the stm 
 experiments have been carried out in a low - temperature ( 5 k ) stm system 
 ( createc germany ) , operated for the measurements 
 presented here with liquid n2 in the cryostat stage , yielding 
 a sample temperature of 85 k. sample cleaning and preparation and in situ stm tip treatments were 
 performed in the preparation chamber .
electrochemically etched w tips 
 have been treated in situ by electron bombardment heating and by field 
 emission via voltage pulses .
the stm images have been recorded in 
 constant current mode , with the bias applied to the sample .
differential 
 conductance ( di / dv versus v ) sts spectra have been recorded with a lock - in technique 
 with a 1.175 khz modulation frequency and 100 mv modulation amplitude . 
 the photoelectron spectroscopy measurements were carried out in a 
 custom - designed system for x - ray ( xps ) and uv photoelectron spectroscopy 
 ( ups ) ( specs germany ) ; mg k radiation was used for core level 
 xps and he i radiation for valence band ups .
the sample work function 
 was measured from the low - energy electron cutoff in ups spectra .
both 
 experimental systems are equipped with leed , which was used to cross - check 
 the identity and quality of the respective ceria surfaces .
the 
 cu(110 ) surface has been cleaned by ar bombardment , 
 700 ev , followed by annealing at 850 k. cerium metal was evaporated 
 from a ta crucible in an electron beam evaporator , and the evaporating 
 flux was measured with a quartz microbalance .
various oxide thin film 
 preparation procedures have been tested , such as reactive evaporation 
 of ce in oxygen atmosphere or postoxidation of ce metal deposited 
 at the clean and oxygen precovered cu surface ; all procedures resulted 
 in the epitaxial growth of 2-d cerium oxide films .
however , the layers 
 with the best structural order have been obtained by the postoxidation 
 method : ce metal was evaporated onto the clean cu(110 ) surface at 
 300350 k and postoxidized in ( 15 )  10 mbar o2 at 750800 k , followed by a few min annealing 
 in o2 at 800850 k. under these preparation conditions , 
 the ceria stoichiometry is close to ceo2 , but slightly 
 understoichiometric ( ceo1.921.96 ) as evidenced 
 by xps ( see figure s3 , si ) . for submonolayer 

oxide coverages , the coexisting cu(110 ) surface patches are oxidized 
 to the ( 2  1)-o reconstruction , if the o2 pressure 
 during postoxidation is kept below 1  10 mbar . for higher oxygen pressures , po2  10 mbar ,
the cu(110 ) surface is oxidized to the c(6 
  2)-o reconstruction , and the ceria overlayer becomes stoichiometric 
 ceo2 . using the postoxidation procedure ,
no influence of 
 the o2 pressure on the 2-d morphology of the ceria overlayer 
 has been observed within the employed pressure range ( 1  10 mbar -5  10 mbar ) , in agreement 
 with reports in the literature .
the ceria 
 surface coverage has been estimated from the inspection of large scale 
 stm images ( 1 monolayer ( ml ) of ( 111)-type ceria corresponds to 7.9 
  10 ce atoms / cm ) . theory .
dft calculations were performed using 
 the quantumespresso code , employing a 
 basis set of plane waves , ultrasoft pseudopotentials , and the perdew  burke 
ernzerhof ( pbe ) exchange - correlation 
 ( xc- ) functional , complemented by the 
 introduction of a hubbard u term on the 
 ce atoms with a value of u = 4.5 ev . in a first scan , the ( 3  11 ) unit cell was approximated 
 with a ( 3  2 ) cell , measuring 7.65  6.88  ( see figure 
 s5 , si ) , where the oxide was elongated 
 by about 3.8% along the y direction ( from 6.62 to 
 6.88  ) . selected simulations were also performed with the much 
 bigger and computationally demanding ( 3  11 ) unit cell .
values 
 of 20 and 200 ry were chosen as the energy cutoff for the selection 
 of the plane waves for the description of the wave function and the 
 electronic density , respectively .
the brillouin zone was sampled at 
 the gamma point only , which is accurate for such big unit cells .
the 
 electronic levels were broadened with a gaussian smearing of about 
 0.002 ry ( 1 ry = 13.606 ev ) and all the calculations were performed 
 spin - polarized .
stm images were simulated applying the tersoff - hamann 
 approach at a constant height of about 
 2  above the oxide surface . along the z axis
, 
 a minimum empty space of 15  was chosen to avoid interactions 
 between replicated cells .
our dft approach predicts an equilibrium value of the cu metal 
 lattice constant of about 2.58  , in good agreement with the 
 experimental value of 2.55  . in the calculations here presented , 

the experimental value of the cu lattice constant was used , and the 
 cu surface was modeled as a slab with six layers frozen in their crystal 
 positions , while the positions of the atoms in the ceox / cuox systems 
 were optimized until the forces where smaller than 10 ev  .
our dft approach accurately predicts 
 the bulk lattice constant of ceo2 fluorite - like crystal 
 structure ( where each ce atom is coordinated by eight o atoms at the 
 vertices of a cube , whereas each o atom is coordinated by four ce 
 atoms at the vertices of a tetrahedron ) : 3.89  , to be compared 
 to an experimental value of 3.91  . as a further validation
, 
 we also calculated the formation energy of an oxygen vacancy at a 
 ( 111 ) ceo2 surface obtaining a value of 4.83 ev , in very 
 good agreement with the literature value of 4.95 ev obtained by fabris .
we also verified that the electronic distribution 
 around the vacancy is correctly described , with two electrons left 
 by the missing oxygen localized on the 4f states of two cerium atoms 
 next to the vacancy , hence shifting their oxidation state from + 4 
 to + 3 .
 an ultrathin two - dimensional ceo2 ( ceria ) phase on a 
 cu(110 ) surface has been fabricated and fully characterized by high - resolution 
 scanning tunneling microscopy , photoelectron spectroscopy , and density 
 functional theory . the atomic lattice structure of the ceria / cu(110 ) 
 system is revealed as a hexagonal ceo2(111)-type monolayer 
 separated from the cu(110 ) surface by a partly disordered cu  o 
 intercalated buffer layer . 
 the epitaxial coupling of the two - dimensional 
 ceria overlayer to the cu(110)-o surface leads to a nanoscopic stripe 
 pattern , which creates defect regions of quasi - periodic lattice distortions . 
 
 the symmetry and lattice mismatch at the interface is clarified to 
 be responsible for the topographic stripe geometry and the related 
 anisotropic strain defect regions at the ceria surface . 
 this ceria 
 monolayer is in a fully oxidized and thermodynamically stable state . 
Methods