Seriously Strange Metals: The Quantum Rebels of Condensed Matter Physics

"Strange Metals and the Quantum Ocean", an illustration. Artwork: NaturPhilosophie with AI

In the classical world of materials science, metals are well-behaved. Their electrons follow predictable rules, their resistivity scales with temperature in a quadratic fashion, and their behaviour is neatly captured by Fermi liquid theory. But in the quantum realm…

When Strange Metals Misbehave

In the quantum world, some metals break these rules.

These are the strange metals. Materials that defy conventional understanding and hint at deeper, more exotic physics.

For over 50 years, physicists have understood current as a flow of charged particles until a new experiment found that in at least one strange material, this understanding falls apart.

The phenomenon of electrons, atoms, spins or other various components inside a solid material is described through Quantum Mechanics. These phenomena are predicted through theory and calculation, and proved through experiments. Therefore, theory, calculation, and experiment are very important factors in Condensed Matter Physics. Image: University of Seoul, South Korea

Discovered in the 1980s during the study of high-temperature superconductors, strange metals have since become a central mystery in Condensed Matter Physics (CMP).

They exhibit linear resistivity with temperature, lack well-defined quasiparticles, and may even conduct electricity without traditional electrons.

In other words, there is a charge, but without carriers. A fluid-like flow.

A Signature of Strangeness: Linear Resistivity

Two diagrams explaining electron flow resistance with temperature. "At 20ºC, free electrons colliding with metal atoms as they flow to the right. At 70ºC, as the temperature increases, the atoms vibrate. It is harder for the electrons to flow (Increase in Resistance)"

In ordinary metals like copper or silver, electrical resistance increases with the square of the temperature due to electron scattering.

Electron Scattering

Electron scattering happens when electrons change direction after interacting with matter – like an atom or another particle.

A diagram showing the basics values involved in a typical elastic glancing collision including masses m1 and m2, velocities v1 and v2 and angles of displacement. — A Classic Elastic Glancing Collision Image: MiniPhysics

When an electron hits another atom, it is displaced from its original trajectory and bounces off in a different direction.

Electrons scatter through a solid in a manner of ways:

not at all: no electron scattering occurs at all and the beam passes straight through,
single scattering: when an electron is scattered just once,
plural scattering: when electron(s) scatter several times,
multiple scattering: when electron(s) scatter many times over.

A diagram illustrating the different possible kinds of interactions of an electron beam with a sample of solid matter. Where K,L,M are the electron shells. N is the sample nucleus. Gamma is a characteristic photon emitted by the ejection of SE (Secondary Electron). And BSE is a Back-Scattered Electron. Electrons follow the usual e- notation. Source: Wikipedia

Electrons are negatively charged, so additionally they get deflected by the electric fields of the atoms.

The likelihood of an electron scattering and the degree of the scattering is a function of the specimen thickness and the mean free path.

This phenomenon happens in solids like metals and semiconductors, affecting how electricity flows.

"A Long Shot in the Cosmic Game of Pool" illustration for "Passing Stars and the Three-Body System" post. Electron scattering is what happens when electrons change direction after interacting with something - like atoms or other particles. Think of it like a game of billiards. Artwork: NaturPhilosophie with AI

Scientists use electron scattering to study atomic structures and even discover tiny particles like quarks.

This scattering typically happens in solids such as metals, semiconductors and insulators. It is a limiting factor in integrated circuits and transistors.

Generally, the resistance of metals increases with increasing temperature, while the resistance of semiconductors decreases with increasing temperature.

The Temperature Coefficient of Resistance

The temperature coefficient of resistance α_t has positive and negative values, depending on the substance.

The equation for Resistance R at temperature T(ºC) or R_T and two graphs showing how the resistance linearly increases as the temperature increases in metals, and how the resistance linearly decreases as the temperature increases in semiconductors. — Resistance Temperature Characteristics Source: Electrical-Information

$\alpha_t = \frac{1}{R_t} \times (\frac{R_T-R_t}{T-t})$

In the case of metals such as gold, silver, copper, and iron, the temperature coefficient of resistance α_t is positive.

