Electron vortices in graphene detected

When an or­din­ary elec­trical con­ductor – such as a metal wire – is con­nec­ted to a bat­tery, the elec­trons in the con­ductor are ac­cel­er­ated by the elec­tric field cre­ated by the bat­tery. While mov­ing, elec­trons fre­quently col­lide with im­pur­ity atoms or va­can­cies in the crys­tal lat­tice of the wire, and con­vert part of their mo­tional en­ergy into lat­tice vi­bra­tions. The en­ergy lost in this pro­cess is con­ver­ted into heat that can be felt, for ex­ample, by touch­ing an in­can­des­cent light bulb.

While col­li­sions with lat­tice im­pur­it­ies hap­pen fre­quently, col­li­sions between elec­trons are much rarer. The situ­ation changes, how­ever, when graphene, a single layer of car­bon atoms ar­ranged in a hon­ey­comb lat­tice, is used in­stead of a com­mon iron or cop­per wire. In graphene, im­pur­ity col­li­sions are rare and col­li­sions between elec­trons play the lead­ing role. In this case, the elec­trons be­have more like a vis­cous li­quid. There­fore, well-​known flow phe­nom­ena such as vor­tices should oc­cur in the graphene layer.

Re­port­ing in the sci­entific journal ex­ternal pageSci­encecall_made, re­search­ers at ETH Zurich in the group of Chris­tian De­gen have now man­aged to dir­ectly de­tect elec­tron vor­tices in graphene for the first time, us­ing a high-​resolution mag­netic field sensor.

Highly sens­it­ive quantum sens­ing mi­cro­scope

The vor­tices formed in small cir­cu­lar disks that De­gen and his co-​workers had at­tached dur­ing the fab­ric­a­tion pro­cess to a con­duct­ing graphene strip only one mi­cro­metre wide. The disks had dif­fer­ent dia­met­ers between 1.2 and 3 mi­cro­metres. The­or­et­ical cal­cu­la­tions sug­ges­ted that elec­tron vor­tices should form in the smal­ler, but not in the lar­ger disks.

To make the vor­tices vis­ible the re­search­ers meas­ured the tiny mag­netic fields pro­duced by the elec­trons flow­ing in­side the graphene. For this pur­pose, they used a quantum mag­netic field sensor con­sist­ing of a so-​called nitrogen-​vacancy (NV) centre em­bed­ded in the tip of a dia­mond needle. Be­ing an atomic de­fect, the NV centre be­haves like a quantum ob­ject whose en­ergy levels de­pend on an ex­ternal mag­netic field. Us­ing laser beams and mi­crowave pulses, the quantum states of the centre can be pre­pared in such a way as to be max­im­ally sens­it­ive to mag­netic fields. By read­ing out the quantum states with a laser, the re­search­ers could de­term­ine the strength of those fields very pre­cisely.

“Be­cause of the tiny di­men­sions of the dia­mond needle and the small dis­tance from the graphene layer – only around 70 nano­metres – we were able to make the elec­tron cur­rents vis­ible with a res­ol­u­tion of less than a hun­dred nano­metres”, says Marius Palm, a former PhD stu­dent in De­gen’s group. This res­ol­u­tion is suf­fi­cient for see­ing the vor­tices.

In­ver­ted flow dir­ec­tion

In their meas­ure­ments, the re­search­ers ob­served a char­ac­ter­istic sign of the ex­pec­ted vor­tices in the smal­ler discs: a re­versal of the flow dir­ec­tion. While in nor­mal (dif­fus­ive) elec­tron trans­port, the elec­trons in strip and disc flow in the same dir­ec­tion, in the case of a vor­tex, the flow dir­ec­tion in­side the disc is in­ver­ted. As pre­dicted by the cal­cu­la­tions, no vor­tices could be ob­served in the lar­ger discs.

“Thanks to our ex­tremely sens­it­ive sensor and high spa­tial res­ol­u­tion, we didn’t even need to cool down the graphene and were able to con­duct the ex­per­i­ments at room tem­per­at­ure”, says Palm. Moreover, he and his col­leagues not only de­tec­ted elec­tron vor­tices, but also vor­tices formed by hole car­ri­ers. By ap­ply­ing an elec­tric voltage from be­low the graphene, they changed the num­ber of free elec­trons in such a way that the cur­rent flow was no longer car­ried by elec­trons, but rather by miss­ing elec­trons, also called holes. Only at the charge neut­ral­ity point, where there is a small and bal­anced con­cen­tra­tion of both elec­trons and holes, the vor­tices dis­ap­peared com­pletely.

“At this mo­ment, the de­tec­tion of elec­tron vor­tices is ba­sic re­search, and there are still lots of open ques­tions”, says Palm. For in­stance, re­search­ers still need to fig­ure out how col­li­sions of the elec­trons with the graphene’s bor­ders in­flu­ence the flow pat­tern, and what ef­fects are oc­cur­ring in even smal­ler struc­tures. The new de­tec­tion method used by the ETH re­search­ers also per­mits tak­ing a closer look at many other exotic elec­tron trans­port ef­fects in meso­scopic struc­tures – phe­nom­ena that oc­cur on length scales from sev­eral tens of nano­metres up to a few mi­cro­metres.