It seems to me that the input files you provide DO NOT give rise to flat bands. 
I tried to run them, since the calculations last after few seconds, and the 
band structure is not flat.

Another question is whether your calculation corresponds to what reported in 
the paper you mention. Indeed, if you look carefully, the calculation reported 
therein concerns a three dimensional structure, that is rather obscure to me 
(see the Brillouin zone path, k-points coordinates change along k_x, k_y and 
k_y whereas you correctly choose a one-dimensional path). 
The paper reports a unit cell a=6.52 A, b=c=1.304 A, which does not correspond 
to a linear chain, because 5-atom linear chains are parallel to x (6.52 ~ 1.306 
* 5), but along y and z they are only 1.3 A far apart. So, try to understand if 
you want to reproduce the results of the paper, or calculate the band structure 
of a linear carbon chain, whose (not flat!) band structure is NOT that reported 
in Fig. 1 of the mentioned paper.

Giovanni



> On 15 May 2015, at 06:27, Zeina Al-Dolami <[email protected]> wrote:
> 
> Dear users and developers,
> I posted the below question more than two weeks ago. However, I have not 
> received any response. Any feedback or suggestion is greatly appreciated. 
> Thanks in advance  
> 
> Zeina 
> ---------- Forwarded message ----------
> From: Zeina Al-Dolami <[email protected] 
> <mailto:[email protected]>>
> Date: Tue, Apr 28, 2015 at 3:54 PM
> Subject: flat band structure
> To: [email protected] <mailto:[email protected]>
> 
> 
> Dear Pwscf's developers and users,
> I have started using quantum espresso recently for my research that focuses 
> on investigating the mechanical and electrical properties of carbon based 
> materials. I ran several examples of wannier90-1.2 to gain more understanding 
> and insight of what I need to consider when running simulations for quantum 
> conductance. However, I have realized that I need to reproduce the band 
> structures of carbon based materials that have been already published then 
> move to using wannier90. I came across this paper 
> http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3469647 
> <http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.3469647> 
> page242. It is basically a linear chain of 5 carbon atoms. Also, Accelrys 
> Software, DMol programme, was used in this paper.  I used the below scf and 
> band files to reproduce the same band structure. However, the band structure 
> that was produced contains flat bands only. I went through the pw-forum to 
> find whether there was similar question or not. I found some discussions 
> related to band structure and other suggestions that I have considered but no 
> success, such as 
> http://qe-forge.org/pipermail/pw_forum/2005-December/078012.html 
> <http://qe-forge.org/pipermail/pw_forum/2005-December/078012.html> . Would 
> you please tell me what I missed in my calculations? It is worth to mention 
> that I have tried to use the same parameters available in this paper in my 
> simulation. Any suggestion and feedback is greatly appreciated. Apologies if 
> my question seems trivial because I am still at the beginning and have no 
> background in this field. Looking forward to hearing from you. Thanks in 
> advance  
> 
> Zeina    
> 
> scf file 
> 
> &CONTROL
>   calculation = 'scf',
>   restart_mode= 'from_scratch',
>   verbosity = 'high'
>   pseudo_dir  = '/pseudo',
>   outdir      = './',
>   prefix      = '5cc',
>   tstress  = .f.,
>   tprnfor  = .t.,
> /
> &SYSTEM
>   ibrav       = 1,
> !  a           = 6.520,
> !  b           = 1.304,
> !  c          = 1.304,
>   celldm(1)   = 12.3210,
>   cosbc       = 0.,
>   cosac       = 0.,
>   cosab       = 0.,
>   nat         = 5,
>   ntyp        = 1,
>   ecutwfc     = 30.,
>   ecutrho     = 240.,
>   occupations = 'smearing',
>   smearing    = 'cold',
>   degauss     = 0.03,
>   nspin       = 1,
> /
> &ELECTRONS
>   mixing_beta = 0.4
>   electron_maxstep = 1000,
>   conv_thr    = 1.D-10,
> /
> ATOMIC_SPECIES
> C 12.0107  C.pbe-rrkjus.UPF
> 
> ATOMIC_POSITIONS (angstrom)
> C        0.183   0.000000000   0.000000000
> C        1.489   0.000000000   0.000000000
> C        2.791   0.000000000   0.000000000
> C        4.093   0.000000000   0.000000000
> C        5.399   0.000000000   0.000000000
> 
> K_POINTS {automatic}
> 6 1 1 0 0 0 
>  
> 
> 
> band file 
> &CONTROL
>   calculation = 'bands',
>   restart_mode= 'from_scratch',
>   verbosity = 'high'
>   pseudo_dir  = '/pseudo',
>   outdir      = './',
>   prefix      = '5cc',
>   tstress  = .f.,
>   tprnfor  = .t.,
> /
> &SYSTEM
>   ibrav       = 1,
> !  a           = 6.520,
> !  b           = 1.304,
> !  c          = 1.304,
>   celldm(1)   = 12.3210,
>   cosbc       = 0.,
>   cosac       = 0.,
>   cosab       = 0.,
>   nat         = 5,
>   ntyp        = 1,
>   ecutwfc     = 30.,
>   ecutrho     = 240.,
>   occupations = 'smearing',
>   smearing    = 'cold',
>   degauss     = 0.03,
>   nspin       = 1,
> /
> &ELECTRONS
>   mixing_beta = 0.4
>   electron_maxstep = 1000,
>   conv_thr    = 1.D-10,
> ! diag_full_acc = .true.
> 
> /
> ATOMIC_SPECIES
> C 12.0107  C.pbe-rrkjus.UPF
> 
> ATOMIC_POSITIONS (angstrom)
> C        0.183   0.000000000   0.000000000
> C        1.489   0.000000000   0.000000000
> C        2.791   0.000000000   0.000000000
> C        4.093   0.000000000   0.000000000
> C        5.399   0.000000000   0.000000000
> 
> K_POINTS {crystal}
> 6
> 0.00000000  0.00000000  0.00000000  1.00000000
> 0.16666667  0.00000000  0.00000000  1.00000000
> 0.33333333  0.00000000  0.00000000  1.00000000
> 0.50000000  0.00000000  0.00000000  1.00000000
> 0.66666667  0.00000000  0.00000000  1.00000000
> 0.83333333  0.00000000  0.00000000  1.00000000
> 
>  
> -- 
> Zeina Al-Dolami
> PhD Candidate
> Microelectronics and Photonics Graduate Program 
> University of Arkansas
> Fayetteville, AR 72701
> Office: PHYS 244
> Email: [email protected] <mailto:[email protected]> 
> <mailto:[email protected]>
> 
> 
> -- 
> Zeina Al-Dolami
> PhD Candidate
> Microelectronics and Photonics Graduate Program 
> University of Arkansas
> Fayetteville, AR 72701
> Office: PHYS 244
> Email: [email protected] <mailto:[email protected]> 
> <mailto:[email protected]>_______________________________________________
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> <http://pwscf.org/mailman/listinfo/pw_forum>
-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: [email protected]
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: http://people.na.infn.it/~cantele

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