A static deformation of graphene can act on its Dirac electrons as a valley-odd magnetic field. In sublattice-gapped graphene this field makes the two valleys add in the parity-odd response rather than cancel. We derive the equilibrium thermodynamics of this effect and separate it from the finite-frequency transport response. At fixed electrochemical potential, reversing the pseudomagnetic field removes every nonzero pseudo-Landau level in the continuum theory. The remaining grand-potential difference is fixed by the spectrally asymmetric zeroth level. The static charge response is a thermally broadened plateau confined to the gap and has no metallic $m/|μ|$ tail. Near a band edge, pseudofield reversal transfers $\mathrm{B}\ln2$ of entropy per unsplit zero-mode state in the low-temperature window. The fixed-$μ$ heat capacity has two side lobes per edge and a universal peak $0.439229\,D_B k_{\mathrm B}$. We then formulate a definite constant-gate-voltage circuit and show that the measured sheet heat capacity depends on the electrical boundary condition. The full massive-Dirac density of states and an exact finite-field pseudo-Landau-level calculation give the same gate crossover in their common limit. At fixed carrier number, the low-temperature edge value is $-2(\ln2)^2 D_B k_{\mathrm B}$, rather than a node. A finite geometric capacitance gives a continuous and experimentally tunable interpolation. Finally, we give a trace-free triaxial strain geometry, a disorder--interaction window, and realistic calorimetric and quantum-capacitance scales. The field-reversal protocol isolates an equilibrium electromechanical anomaly without a real magnetic field.
A static deformation of graphene can act on its Dirac electrons as a valley-odd magnetic field. In sublattice-gapped graphene this field makes the two valleys add in the parity-odd response rather than cancel. We derive the equilibrium thermodynamics of this effect and separate it from the finite-frequency transport response. At fixed electrochemical potential, reversing the pseudomagnetic field removes every nonzero pseudo-Landau level in the continuum theory. The remaining grand-potential difference is fixed by the spectrally asymmetric zeroth level. The static charge response is a thermally broadened plateau confined to the gap and has no metallic m/∣μ∣ tail. Near a band edge, pseudofield reversal transfers Bln2 of entropy per unsplit zero-mode state in the low-temperature window. The fixed-μ heat capacity has two side lobes per edge and a universal peak 0.439229DBkB. We then formulate a definite constant-gate-voltage circuit and show that the measured sheet heat capacity depends on the electrical boundary condition. The full massive-Dirac density of states and an exact finite-field pseudo-Landau-level calculation give the same gate crossover in their common limit. At fixed carrier number, the low-temperature edge value is −2(ln2)2DBkB, rather than a node. A finite geometric capacitance gives a continuous and experimentally tunable interpolation. Finally, we give a trace-free triaxial strain geometry, a disorder--interaction window, and realistic calorimetric and quantum-capacitance scales. The field-reversal protocol isolates an equilibrium electromechanical anomaly without a real magnetic field.
Non-Hermitian band descriptions capture how loss, gain, and environmental coupling reshape quantum matter, yet most experimental probes remain wave based or dynamical. Here we develop an equilibrium charge-response route to spectral compression in Dirac materials. In the real-spectrum regime, invariance of the particle-number operator under the similarity transformation makes the quantum capacitance exactly that of the Hermitian partner, so the whole non-Hermitian content is carried by the Petermann factor. In a minimal nonreciprocal graphene model, hopping imbalance suppresses the Dirac velocity, enhancing the low-energy density of states and the capacitance as an exceptional point is approached. At charge neutrality the capacitance stays linear in temperature, with its slope enhanced relative to the Hermitian value. A perpendicular magnetic field recasts the same compression as a collapse of the Landau-level ladder, drawing more levels into the thermal window. In two dimensions, the capacitance enhancement relative to the Hermitian partner coincides exactly with the Petermann factor, even though the two have entirely different origins. This relation provides a controlled starting point for extending equilibrium thermodynamic probes to non-Hermitian electronic systems with interactions, disorder, and reservoir coupling.