In the case of semiconductors, such as germanium, insulators, and carbon, the temperature coefficient of resistance α_t is negative.

The temperature coefficient of resistance α_t indicates how much the resistance changes when the resistance of 1 Ω rises by 1 ℃.

However, strange metals – such as the cuprates (copper-oxide high-temperature superconductors) – show a linear increase in resistivity with temperature, even at extremely low temperatures.

Cuprate Superconductors

Cuprate superconductors are a family of high-temperature superconducting materials made of copper oxide (CuO₂) layers, interspersed with layers of other metal oxides, which act as charge reservoirs.

These materials exhibit superconductivity at much higher temperatures than conventional superconductors, making them a key focus in Condensed Matter Physics.

A diagram illustrating the Cuprate Phase Mystery. Theorists are unable to explain why the superconducting transition temperature (thick black line) is so high in the cuprates. However, if they could understand the behaviour of the cuprates in the pseudogap region (blue), they might be able to explain high-temperature superconductivity. — The Cuprate Phase Diagram Mystery: The properties of the cuprates vary with temperature (y-axis) and the doping per unit cell of CuO₂ (x-axis). The origin of high-temperature superconductivity in cuprate materials is one of the biggest puzzles in Physics, but the behaviour of these materials when they are not superconducting is an even bigger mystery. Image: PhysicsWorld (2000)

Discovered in 1986, the cuprate superconductors hold the record for highest superconducting transition temperature (T_c) under ambient pressure to date.

Cuprate high-temperature superconductors have the following properties:

They have a layered perovskite-like structure, with weakly coupled CuO₂ planes where superconductivity primarily occurs.

They can be hole-doped or electron-doped, which significantly affects their superconducting properties.

Lanthanum Cuprate High-Temperature Superconductor Structure Source: PHysicsHarvard. — Lanthanum Cuprate High-Temperature Superconductor Structure Source: PhysicsHarvard.

Unlike traditional superconductors, cuprates are believed to rely more on electron-electron interactions rather than electron-phonon interactions.

There are 3 main families of hole-doped cuprate high temperature superconductors(HTSC) being studied today.

Each material is accessible to different experimental techniques. For example, it is easy to measure the electronic density of states of Bi₂Sr₂CaCu₂O_8+x, but harder to ascertain its magnetic properties.

Because of this, the field of high-T_c research is rife with conflict and apparent contradictions.

The high critical temperature T_c‘s and critical magnetic fields of these materials have been crucial for technological applications.

Some cuprates, like Yttrium Barium Copper Oxide (YBCO), superconduct above liquid nitrogen temperatures, making them more practical for applications.

Moreover, their intriguing superconducting and normal state properties have continually challenged our conventional understanding of solids, stimulating research on strongly correlated electron systems.

Scientists are still investigating the exact mechanism behind cuprate superconductivity, with theories suggesting spin fluctuations and strong electron correlations play a crucial role.

At the forefront of quantum material research, advanced techniques like Angle-Resolved PhotoEmission Spectroscopy (ARPES) are used to study their electronic properties.

This linearity is not just a curiosity.

Indeed it suggests that the electrons in these materials are not behaving like individual particles. Instead, they may be part of a strongly entangled quantum soup, where traditional descriptions of particle motion break down.

Beyond Electrons: Charge Without Carriers?

One of the most startling findings in recent years is that:

Electric current in strange metals may not be carried by electrons at all.

In a 2023 experiment, researchers observed current flowing through a microscopic strand of strange metal so smoothly that it defied the idea of discrete charge carriers.

This behaviour is akin to watching a fluid flow without molecules, suggesting that the charge transport mechanism in strange metals might involve collective quantum states or emergent excitations that are fundamentally different from electrons.

Strange metallicity often appears near quantum critical points – transitions between different quantum phases of matter at absolute zero.

