Researchers Observed A Crystal That Consists Only Of Electrons (Physics)

Researchers at ETH Zurich have succeeded in observing a crystal that consists only of electrons. Such Wigner crystals were already predicted almost ninety years ago but could only now be observed directly in a semiconductor material.

Crys­tals have fas­cin­ated people through the ages. Who hasn’t ad­mired the com­plex pat­terns of a snow­flake at some point, or the per­fectly sym­met­rical sur­faces of a rock crys­tal? The ma­gic doesn’t stop even if one knows that all this res­ults from a simple in­ter­play of at­trac­tion and re­pul­sion between atoms and elec­trons. A team of re­search­ers led by Ataç Im­amoğlu, pro­fessor at the In­sti­tute for Quantum Elec­tron­ics at ETH Zurich, have now pro­duced a very spe­cial crys­tal. Un­like nor­mal crys­tals, it con­sists ex­clus­ively of elec­trons. In do­ing so, they have con­firmed a the­or­et­ical pre­dic­tion that was made al­most ninety years ago and which has since been re­garded as a kind of holy grail of con­densed mat­ter phys­ics. Their res­ults were re­cently pub­lished in the sci­entific journal “Nature”.

A decades-​old pre­dic­tion

“What got us ex­cited about this prob­lem is its sim­pli­city”, says Im­amoğlu. Already in 1934 Eu­gene Wigner, one of the founders of the the­ory of sym­met­ries in quantum mech­an­ics, showed that elec­trons in a ma­ter­ial could the­or­et­ic­ally ar­range them­selves in reg­u­lar, crystal-​like pat­terns be­cause of their mu­tual elec­trical re­pul­sion. The reas­on­ing be­hind this is quite simple: if the en­ergy of the elec­trical re­pul­sion between the elec­trons is lar­ger than their mo­tional en­ergy, they will ar­range them­selves in such a way that their total en­ergy is as small as pos­sible.

For sev­eral dec­ades, how­ever, this pre­dic­tion re­mained purely the­or­et­ical, as those “Wigner crys­tals” can only form un­der ex­treme con­di­tions such as low tem­per­at­ures and a very small num­ber of free elec­trons in the ma­ter­ial. This is in part be­cause elec­trons are many thou­sands of times lighter than atoms, which means that their mo­tional en­ergy in a reg­u­lar ar­range­ment is typ­ic­ally much lar­ger than the elec­tro­static en­ergy due to the in­ter­ac­tion between the elec­trons.

Elec­trons in a plane

To over­come those obstacles, Im­amoğlu and his col­lab­or­at­ors chose a wafer-​thin layer of the semi­con­ductor ma­ter­ial mo­lyb­denum disel­en­ide that is just one atom thick and in which, there­fore, elec­trons can only move in a plane. The re­search­ers could vary the num­ber of free elec­trons by ap­ply­ing a voltage to two trans­par­ent graphene elec­trodes, between which the semi­con­ductor is sand­wiched. Ac­cord­ing to the­or­et­ical con­sid­er­a­tions the elec­trical prop­er­ties of mo­lyb­denum disel­en­ide should fa­vour the form­a­tion of a Wigner crys­tal – provided that the whole ap­par­atus is cooled down to a few de­grees above the ab­so­lute zero of minus 273.15 de­grees Celsius.

How­ever, just pro­du­cing a Wigner crys­tal is not quite enough. “The next prob­lem was to demon­strate that we ac­tu­ally had Wigner crys­tals in our ap­par­atus”, says To­masz Smoleński, who is the lead au­thor of the pub­lic­a­tion and works as a postdoc in Im­amoğlu’s labor­at­ory. The sep­ar­a­tion between the elec­trons was cal­cu­lated to be around 20 nano­metres, or roughly thirty times smal­ler than the wavelength of vis­ible light and hence im­possible to re­solve even with the best mi­cro­scopes.

Electrons in a material usually behave like a disordered liquid (left), but can form a regular Wigner crystal (right) under particular conditions.
Elec­trons in a ma­ter­ial usu­ally be­have like a dis­ordered li­quid (left), but can form a reg­u­lar Wigner crys­tal (right) un­der par­tic­u­lar con­di­tions.   © ETH Zurich

De­tec­tion through ex­citons

Us­ing a trick, the phys­i­cists man­aged to make the reg­u­lar ar­range­ment of the elec­trons vis­ible des­pite that small sep­ar­a­tion in the crys­tal lat­tice. To do so, they used light of a par­tic­u­lar fre­quency to ex­cite so-​called ex­citons in the semi­con­ductor layer. Ex­citons are pairs of elec­trons and “holes” that res­ult from a miss­ing elec­tron in an en­ergy level of the ma­ter­ial. The pre­cise light fre­quency for the cre­ation of such ex­citons and the speed at which they move de­pend both on the prop­er­ties of the ma­ter­ial and on the in­ter­ac­tion with other elec­trons in the ma­ter­ial – with a Wigner crys­tal, for in­stance.

The peri­odic ar­range­ment of the elec­trons in the crys­tal gives rise to an ef­fect that can some­times be seen on tele­vi­sion. When a bi­cycle or a car goes faster and faster, above a cer­tain ve­lo­city the wheels ap­pear to stand still and then to turn in the op­pos­ite dir­ec­tion. This is be­cause the cam­era takes a snap­shot of the wheel every 40 mil­li­seconds. If in that time the reg­u­larly spaced spokes of the wheel have moved by ex­actly the dis­tance between the spokes, the wheel seems not to turn any­more. Sim­il­arly, in the pres­ence of a Wigner crys­tal, mov­ing ex­citons ap­pear sta­tion­ary provided they are mov­ing at a cer­tain ve­lo­city de­term­ined by the sep­ar­a­tion of the elec­trons in the crys­tal lat­tice.

First dir­ect ob­ser­va­tion

“A group of the­or­et­ical phys­i­cists led by Eu­gene Demler of Har­vard Uni­ver­sity, who is mov­ing to ETH this year, had cal­cu­lated the­or­et­ic­ally how that ef­fect should show up in the ob­served ex­cit­a­tion fre­quen­cies of the ex­citons – and that’s ex­actly what we ob­served in the lab”, Im­amoğlu says. In con­trast to pre­vi­ous ex­per­i­ments based on planar semi­con­duct­ors, in which Wigner crys­tals were ob­served in­dir­ectly through cur­rent meas­ure­ments, this is a dir­ect con­firm­a­tion of the reg­u­lar ar­range­ment of the elec­trons in the crys­tal. In the fu­ture, with their new method Im­amoğlu and his col­leagues hope to in­vest­ig­ate ex­actly how Wigner crys­tals form out of a dis­ordered “li­quid” of elec­trons.

Featured image: A Wigner crys­tal of elec­trons (red) in­side a semi­con­ductor ma­ter­ial (blue/grey).© ETH Zurich


Smoleński T, Dol­girev PE, Kuh­len­kamp C et al. Sig­na­tures of Wigner crys­tal of elec­trons in a mono­layer semi­con­ductor. Nature 595, 53–57 (2021) .DOI: 10.1038/s41586-​021-03590-4

Provided by ETH Zurich

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