We consider a recent proposal for a physical realization of the Sachdev-Ye-Kitaev (SYK) model in the zeroth-Landau-level sector of an irregularly shaped graphene flake. We study in detail charge transport signatures of the unique non-Fermi-liquid state of such a quantum dot coupled to noninteracting leads. The properties of this setup depend essentially on the ratio p between the number of transverse modes in the lead M and the number of the fermion degrees of freedom N on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. Our proposed setup gives access to the nontrivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. The dimensionless linear-response conductance acquires distinct p and 1/p dependencies for the two phases, respectively, in the low-temperature limit, with a universal jump at the transition. We find that corrections scale linearly and quadratically in either temperature or frequency on the two sides of the transition. In the weak-tunneling regime, we find differential conductance proportional to the inverse square root of the applied voltage bias U. This dependence is replaced by a conventional Ohmic behavior with constant conductance proportional to 1/T for bias energy eU smaller than temperature scale kBT. We also describe the out-of-equilibrium current-bias characteristics and discuss various crossovers between the limiting behaviors mentioned above.
After its first isolation by Geim and Novoselov in 2004, graphene has grown quickly into an independent subfield of contemporary condensed matter physics, counting thousands of publications. This material has attracted so much attention not only because it is truly two-dimensional -- a feature long thought to be impossible to be realized in nature -- but also because it is the prime representative of a new class of condensed matter systems, the Dirac materials, whose electronic spectrum disperses linearly around isolated points in the Brillouin zone. An outstanding consequence of this linear energy-momentum dispersion is the collapse of the Fermi surface to isolated points at charge neutrality, accompanied by a vanishing single-particle density of states. While this feature of the noninteracting model is what separates graphene from most other, more conventional condensed matter systems, giving rise to many of its astounding physical properties, it leads to severe computational complications when extending the model to contain two-body interactions and/or disorder. In this thesis we consider both extensions separately. After rigorously deriving the low-energy quantum field theory from a tight-binding model and establishing the one-particle irreducible (1PI) vertex functions as the fundamental building blocks of correlation functions, we construct a nonperturbative formalism for the calculation of these vertex functions using the well-established functional renormalization group (fRG). By combining the fRG with the Keldysh formalism, accounting for possible external electromagnetic fields and nontrivial initial correlations, this framework is capable of handling thermal equilibrium and true nonequilibrium alike. To circumvent some of the technical problems of the standard fRG formalism when treating fermionic systems at finite density, we also explore a variant of the fRG, where the chemical potential is interpreted as a flow parameter. We obtain hierarchical sets of flow equations, which describe the change of the 1PI vertex functions upon varying an artificial cutoff scale or the chemical potential, respectively. These nonperturbative formalisms have been used to calculate the renormalization of the Fermi velocity and the static dielectric function at finite temperature and density in the strong coupling regime as an explicit demonstration of their capabilities. Since the Keldysh fRG is an exact formulation of quantum field theory, in particular when external magnetic fields are present, it should be possible to describe the fractional quantum Hall effect in this framework. However, the typical truncation schemes that are currently available to approximately solve the fRG flow equation fail to account for the nontrivial correlation effects necessary to access the fractional quantum Hall regime. To circumvent this problem we consider a modified field theory, where these correlations are implemented ``by hand'' via a Chern-Simons gauge field, coupling to the fermions in addition to the Coulomb interaction term. This modified field theory is analyzed in a stationary phase approximation including Gaussian fluctuations. The electromagnetic response tensor is calculated in the random phase approximation, yielding the Hall conductivities. In the second part of this thesis we consider disordered Dirac fermions in the absence of two-particle interactions. After sketching how the most general disorder potential for Dirac fermions arises from a tight-binding model, we first consider an explicit physical scenario, a disordered graphene pn junction in the presence of a quantizing magnetic field perpendicular to the graphene sheet. We derive an effective one-dimensional theory for the chiral states that propagate along the junction interface and calculate the full conductance distribution in the crossover between the clean and the strong-disorder limit, via an exact solution of a Fokker-Planck equation. Lastly, we develop a nonperturbative approach to calculate the disorder induced self-energy that is based on exact Schwinger-Dyson equations and Ward identities, not only for graphene, but also for other paradigmatic semimetals with a nodal point dispersion.
