Condensed Matter Physicist (PhD)

Remote • Contract • via Mercor

About this role

About the work

CritPt is a public benchmark of research-level physics challenges, built to test whether frontier AI models can carry out genuine physics research reasoning rather than textbook problem solving. The benchmark paper is arXiv:2509.26574 and we recommend reading it before applying. It will tell you quickly whether this work interests you.

We are engaging physicists to work on research-level physics problems in their own subfield. Depending on where your publication record fits, that can mean creating problems, solving them, reviewing completed work, or auditing it. We agree the specific assignment with you once you are matched to an area.

This is research-grade work rather than volume work. Whatever you produce has to be complete enough for another specialist in your subfield to follow and verify independently, so written reasoning is part of every assignment.

Research areas in this panel

Nineteen areas. We match narrowly: you need to have published on one of these specific phenomena, not in condensed matter broadly. Each area lists the methods it requires.

1. One-dimensional field theory: bosonization, Majorana and Ising-Luttinger sectors, RG: Abelian bosonization, Majorana fermion field theory in one dimension, coupled Ising and Luttinger-liquid sectors, scaling dimensions of vertex operators, one-loop renormalization-group flow equations, operator product expansion, commensurate-incommensurate transition.

2. Parafermion zero modes, non-Abelian braiding, FQH-superconductor heterostructures: Parafermion zero modes, ZN parafermion algebra, non-Abelian braiding statistics, fusion channels of topological defects, fractional Josephson effect, adiabatic evolution and Berry phases, fractional quantum Hall-superconductor heterostructures.

3. Rational CFT, Verlinde lines, non-Abelian quantum Hall edge theories: Rational conformal field theory on the torus, Verlinde lines as topological defect lines, modular S matrix and the Verlinde formula, Moore-Read non-Abelian quantum Hall state, chiral edge theories of quantum Hall states, fusion categories and non-invertible symmetries, modular invariance of the primary field spectrum.

4. SPT and Haldane phase, matrix product states, decoherence of topological order: AKLT valence-bond-solid model, Haldane phase and symmetry-protected topological order, string order parameters, matrix product states, transfer-matrix evaluation of correlation functions, Kraus-operator quantum channels, decoherence-induced mixed-state topological order.

5. Flat-band Hubbard models, flat-band ferromagnetism, Hartree-Fock and DQMC: Checkerboard-lattice Hubbard model, topological nearly flat bands, flat-band ferromagnetism, Hartree-Fock mean-field theory, Stoner ferromagnetic instability, interaction-driven quantum phase transitions, determinant quantum Monte Carlo.

6. SYK model, large-N disordered fermions, Schwinger-Dyson thermodynamics: Sachdev-Ye-Kitaev model, low-rank random couplings, Majorana fermions, quenched disorder averaging, large-N melonic diagrammatics, Schwinger-Dyson equations, thermodynamic free energy, residual zero-temperature entropy.

7. Correlated electron transport: Hubbard model, Kubo formalism, diagrammatic perturbation theory: Hubbard model, Fermi-liquid theory, Kubo linear-response formalism, perturbative diagrammatic expansion in the interaction, Matsubara Green's function technique, vertex corrections and momentum relaxation, electron-electron scattering on a lattice, low-density expansion near a band edge.

8. Wigner crystallization, two-component Coulomb systems, quantum melting: Wigner crystallization, two-component Coulomb crystallization, critical mass ratio for quantum crystals, electron-hole bilayers, Wigner-Seitz coupling parameter, Lindemann criterion for quantum melting, dimensional analysis of competing energy scales, quantum Monte Carlo phase diagrams.

9. Quantum geometry, Wannier obstruction, Z2 topological invariants (Kane-Mele and Wilson loop): Quantum geometric tensor, quantum metric, gauge-invariant Wannier spread, maximally localized Wannier functions, Kane-Mele time-reversal Z2 invariant, Wilson loop and Wannier charge center winding, continuum models with plane-wave expansion, Wannier obstruction and exponential localization, Rashba spin-orbit coupling.

10. Hatsugai-Kohmoto model, Mott physics, quasiparticle scattering and RG stability: Hatsugai-Kohmoto model, Mott insulators and Hubbard bands, Fermi liquid theory, quasiparticle scattering rates and lifetimes, phase-space constraints on fermion-fermion scattering, renormalization-group stability of interacting fixed points.

11. Schwinger-Keldysh EFT, dissipative hydrodynamics, fracton and multipole symmetries: Schwinger-Keldysh effective field theory, dissipative hydrodynamics, multipole and dipole symmetries, fracton phases of matter, spontaneous symmetry breaking and Goldstone stiffness, superfluid stiffness and susceptibilities, derivative expansion power counting, hydrodynamic mode dispersion relations.

12. Quantum Monte Carlo for the 2D electron gas: DMC, finite-size corrections: Diffusion Monte Carlo, Slater-Jastrow trial wave functions, two-dimensional finite-size corrections and thermodynamic-limit extrapolation, periodic boundary conditions with long-range Coulomb interactions, static structure factor and pair correlation functions, random phase approximation for long-wavelength fluctuations, Fermi liquid theory.