Quantum Criticality: Where Scale Vanishes

Near a quantum critical point, fluctuations of an order parameter (e.g., spin or charge density waves) can lead to non-Fermi liquid behaviour and linear resistivity.

A combined schematic illustration of a quantum critical point showing the phase diagram (a) and the
growth of droplets of quantum critical matter near the quantum critical point (b). — Quantum Criticality: a) Schematic phase diagram near a quantum critical point. Quantum critical points distort the fabric of the phase diagram creating a ‘V-shaped’ phase of quantum critical matter fanning out to finite temperatures from the quantum critical point. b) As matter is tuned to quantum criticality, ever-larger droplets of nascent order develop. On length-scales greater than these droplets, electrons propagate as waves. Source: Coleman & Schofield/Nature (2005)

At these points, fluctuations occur at all length and time scales, and the system becomes highly sensitive to external parameters.

This proximity to quantum criticality may explain the scale-invariant behaviour of strange metals, where no single energy scale dominates. It also links strange metals to holographic duality and black hole physics, where similar scale-free behaviour emerges.

Inside the droplet, the intense fluctuations radically modify the motion of the electron, and may lead to it breaking up into its constituent spin and charge components. Physics inside the
V-shaped region of the phase diagram (a) probes the interior of the quantum critical points (D), whereas the physics in the normal metal (N) or antiferromagnet (A) reflects their exterior.

If, as suspected, quantum critical matter is universal, then no information about the microscopic nature of the material penetrates into the droplets.

Making an analogy with a black hole, the passage from non-critical, to critical quantum matter involves crossing a ‘material event horizon’. Experiments that tune a material from the normal metal past a quantum critical point force electrons through the ‘horizon’ in the phase diagram, into the interior of the quantum critical matter, from which they ultimately re-emerge through a second horizon on the other side into a new universe of magnetically ordered matter.

Bosonic Strange Metals and Cooper Pair Chaos

Traditionally, strange metallic behaviour was observed in systems where electrons (fermions) are the charge carriers.

The Landau-Fermi Liquid Theory

The Fermi liquid theory is a fundamental concept in Condensed Matter Physics (CMP) that describes the behaviour of interacting fermions, particularly conduction electrons in metals at low temperatures.

Developed by Lev Landau in 1956, the theory explains why some properties of an interacting fermion system resemble those of a non-interacting Fermi gas, while others differ.

Two diagrams (a) A gas of atoms reaches quantum degeneracy when the matter waves of neighbouring atoms overlap - i.e. when the thermal de Broglie wavelength, which increases as the temperature falls, becomes about as large as the mean spacing, d, between atoms. The gas then exhibits quantum behaviour, such as Bose-Einstein condensation (for bosons), and Fermi pressure and Pauli blocking (for fermions). (b) At absolute zero, gaseous boson atoms all end up in the lowest energy state. Fermions, in contrast, fill the available states with one atom per state - shown here for a one-dimensional harmonic confining potential. The energy of the highest filled state at T = 0 is the Fermi energy, E_F. The Fermi temperature, T_F=E_F/k_B, where k_B is Boltzmann's constant, marks the crossover from the classical to the quantum regime. At about T_F/2, the wavelength is equal to the mean interparticle spacing. Source: PhysicsWorld — A Fermi Gas of Atoms Source: PhysicsWorld

Identical fermions cannot occupy the same quantum state at the same time. Bosons, however, can share quantum states. But to observe this fundamental difference, gases of bosons or fermions have to be chilled to ultra-low temperatures, where individual quantum states have a high chance of being occupied.

At these low temperatures, bosons will eagerly fall into a single quantum state to form a Bose-Einstein condensate, whereas fermions tend to fill energy states from the lowest up, with one particle per quantum state. At high temperatures, in contrast, bosons and fermions spread out over many states with, on average, much less than one atom per state.

The key idea is that even when electrons interact strongly, their collective behaviour can still be understood in terms of quasiparticles – entities that behave like free electrons, but with modified properties such as effective mass.

The Landau-Fermi Theory provides a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures.

