Arcade Fire are, on the surface of it, unlikely contenders to be one of the world’s biggest bands. Thirty-year-old singer-songwriter Win Butler, his wife Régine Chassagne and the rest of the Montreal eight-piece produce songs of spiritual yearning and pain, documenting a future for America that is cold, conflicted and apocalyptic. Their death-inspired 2004 debut Funeral launched them slowly, but increasingly stratospherically, into listeners’ heavy hearts, evoking deep hopes and fears, and countering the plastic sheen of modernity with emotional belters.

The tense, frustrated sound of follow-up Neon Bible reflected the stress of the band’s heavy touring commitments, and their growing disgust at Bush’s America (Butler grew up in the suburbs of Houston, Texas, but met his wife while studying at McGill University, Montreal). It was a difficult, at times ponderous, album that would have given any other band’s career a knock. Not so Arcade Fire, who took one year off, then spent another two years recording a deceptively simple but strikingly good third effort, August’s The Suburbs, and have now returned to a touring schedule that, this fortnight, takes in the SECC. Their surly, awkward cool is still intact (note Wayne ‘Flaming Lips’ Coyne calling them ‘pricks’ last year and bemoaning their ‘pompousness’), and their ability to fill stadium-sized venues seems stronger than ever.

Not bad going for a band who’ve always held the darkness of the soul up as prominently as their guitar hooks. Their biggest ‘hit’ has been ‘Rebellion: Lies’, a Funeral track about the possibility of sleeping forever. In a List interview in 2008 Butler described its first live outing: ‘I announced it something like, “I’ve been doing an experiment and I’ve figured out that you get to a point where you feel like you’re going to die, being awake, but if you actually just keep going then you never have to sleep ever again.” It was like a Pied Piper kind of idea, of leading the kids down the street. Basically a lie but a very heartfelt lie.’

Whereas, on Funeral, Butler’s vision covered Middle America in apocalyptic snow, The Suburbs is more obsessed with the generic concrete and simmering paranoia of the US as it is now. The album deals with disillusionment, sprawling nothingness and teenage boredom spilling over into conflict. It’s creation was inspired, Butler has suggested, by a photograph that an old schoolfriend sent him, showing the friend and his young daughter in front of their local mall. In Spike Jonze’s video for the album’s title track this spiritless concrete is turned into a washed-out indie reality, which, harrowingly, becomes the theatre for suburban warfare.

Live, you realise the sadness of war follows closely behind the band’s Pied Piper fantasies. Régine Chassagne was born in Haiti, and earlier this year wrote a moving article for The Observer following the devastating earthquake that compounded problems caused by years of brutal military dictatorship. On Funeral track ‘Haiti’, she fantasises in French about the ghosts of her unborn Haitian cousins. It’s a moving track to play live, Butler says: ‘The lyrics of ‘Haiti’ are one of the best things me and Régine ever did. I guess that kind of chokes me up when I hear it.’

At the SECC the band will be joined by freak-folk poster boy Devendra Banhart, playing out material from his 2009 album What Will We Be. It’s rare that emotional impact outweighs either glitzy, voguish pop, or laddish rock’n’roll posturing, but this gig is one that proves that music for the heavy heart still has a loyal following.

SECC, Glasgow, Sun 12 Dec.