Professor de Haas adjusted his glasses.

“Electrons are the tiny particles – or, rather, clouds of matter – that bind atoms together to form the amazing variety of chemical compounds all around us. Electrons also carry current in the electronics we use every day...Which reminds me: please put away your phones and laptops.”

Levina L. was among those who rolled their eyes, but complied.

“Conductors are the materials that excel at carrying electrical current. An example would be the aluminum foil wrapped around your classmate’s sandwich.”

Mid-bite, Klaus v. K. looked up from his homemade hoagie. Everyone was laughing. Confused and embarrassed, Klaus scanned the classroom. As his eyes met Levina’s, she smiled and pointed to her own chin, letting him know he had something on his. Klaus quickly wiped off a drop of mayo and smiled back.

“In conductors, electrons are compelled to move in the direction opposite the electric field. But electrons also scatter – with one another, with jiggling ions, with material imperfections – and they end up moving in many different directions. Scattering is the cause of electrical resistance.”

Professor de Haas smiled. “Electrons in conductors are like partying college students: they follow free food and alcohol, but bump into one another, into door frames and fire hydrants, and afterwards can’t figure out which way they’re supposed to go.” The class laughed. Levina’s and Klaus’s eyes met.

Levina and Klaus shared their first kiss at a party thrown by their whiz-in-the-lab classmate, Mike Faraday.

The pair spent their undergraduate years in a haze of deep infatuation, punctuated by classes, homework, and friends.

They joined a challenging graduate program, where Levina focused on theory and Klaus on experiment. They worked long hours, drank bad coffee with their labmates, ate microwaved ramen noodles, and converged at home every night, exhausted, happy, their minds on fire. Life was perfect.

In graduate school they met Alice, who was in a long-distance relationship with Bob. Alice and Bob had been high-school sweethearts, deeply connected, seemingly reading each other’s minds.

Close to graduation, Levina and Klaus got married in a small ceremony. Alice was the maid of honor, Mike the best man.

Professor de Haas drew a rectangle on the board. “Let’s say this rectangle is made from a thin conducting material, and we put it in a high magnetic field pointing out of the board.” de Haas made a fist, his thumb out, toward the class. “Now let’s say we have an electron on the conductor’s left side, and it wants to go to the right. It turns out, this electron will have to move along the top edge.”

“Imagine you have a thin strand of cotton candy. Stretch the strand horizontally and place it within the rectangle, just below the top edge – one end on the left, the other on the right. This fluffy cotton-candy strand is a probability cloud: it shows where our electron, moving left to right in the magnetic field, is most likely to be found. As that’s near the top edge, the probability cloud is called an edge state.” Everyone took notes as de Haas spoke. “Electrons that move right to left have their edge states near the rectangle bottom. Also, the faster an electron moves, the closer to the edge it has to travel.”

“Now imagine our electron, going left to right, hits something. Could it end up moving right to left? For that to happen, the electron would have to jump all the way across, from the top edge to the bottom one… This chasm is insurmountable, because the edge states are so thin, much thinner than the distance between them, so they don’t touch...Which means the jump cannot happen, and the electron doesn’t lose its way.”

“Magnetic field has a powerful influence over electrons,” de Haas held his index finger up for emphasis. “It helps focus electron paths, separates those aiming toward different ends, and removes the distraction of scattering. Electrons become perfect current carriers, moving along their edge, purposeful, relentless.”

After graduate school, Levina and Klaus found positions in the same city --- his at a university, hers at a national laboratory. Two years in, they heard that Alice and Bob had disentangled; living apart took its toll. Levina and Klaus felt sorry and a bit smug, certain they’d always be together.

Levina had a baby boy, whom they named after Mike. Klaus and Mike worked in similar fields, but Mike was more successful, a superstar at an elite university, focused solely on his work. When Mike flew in to meet his godson and namesake, Klaus felt anger and envy he’d never known he harbored. After Mike’s departure, these feelings became all-consuming.

Klaus started working longer hours; he worked every weekend, every holiday. After Mikey had turned one, Klaus received a job offer at a prestigious university far away. There was no job there for Levina, so she wouldn’t leave her current one, where she could enjoy both her science and her baby.

Klaus moved alone and his new research group expanded rapidly. He sounded happy and fulfilled.

His visits grew shorter and further apart.

“Will you be here for Mikey’s birthday?” asked Levina, as Mikey was about to turn five. “You missed the last two.”

“I don’t know, maybe. I have some deadlines afterwards...”

"Klaus, I’m tired of your maybes.” Levina’s voice trembled. “There are only two possibilities: yes or no. Will you be here?"

“No. I’m sorry. I can’t.”

Levina and Klaus exited the courtroom after signing the divorce papers. They mumbled their goodbyes with barely a glance at each other.

Klaus turned left and walked east, along the north wall and toward the street exit, where he would catch a ride to the airport.

Levina turned right, crossed the hallway, and walked west along the south wall. She headed to the park, where Mikey was playing with Alice.

Their paths were a hallway width and an insurmountable chasm apart.

Related Information: Lev Landau (who inspired Levina’s name), Klaus von Klitzing, and Wander Johannes de Haas were key contributors to the understanding of the quantum Hall effect and related phenomena (such as the formation of edge states and their role in suppressing scattering, which leads to vanishing longitudinal resistance described in the story). Michael Faraday is a famous 18th century scientist who discovered semiconductors, contributed greatly to modern electromagnetism, and was known for his facility in the laboratory. Alice and Bob are the names commonly given to people who transmit and receive information in quantum information experiments, including those on quantum entanglement.