Periodic Reporting for period 5 - HQMAT (New Horizons in Quantum Matter: From Critical Fluids to High Temperature Superconductivity)
Okres sprawozdawczy: 2025-01-01 do 2025-06-30
When many electrons interact with each other, they form “quantum liquids” that behave in ways very different from what we might expect if the electrons acted independently. These systems are extremely challenging to describe, because quantum mechanics and collective behavior are intertwined. The Horizons in Quantum Matter (HQMAT) project is about developing new ideas and mathematical tools to explain these complex states of matter, predict how they will behave in different materials, and guide experiments that can test these predictions.
One particularly exciting direction is the theory of superconductivity—materials that can conduct electricity with absolutely no resistance. Superconductors already have applications in powerful magnets used in MRI machines and particle accelerators, but new types could revolutionize energy transmission or even enable quantum computers. In recent years, researchers have discovered that when sheets of carbon atoms (graphene) are stacked at specific angles, they can host entirely new electronic states. These two-dimensional materials are now at the frontier of research, offering a unique window into the world of strongly interacting electrons and raising the possibility of designing superconductors with tailored properties.
In this project, our main goals are:
1. Quantum critical metals – to understand unusual metallic states that appear near quantum phase transitions and may hold the key to high-temperature superconductivity.
2. Strongly correlated electron liquids – to describe systems where interactions are so strong that the simple picture of independent electrons completely fails.
3. Novel 2D materials – to develop models for layered and moiré materials, such as twisted graphene, and to predict surprising new phenomena that could emerge in them.
One particularly exciting direction is the theory of superconductivity—materials that can conduct electricity with absolutely no resistance. Superconductors already have applications in powerful magnets used in MRI machines and particle accelerators, but new types could revolutionize energy transmission or even enable quantum computers. In recent years, researchers have discovered that when sheets of carbon atoms (graphene) are stacked at specific angles, they can host entirely new electronic states. These two-dimensional materials are now at the frontier of research, offering a unique window into the world of strongly interacting electrons and raising the possibility of designing superconductors with tailored properties.
In this project, our main goals are:
1. Quantum critical metals – to understand unusual metallic states that appear near quantum phase transitions and may hold the key to high-temperature superconductivity.
2. Strongly correlated electron liquids – to describe systems where interactions are so strong that the simple picture of independent electrons completely fails.
3. Novel 2D materials – to develop models for layered and moiré materials, such as twisted graphene, and to predict surprising new phenomena that could emerge in them.
• Theory of the strange metal Sr₃Ru2O₇ and related materials.
“Strange metals” are systems where the usual rules for how electrons move in metals simply fail. Understanding them has been one of the central puzzles of condensed matter physics for decades. The compound Sr₃Ru2O₇ provides one of the clearest examples of this strange behavior. We developed a theory that successfully explains much of its unusual physics. The theory makes several unexpected predictions—some already verified by experiments—and provides new directions for exploring related materials. This marks a major step toward a general understanding of strange metals.
• Hierarchy of energy scales near quantum criticality.
When a metal is tuned to the brink of a phase transition—say, on the verge of becoming magnetic—it enters the realm of “quantum criticality.” These systems are rich in exotic phenomena and often host superconductivity at unexpectedly high temperatures. Despite their apparent simplicity, they are extremely challenging to describe theoretically. Using large-scale computer simulations, we developed a method that allows us to probe these metals without uncontrolled approximations. This enabled us to map out the sequence of “crossovers” the system undergoes as it approaches the critical point. By combining numerical simulations with analytical insights, we established a clear physical picture of quantum critical metals—an advance that helps explain why these materials are fertile ground for superconductivity.
• Numerically exact simulations for moiré quantum critical metals.
One of the most exciting developments of recent years has been the discovery of exotic phases of matter, including superconductivity, in twisted bilayer graphene. At a special “magic” twist angle, the electronic bands become extremely flat, amplifying the effects of interactions between electrons. Theoretical tools to describe such systems are scarce. We developed a new simulation method for twisted bilayer graphene at charge neutrality that captures the essential physics with minimal approximations, while still being computationally feasible. This approach opens a new window into the unusual behavior of graphene moiré systems and provides a benchmark for future theoretical work.
• Cascade of phase transitions and the Pomeranchuk effect in twisted bilayer graphene.
In close collaboration with experimental groups, we studied the puzzling electronic phases of magic-angle twisted bilayer graphene (MATBG). Together with S. Ilani’s group at Weizmann, we explained striking measurements of electronic compressibility in terms of a “cascade” of phase transitions, where electrons fill different spin and valley states one by one as the density is tuned. Further work with the Ilani (WIS) and Young (UCSB) groups uncovered an electronic version of the “Pomeranchuk effect” (originally known in liquid helium-3), where a liquid-like electronic state transforms into a more resistive state due to the entropy carried by electron spins. Our theoretical predictions of unusually large entropy were borne out experimentally. These discoveries reshaped the field’s understanding of MATBG and were widely covered in the scientific community and the popular press.
• Superconductivity and correlated states in multilayer graphene.