13. Dirac materials transport: Coulomb disorder, nonlinear screening, Boltzmann transport: Dirac fermions in graphene, charged impurity Coulomb disorder, nonlinear screening and Thomas-Fermi theory, electron-hole puddles, self-consistent transport theory, topological insulator surface states, long-range versus short-range scattering, Boltzmann transport and mean free path.

14. Topological crystalline insulators: disclinations, fractional charge, filling anomaly: Topological crystalline insulators, band representations and Wyckoff positions, Wannier orbital angular momentum under rotation symmetry, disclination defects and Frank angle, translation-equivalence classes of lattice defects, fractional charge quantization, filling anomaly, discrete shift invariant.

15. Kitaev honeycomb model, Z2 gauge theory, exactly solvable spin liquids: Kitaev honeycomb model, Majorana fermionization of spins, Z2 lattice gauge theory and flux sectors, exactly solvable quantum spin liquids, fermion parity projection onto physical states, topological ground-state degeneracy on a torus, Bogoliubov-de Gennes diagonalization, exact diagonalization of finite lattices.

16. Semiclassical thermoelectric transport: anisotropic Seebeck, bipolar conduction: Semiclassical Boltzmann transport theory, relaxation-time approximation, anisotropic effective-mass tensors, Seebeck coefficient and thermopower, bipolar transport in intrinsic semiconductors, axis-dependent conduction polarity, two-band electronic structure models.

17. Inelastic neutron scattering theory: multiphonon expansion, dynamic structure factor: Inelastic neutron scattering, multiphonon expansion of the scattering law, quantum harmonic oscillator response, incoherent dynamic structure factor, Debye-Waller factor, bound-atom scattering cross section, low-temperature limit of the scattering law, neutron total cross section.

18. Magnetic space groups, neutron-diffraction magnetic structure, magneto-optics: Magnetic space groups, Belov-Neronova-Smirnova notation, Wyckoff position analysis, magnetic propagation vectors from neutron diffraction, multi-k magnetic structures, irreducible representation analysis of magnetic order, time-reversal symmetry breaking, symmetry-adapted tensor properties, magneto-optic Kerr effect.

19. Crystallography of modulated structures: kinematic diffraction, superspace symmetry: Kinematic diffraction theory, crystal structure factor, displacively modulated crystal structures, satellite and superlattice reflections, reciprocal lattice and Brillouin zone indexing, diffraction selection rules and extinction conditions, superspace symmetry of modulated crystals, longitudinal static strain waves in crystals.

Methods we expect to find in your own publications

You should be able to point to your own papers demonstrating at least one of the following families:

• Field-theoretic: bosonization, conformal field theory on the torus, Schwinger-Keldysh effective field theory, renormalization-group flow
• Many-body numerics: quantum Monte Carlo (diffusion and determinant), exact diagonalization, matrix product states, transfer-matrix methods
• Band theory and topology: Wannier functions, Berry phases, Wilson loops, Wyckoff positions, band representations
• Response and transport: Kubo linear response, Matsubara Green's functions, diagrammatic perturbation theory, Boltzmann transport
• Scattering and symmetry analysis: neutron scattering theory, magnetic space groups, irreducible representation analysis, kinematic diffraction

Who we are looking for

A PhD in condensed matter physics or a closely related field. This is a hard requirement. Postdoctoral researchers, research scientists and junior faculty are the strongest fit. Senior PhD students with a strong first-author record are welcome to apply.

Published work on the specific phenomenon above, not the adjacent one. This is the single most common reason we decline otherwise excellent physicists. Publishing on topological order generally is not enough if your papers are not on the particular model in question. Command of the methods is not enough if you have not published on the phenomenon itself.

A verifiable publication record. Three to five representative papers with arXiv IDs or DOIs, ideally from the last five years. First author strongly preferred. Every paper you list will be checked against the public record.

Working proficiency with LaTeX, Python, SymPy and Jupyter. Some familiarity with an agentic coding extension in VS Code is useful. Gaps here are acceptable if you declare them honestly.

English at B2 or above, including written reasoning. A large part of the value you add is how clearly you set out your argument.

Application steps

• Apply and complete the attached form. Basic information, education, research experience, your method self-attestation, and up to five of the areas above that you are the best fit for. For each area you select, give an arXiv ID or DOI of your own paper as proof, with your author position and the methods it demonstrates. A selection without proof is not scored.
• We verify your papers and authorship against the public record.
• Then one of two things happens. Either we onboard you directly, or we invite you to a short live alignment call to agree the area and the assignment with you.
• A brief 30 to 45 minute assessment may be added, but only where we need it. Most applicants will not see one.

Commitment and rate

10 hours per week, sustained across an 8 to 10 week window, starting immediately. Remote and asynchronous with no fixed hours.

$80 to $110 per hour, set by depth of subdomain match.

Details

• Pay: $80 to $110/hr
• Company: Mercor
• Location: Remote
• Eligible locations: Worldwide (no restriction)
• Platform: Mercor