
(
2014
).
29.
A.
Ninarello
,
L.
Berthier
, and
D.
Coslovich
, “
Models and algorithms for the next generation of glass transition studies
,”
Phys. Rev. X
7
,
021039
(
2017
).
30.
L.
Berthier
and
D. R.
Reichman
, “
Modern computational studies of the glass transition
,” arXiv:2208.02206 (
2022
).
31.
A. D. S.
Parmar
,
M.
Ozawa
, and
L.
Berthier
, “
Ultrastable metallic glasses in silico
,”
Phys. Rev. Lett.
125
,
085505
(
2020
).
32.
J. F.
Berret
and
M.
Meißner
, “
How universal are the low temperature acoustic properties of glasses?
,”
Z. Phys. B: Condens. Matter
70
,
65
72
(
1988
).
33.
W.
Ji
, “
Toward understanding the depletion of two-level systems in ultrastable glasses
,” arXiv:2112.10105 (
2021
).
34.
B.
Doliwa
and
A.
Heuer
, “
Energy barriers and activated dynamics in a supercooled Lennard-Jones liquid
,”
Phys. Rev. E
67
,
031506
(
2003
).
35.
R. A.
Denny
,
D. R.
Reichman
, and
J. P.
Bouchaud
, “
Trap models and slow dynamics in supercooled liquids
,”
Phys. Rev. Lett.
90
,
025503
(
2003
).
36.
F. H.
Stillinger
and
T. A.
Weber
, “
Hidden structure in liquids
,”
Phys. Rev. A
25
,
978
(
1982
).
37.
F.
Sciortino
, “
Potential energy landscape description of supercooled liquids and glasses
,”
J. Stat. Mech.: Theory Exp.
2005
,
P05015
.
38.
A.
Heuer
, “
Exploring the potential energy landscape of glass-forming systems: From inherent structures via metabasins to macroscopic transport
,”
J. Phys.: Condens. Matter
20
,
373101
(
2008
).
39.
H.
Jónsson
,
G.
Mills
, and
K. W.
Jacobsen
, “
Nudged elastic band method for finding minimum energy paths of transitions
,” in
Classical and Quantum Dynamics in Condensed Phase Simulations
, edited by
B. J.
Berne
,
G.
Ciccotti
, and
D. F.
Coker
(
World Scientific
,
Singapore
,
1998
).
40.
G.
Henkelman
and
H.
Jónsson
, “
Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
,”
J. Chem. Phys.
113
,
9978
9985
(
2000
).
41.
M. T.
Loponen
,
R. C.
Dynes
,
V.
Narayanamurti
, and
J. P.
Garno
, “
Measurements of the time-dependent specific heat of amorphous materials
,”
Phys. Rev. B
25
,
1161
(
1982
).
42.
R.
Gutiérrez
,
S.
Karmakar
,
Y. G.
Pollack
, and
I.
Procaccia
, “
The static lengthscale characterizing the glass transition at lower temperatures
,”
Europhys. Lett.
111
,
56009
(
2015
).
43.
W.
Kob
and
H. C.
Andersen
, “
Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function
,”
Phys. Rev. E
51
,
4626
4641
(
1995
).
44.
S.
Sastry
, “
Liquid limits: Glass transition and liquid-gas spinodal boundaries of metastable liquids
,”
Phys. Rev. Lett.
85
,
590
593
(
2000
).
45.
V.
Testard
,
L.
Berthier
, and
W.
Kob
, “
Influence of the glass transition on the liquid-gas spinodal decomposition
,”
Phys. Rev. Lett.
106
,
125702
(
2011
).
46.
S.
Plimpton
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
,
1
19
(
1995
).
47.
L.
Berthier
,
E.
Flenner
,
C. J.
Fullerton
,
C.
Scalliet
, and
M.
Singh
, “
Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids
,”
J. Stat. Mech.: Theory Exp.
2019
,
064004
.
48.
M. D.
Ediger
,
C. A.
Angell
, and
S. R.
Nagel
, “
Supercooled liquids and glasses
,”
J. Phys. Chem.
100
,
13200
13212
(
1996
).
49.
Y. S.
Elmatad
,
D.
Chandler
, and
J. P.
Garrahan
, “
Corresponding states of structural glass formers. II
,”
J. Phys. Chem. B
114
,
17113
17119
(
2010
).
50.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
(
Academic Press
,
1996
).
51.
W.
E
,
W.
Ren
, and
E.
Vanden-Eijnden
, “
String method for the study of rare events
,”
Phys. Rev. B
66
,
052301
(
2002
).
52.
E.
Bitzek
,
P.
Koskinen
,
F.
Gähler
,
M.
Moseler
, and
P.
Gumbsch
, “
Structural relaxation made simple
,”
Phys. Rev. Lett.
97
,
170201
(
2006
).
53.
J.
Guénolé
,
W. G.
Nöhring
,
A.
Vaid
,
F.
Houllé
,
Z.
Xie
,
A.
Prakash
, and
E.
Bitzek
, “
Assessment and optimization of the fast inertial relaxation engine (FIRE) for energy minimization in atomistic simulations and its implementation in LAMMPS
,”
Comput. Mater. Sci.
175
,
109584
(
2020
).
54.
W.
E
,
W.
Ren
, and
E.