Fermi liquid theory applies to various systems, including:

normal metals (non-superconducting),
liquid He-3, which remains a Fermi liquid at low temperatures,
heavy fermion materials, where electron interactions significantly increase their effective mass,
nucleons (protons and neutrons) in atomic nuclei.

A crucial aspect of the theory is adiabaticity, meaning that if interactions are introduced gradually, the system’s ground state transforms smoothly without abrupt changes. This allows physicists to study complex many-body systems using relatively simple approximations.

But, a 2022 study revealed strange metallicity in a bosonic system, where charge is carried by Cooper pairs – bound states of two electrons that have a bosonic behaviour.

Cooper Pairs

A Cooper pair is a bound state of two electrons (or other fermions) that move through a crystal lattice in a correlated fashion.

Despite their like charges and natural repulsion, these electrons pair up at very low temperatures due to an indirect attraction mediated by phonons – quantized vibrations of the lattice.

Wait… WHAT?

Passing Electrons Distort High-Temperature Superconductor Crystalline Structure Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation. An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction distorts the ion lattice, moving the ions slightly toward the electron, increasing the positive charge density of the lattice in the vicinity. Source: PhysicsHarvard.

Here’s why this is surprising.

An electron moving through the lattice slightly distorts the positively charged ions, creating a region of increased positive charge.

This distortion lingers just long enough to attract a second electron – one with opposite spin and momentum.

The two electrons become weakly bound over long distances, often hundreds of nanometers apart, thus forming a Cooper pair.

This mechanism was first described by Leon Cooper in 1956 and later incorporated into the BCS theory (Bardeen-Cooper-Schrieffer), which earned the trio the 1972 Nobel Prize in Physics.

One of the first steps toward a theory of superconductivity was the realization that there must be a band gap separating the charge carriers from the state of normal conduction.

BCS Theory of SuperConductivity

The critical temperature for superconductivity must be a measure of the band gap, since the material could lose superconductivity if thermal energy could get charge carriers across the gap.

The critical temperature T_C was found to depend upon isotopic mass. It certainly would not if conduction happened by free electrons alone.

A diagram illustrating the BCS Therory of Superconductivity. A band gap was implied by the very fact that the resistance is precisely zero. If charge carriers can move through a crystal lattice without interacting at all, it must be because their energies are quantized such that they do not have any available energy levels within reach of the energies of interaction with the lattice.
A band gap is suggested by specific heats of materials like vanadium. The fact that there is an exponentially increasing specific heat as the temperature approaches the critical temperature from below implies that thermal energy is being used to bridge some kind of gap in energy. As the temperature increases, there is an exponential increase in the number of particles which would have enough energy to cross the gap. — BCS Theory of Superconductivity Source: HyperPhysics

This made it evident that the superconducting transition involved some kind of interaction with the crystal lattice.

Single electrons could be eliminated as the charge carriers in superconductivity since with a system of fermions you do not have energy gaps.

All available levels up to the Fermi energy fill up.

The needed boson behaviour was consistent with having coupled pairs of electrons with opposite spins.

The isotope effect described above suggested that the coupling mechanism involved the crystal lattice, so this gave rise to the phonon model of coupling envisioned with Cooper pairs.

Why are Cooper pairs so special?

In conventional superconductors, the pairing is due to electron-phonon interactions.

In unconventional superconductors (like cuprates), the pairing mechanism is still debated – possibly involving spin fluctuations or other exotic interactions.

While individual electrons are fermions (and obey the Pauli exclusion principle), a Cooper pair has integer spin and behaves like a boson. This means many pairs can occupy the same quantum state.

In the superconducting state, all Cooper pairs condense into a single macroscopic quantum state. This collective behaviour prevents scattering, allowing current to flow with zero resistance.

Breaking a Cooper pair requires a minimum energy. This energy gap protects the superconducting state from thermal disruptions.

This discovery implies that strange metallicity is not limited to fermionic systems and may be a universal feature of quantum matter, governed by principles that transcend particle statistics.