Beyond twisted bilayers, researchers have turned to graphene stacks with three or more layers, where the stacking order itself creates new possibilities. Our theoretical work showed that rhombohedral trilayer and tetralayer graphene naturally host electronic states with an annular-shaped Fermi surface—composed of two concentric rings in momentum space. Remarkably, this geometry allows repulsive electron interactions to stabilize superconductivity, often with exotic chiral (handed) pairing. In collaboration with experiments, we identified how such states can be tuned using gate voltages and electric fields. Experiments revealed highly spin-polarized metallic phases—sometimes called half- and quarter-metals—providing clear evidence of strong electron correlations. Additional theoretical studies uncovered “intervalley coherence,” a new type of ordering where electrons in graphene’s two valleys lock together. These advances show that multilayer graphene is not just another material system, but a highly tunable platform where superconductivity, magnetism, and novel quantum orders naturally intertwine. Together, these findings position multilayer graphene as one of the most promising playgrounds for discovering and controlling new states of quantum matter.
“Strange metals” are systems where the usual rules for how electrons move in metals simply fail. Understanding them has been one of the central puzzles of condensed matter physics for decades. The compound Sr₃Ru2O₇ provides one of the clearest examples of this strange behavior. We developed a theory that successfully explains much of its unusual physics. The theory makes several unexpected predictions—some already verified by experiments—and provides new directions for exploring related materials. This marks a major step toward a general understanding of strange metals.
• Hierarchy of energy scales near quantum criticality.
When a metal is tuned to the brink of a phase transition—say, on the verge of becoming magnetic—it enters the realm of “quantum criticality.” These systems are rich in exotic phenomena and often host superconductivity at unexpectedly high temperatures. Despite their apparent simplicity, they are extremely challenging to describe theoretically. Using large-scale computer simulations, we developed a method that allows us to probe these metals without uncontrolled approximations. This enabled us to map out the sequence of “crossovers” the system undergoes as it approaches the critical point. By combining numerical simulations with analytical insights, we established a clear physical picture of quantum critical metals—an advance that helps explain why these materials are fertile ground for superconductivity.
• Numerically exact simulations for moiré quantum critical metals.
One of the most exciting developments of recent years has been the discovery of exotic phases of matter, including superconductivity, in twisted bilayer graphene. At a special “magic” twist angle, the electronic bands become extremely flat, amplifying the effects of interactions between electrons. Theoretical tools to describe such systems are scarce. We developed a new simulation method for twisted bilayer graphene at charge neutrality that captures the essential physics with minimal approximations, while still being computationally feasible. This approach opens a new window into the unusual behavior of graphene moiré systems and provides a benchmark for future theoretical work.
• Cascade of phase transitions and the Pomeranchuk effect in twisted bilayer graphene.
In close collaboration with experimental groups, we studied the puzzling electronic phases of magic-angle twisted bilayer graphene (MATBG). Together with S. Ilani’s group at Weizmann, we explained striking measurements of electronic compressibility in terms of a “cascade” of phase transitions, where electrons fill different spin and valley states one by one as the density is tuned. Further work with the Ilani (WIS) and Young (UCSB) groups uncovered an electronic version of the “Pomeranchuk effect” (originally known in liquid helium-3), where a liquid-like electronic state transforms into a more resistive state due to the entropy carried by electron spins. Our theoretical predictions of unusually large entropy were borne out experimentally. These discoveries reshaped the field’s understanding of MATBG and were widely covered in the scientific community and the popular press.
• Superconductivity and correlated states in multilayer graphene.
Beyond twisted bilayers, researchers have turned to graphene stacks with three or more layers, where the stacking order itself creates new possibilities. Our theoretical work showed that rhombohedral trilayer and tetralayer graphene naturally host electronic states with an annular-shaped Fermi surface—composed of two concentric rings in momentum space. Remarkably, this geometry allows repulsive electron interactions to stabilize superconductivity, often with exotic chiral (handed) pairing. In collaboration with experiments, we identified how such states can be tuned using gate voltages and electric fields. Experiments revealed highly spin-polarized metallic phases—sometimes called half- and quarter-metals—providing clear evidence of strong electron correlations. Additional theoretical studies uncovered “intervalley coherence,” a new type of ordering where electrons in graphene’s two valleys lock together. These advances show that multilayer graphene is not just another material system, but a highly tunable platform where superconductivity, magnetism, and novel quantum orders naturally intertwine. Together, these findings position multilayer graphene as one of the most promising playgrounds for discovering and controlling new states of quantum matter.
1. Analyzing quantum criticality in metals, including new results on the hierarchy of energy scales and crossovers upon approaching the critical point, the behavior of the electronic specific heat, and the scaling of superconductivity with parameters of the electronic structure.
2. Discovery of new mechanisms for "Strange Metal" behavior where the traditional Fermi liquid theory breaks down, and suggesting new ways forward to verify these new mechanisms experimentally.
3. Developing a technique to simulate the behavior of correlated electrons in magic-angle twisted bilayer graphene with minimal approximations, and extracting detailed information about its electronic properties.
4. Developing a theory of novel electronic states and unconventional superconductivity from Coulomb interactions in rhombohedral multilayer graphene, including a prediction of topological chiral superconductivity.
2. Discovery of new mechanisms for "Strange Metal" behavior where the traditional Fermi liquid theory breaks down, and suggesting new ways forward to verify these new mechanisms experimentally.
3. Developing a technique to simulate the behavior of correlated electrons in magic-angle twisted bilayer graphene with minimal approximations, and extracting detailed information about its electronic properties.
4. Developing a theory of novel electronic states and unconventional superconductivity from Coulomb interactions in rhombohedral multilayer graphene, including a prediction of topological chiral superconductivity.