Vanden-Eijnden
, “
Simplified and improved string method for computing the minimum energy paths in barrier-crossing events
,”
J. Chem. Phys.
126
,
164103
(
2007
).
55.
G.
Henkelman
,
B. P.
Uberuaga
, and
H.
Jónsson
, “
A climbing image nudged elastic band method for finding saddle points and minimum energy paths
,”
J. Chem. Phys.
113
,
9901
9904
(
2000
).
56.
C.
Scalliet
,
L.
Berthier
, and
F.
Zamponi
, “
Nature of excitations and defects in structural glasses
,”
Nat. Commun.
10
,
5102
(
2019
).
57.
Q.
Liao
and
L.
Berthier
, “
Hierarchical landscape of hard disk glasses
,”
Phys. Rev. X
9
,
011049
(
2019
).
58.
C.
Artiaco
,
P.
Baldan
, and
G.
Parisi
, “
Exploratory study of the glassy landscape near jamming
,”
Phys. Rev. E
101
,
052605
(
2020
).
59.
G. H.
Vineyard
, “
Frequency factors and isotope effects in solid state rate processes
,”
J. Phys. Chem. Solids
3
,
121
127
(
1957
).
60.
R. B.
Lehoucq
,
D. C.
Sorensen
, and
C.
Yang
,
ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
(
Society for Industrial and Applied Mathematics
,
1998
).
61.
G.
Frossati
,
J. l.
Gilchrist
,
J. C.
Lasjaunias
, and
W.
Meyer
, “
Spectrum of low-energy dipolar states in hydrated vitreous silica
,”
J. Phys. C: Solid State Phys.
10
,
L515
(
1977
).
62.
V.
Jakšić
and
J.
Segert
, “
On the Landau–Zener formula for two-level systems
,”
J. Math. Phys.
34
,
2807
2820
(
1993
).
63.
T.
Vegge
,
J. P.
Sethna
,
S.-A.
Cheong
,
K. W.
Jacobsen
,
C. R.
Myers
, and
D. C.
Ralph
, “
Calculation of quantum tunneling for a spatially extended defect: The dislocation kink in copper has a low effective mass
,”
Phys. Rev. Lett.
86
,
1546
1549
(
2001
).
64.
C.
Lévesque
,
S.
Roorda
,
F.
Schiettekatte
, and
N.
Mousseau
, “
Internal mechanical dissipation mechanisms in amorphous silicon
,”
Phys. Rev. Mater.
6
,
123604
(
2022
); arXiv:2209.02342 [cond-mat].
65.
M.
Ozawa
,
C.
Scalliet
,
A.
Ninarello
, and
L.
Berthier
, “
Does the Adam-Gibbs relation hold in simulated supercooled liquids?
,”
J. Chem. Phys.
151
,
084504
(
2019
).
66.
C.
Scalliet
,
B.
Guiselin
, and
L.
Berthier
, “
Thirty milliseconds in the life of a supercooled liquid
,”
Phys. Rev. X
12
,
041028
(
2022
); arXiv:2207.00491.
67.
T. A.
Weber
and
F. H.
Stillinger
, “
Local order and structural transitions in amorphous metal-metalloid alloys
,”
Phys. Rev. B
31
,
1954
1963
(
1985
).
68.
K.
González-López
,
M.
Shivam
,
Y.
Zheng
,
M. P.
Ciamarra
, and
E.
Lerner
, “
Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions
,”
Phys. Rev. E
103
,
022605
(
2021
).
69.
L.
Wang
,
A.
Ninarello
,
P.
Guan
,
L.
Berthier
,
G.
Szamel
, and
E.
Flenner
, “
Low-frequency vibrational modes of stable glasses
,”
Nat. Commun.
10
,
26
(
2019
).
70.
G.
Kapteijns
,
E.
Bouchbinder
, and
E.
Lerner
, “
Universal nonphononic density of states in 2D, 3D, and 4D glasses
,”
Phys. Rev. Lett.
121
,
055501
(
2018
).
71.
L.
Wang
,
L.
Fu
, and
Y.
Nie
, “
Density of states below the first sound mode in 3D glasses
,”
J. Chem. Phys.
157
,
074502
(
2022
); arXiv:2206.05270.
72.
D.
Khomenko
,
D. R.
Reichman
, and
F.
Zamponi
, “
Relationship between two-level systems and quasilocalized normal modes in glasses
,”
Phys. Rev. Mater.
5
,
055602
(
2021
).
73.
G.
Folena
and
P.
Urbani
, “
Marginal stability of soft anharmonic mean field spin glasses
,”
J. Stat. Mech.: Theory Exp.
2022
,
053301
.
74.
L.
Berthier
, “
Self-induced heterogeneity in deeply supercooled liquids
,”
Phys. Rev. Lett.
127
,
088002
(
2021
).
75.
M.
Marchi
and
D.
Chandler
, “
Path-integral calculation of the tunnel splitting in aqueous ferrous–ferric electron transfer
,”
J. Chem. Phys.
95
,
889
894
(
1991
).
76.
C. L.
Vaillant
,
D. J.
Wales
, and
S. C.
Althorpe
, “
Tunneling splittings from path-integral molecular dynamics using a Langevin thermostat
,”
J. Chem. Phys.
148
,
234102
(
2018
); arXiv:1803.04433.
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