Theoretical Models: SYK and Beyond…

Over the past few years, many physicists worldwide have conducted research investigating chaos in quantum systems composed of strongly interacting particles, also known as Many-Body Chaos.

In a quantum system a probability map replaces the ball, but chaos and memory of classical trajectories also exist. Credit: IST Austria/Maksym Serbyn — Deeper understanding of quantum chaos may be the key to quantum computers. The information processed and stored on these computers will be dependent on keeping the atoms in more than one state at any time, it is a constant battle to keep the particles from settling into an equilibrium. Source: PhysicsWorld

Many-body Quantum Chaos refers to the complex, seemingly random behaviour that emerges in quantum systems with many interacting particles.

Unlike classical chaos, which stems from sensitivity to initial conditions, quantum chaos in many-body systems is revealed through statistical patterns in energy levels, rapid entanglement growth, and the scrambling of quantum information – often linked to thermalization and the breakdown of integrability.

The study of Many-Body Chaos has broadened the current understanding of quantum thermalization – the process through which quantum particles reach thermal equilibrium by interacting with one another. It revealed surprising connections between microscopic physics and the dynamics of black holes.

In everyday life, particles will bounce off one another until they explore the entire space, settling eventually into a state of equilibrium. This process is called thermalization.

A quantum scar is when a special configuration or pathway leaves an imprint on the particles’ state that keeps them from filling the entire space. This prevents the systems from reaching thermalisation and allows them to maintain some quantum effects.

To explain strange metals, physicists have turned to exotic models like the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly interacting particles with maximal quantum chaos.

The Sachdev-Ye-Kitaev (SYK) model

The SYK model captures many features of strange metals, including their entropy and transport properties.

It is a solvable quantum model that describes a system of strongly interacting particles with no well-defined quasiparticles. It has become a powerful tool for understanding both:

Non-FermiLliquid behaviour of strange metals,
Quantum Microstates of black holes in certain gravity theories.

A schematic phase diagram showing the behavior of the Sachdev-Ye-Kitaev Model for different regimes of temperature and system size. From high to low temperature, the model transitions from behaving like interacting particles, to a semiclassical black hole, to a highly quantum black hole. Credit: Kobrin et al. — The Sachdev-Ye-Kitaev model Image: MiniPhysics

This model reveals that both systems exhibit maximal quantum chaos, meaning they scramble information as fast as possible under quantum laws. This scrambling is what links the “ringing” of black holes to the dissipative behaviour of strange metals.

In addition to hypothesizing this rapid spread of information in certain high-dimensional systems, previous studies proved that there is a universal speed limit on the rate at which this ‘chaos’ can develop. Interestingly, the only known or hypothesized systems that reach this limit are closely related to black holes, or more specifically, the quantum theories that describe black holes.

A major surprise was when researchers predicted that the SYK model also saturates the universal bound on chaos.

This insight led to further analyses indicating that the low-temperature properties of the SYK model are effectively equivalent to that of a charged black hole.

This model reveals that both systems exhibit maximal quantum chaos, meaning they scramble information as fast as possible under quantum laws.

This scrambling is what links the “ringing” of black holes to the dissipative behaviour of strange metals.

The SYK model provides numerical evidence that strongly interacting quantum systems without quasiparticles can exhibit maximal chaos and Planckian dissipation, mirroring the thermalization dynamics observed in black hole horizons.

Planckian Dissipation and High Transition Temperatures. Image: Zaanen (2004)

Homes et al. (2004) established a universal relation between the superfluid density, the normal-state conductivity and the transition temperature for high-temperature, copper-oxide superconductors.

Further insight comes from a dimensional analysis of the equation: given that both sides of the equation must have units of s^-2, the identification of the transition temperature with units of inverse seconds brings Planck’s constant $h$ into play.

$\tau (T_c) \approx h/(2 \pi k_B T_c)$

This quantum connection is the crux of the matter. Bearing in mind Uemura’s law, the quantum physical constraint on the relaxation time – Planckian dissipation – explains why the transition temperature for copper oxides is so high.