Quantum Hall effects (QHE) host one-dimensional topologically-protected edge channels, which can serve as an essential ingredient in exotic quantum electronic systems. Yet the manual reconstruction of Landau-level topology, by electrostatic confinement or symmetry breaking, remains experimentally challenging. Here, we show that interfacial charge transfer in between CrOCl and large-angle twisted bilayer graphene offsets the two otherwise decoupled Dirac Landau-level ladders in each graphene layer, creating a new sequence of composite filling configurations. At charge neutrality, the composited (+2,−2) state involves only the zeroth Landau levels and becomes fully insulating, with longitudinal resistance reaching the GΩ regime. By contrast, higher composite zero-filling quantum Hall states, including (+6,−6) and (+10,−10), retain counter-propagating helical edge channels and exhibit pronounced non-local transport, reaching up to 50% of the local response. We attribute such switching-behavior to the Landau-spinor Hilbert space -- as the filling is reduced from (+6,−6) to (+2,−2), the orthogonal N=±1 orbital components are removed, eliminating the edge-compatible channel and gapping both bulk and boundary transport. The interaction nature of the observed gapped sates was further examined both experimentally and theoretically. Our results suggest that charge transfer provides a direct route to engineer artificial quantum Hall insulators, opening possibilities for wavefunction-selective control of helical edge modes.
We establish scaling relations governing the equilibrium thermodynamics of real-spectrum non-Hermitian Dirac fermions in a magnetic field. Assuming thermalization with respect to the quasi-Hermitian Hamiltonian, a similarity transformation maps the system at the same applied field onto a Hermitian Dirac model with reduced velocity, while the Landau-level spectrum also admits a representation in terms of a reduced effective magnetic field. This structure yields scaling relations for the chemical potential, entropy, heat capacities, and orbital magnetic response in different thermodynamic ensembles. At fixed projected filling factor (PFF), the self-consistent chemical potential follows the compressed ladder of Landau levels, and the canonical thermodynamic functions are rescaled Hermitian responses. At fixed chemical potential, Landau-level crossings generate oscillatory caloric and magnetic responses governed by the same spectral compression. Quasistatic non-Hermitian deformation at fixed PFF further yields adiabatic temperature scaling. More broadly, these results establish a thermodynamic framework for real-spectrum non-Hermitian quantum matter and provide a starting point for incorporating the effects of interactions and disorder within the same formalism.
Free entanglement—the milestone of any quantum information processing scheme—among the π -electronic spin and its spatial states in graphene, as a function of temperature, is the main concern of the present report. It is assumed that a perpendicular magnetic field generates the Landau levels so that a coupling with the pseudo-spin (sublattice) states is enacted. Moreover, the pseudo-Rashba spin–orbit interaction (SOI), responsible for the coupling of spin and sublattice states, is also taken into account. From the structure of the total Hamiltonian, we introduce a Casimir operator which, in due turn, assists the development of a simple but efficient algorithm for our numerical computation. We then proceed by constructing the thermal density operator, its partially transposed one and, thereby, compute the negativity, the proper measure of free hybrid entanglement, at any temperature. Our results show that the negativity is nonvanishing at absolute zero temperature due to the fact that the ground state is an entangled one. Moreover, our results indicate that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement (free) is maximal strongly depend on the magnetic field and pseudo-Rashba spin–orbit strength; decreasing the magnetic field and/or increasing the pseudo-Rashba parameter (PRP) enhances the maximal entanglement monotonically. As the temperature increases, however, it is shown that the negativity decreases asymptotically to zero. As a result, there exists distillable entanglement amid the π -electronic spin and its spatial states in graphene at any finite temperature .