These models also connect strange metals to holographic duality.

The Holographic Principle

Physicists exploring holography suggest that quantum entanglement may be fundamental to spacetime’s geometry itself, weaving a cosmic web of connections.

The Holographic Principle is one of the most profound ideas in modern Theoretical Physics. It suggests that all of the information contained within a volume of space can be fully described by the data encoded on its boundary – like a hologram.

This radical concept challenges our classical understanding of reality, implying that the three-dimensional universe we experience might be the projection of a deeper, lower-dimensional Physics.

Strange metals are the smoky mirrors where holographic gravity reveals its quantum secrets because in holographic duality, the chaotic, strongly entangled behaviour of strange metals maps onto the dynamics of black holes in a higher-dimensional spacetime, where gravity encodes their quantum complexity.

This conclusion suggests that their behaviour might be described by a dual gravitational theory – possibly involving black hole analogues in higher-dimensional spacetimes.

Strange metals and black holes may seem two unrelated phenomena. However they are connected by deep principles of Quantum Physics, particularly through their shared relationship with Planckian dissipation and quantum chaos.

Black Holes and Gravitation Theory

Black holes, particularly after merging, exhibit “ringing” or quasinormal mode echoes – vibrations that decay over time.

The decay rate is also governed by the same constants and thought to represent the fastest possible relaxation time allowed by Quantum Mechanics.

A diagram illustrating Light Echoes (emerging) From Behind a Black Hole. XMM-Newton has made the first ever observation of light coming from behind a black hole. The key reads: Black hole - Diameter 30 million km, 10 million times the mass of our Sun, Light Echoes, Corona - 60 million km high above black hole, producing X-rays, Flare - Extremely bright flash of X-rays lasting 2.5 hours. 1. Hot, spinning disk of gas falling into black hole. 2. Corona produces bright flares of X-ray light. 3. X-rays reflect off the disk. 4. X-ray echoes from behind the black hole are bent around it by extreme gravity.

The echoes in black holes and the sluggish, viscous conductivity in strange metals both reflect a deeply entangled quantum state – one where information spreads rapidly and irreversibly.

In both cases, the system’s response to perturbations is dictated not by Classical Mechanics, but by universal quantum bounds.

Both strange metals and black holes exhibit behaviours governed by universal quantum limits.

Implications for High-Temperature Superconductivity

Strange metals are a class of materials where electrical resistivity scales linearly with temperature, and electrons dissipate energy as fast as Quantum Mechanics allows – a behaviour tied to Planck’s constant and Boltzmann’s constant.

Often, they are found in the normal state of high-temperature superconductors, just above the critical temperature where superconductivity sets in. This has led many to believe that understanding strange metallicity is key to unlocking the secrets of unconventional superconductivity.

If strange metals are a precursor phase to superconductivity, then their exotic behaviour might hold the clues to designing new materials that superconduct at room temperature – a holy grail of Modern Physics.

Strange Metals Research – From Lasers to Lattices

Studying strange metals is notoriously difficult.

Their behaviour emerges under extreme conditions – low temperatures, high pressures, or finely tuned doping levels. Moreover, their lack of quasiparticles makes traditional spectroscopic techniques less effective.

So, future research into strange metals and superconductivity will likely involve:

ultrafast spectroscopy to probe nonequilibrium dynamics,
quantum simulations using cold atoms or programmable quantum devices, and
machine learning to identify hidden patterns in experimental data.

A New Phase of Matter?

Strange metals are not just oddities.

They may represent an entirely new phase of quantum matter, governed by principles that challenge our deepest assumptions about particles, charge and entropy.

They blur the line between condensed matter and high-energy physics, between electrons and spacetime, between the tangible and the theoretical.

In a way, strange metals are like quantum chimeras – part metal, part mystery, and wholly fascinating.

They remind us that even in the seemingly well-charted territory of solid-state physics, there are still frontiers as wild and wondrous as the Cosmos itself.