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Condensed Matter

Condensed Matter is an international, peer-reviewed, open access journal on the physics of condensed matter published quarterly online by MDPI.

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All Articles (661)

  • Feature Paper
  • Article
  • Open Access

Bond-stretching phonons in hole-doped cuprates exhibit pronounced anomalies in momentum regions where charge correlations are observed, indicating a strong coupling between lattice dynamics and the charge sector. Motivated by this phenomenology, we develop a minimal theoretical framework to clarify how the bond-stretching phonon is renormalized by the proximity to charge-order instabilities and why short-ranged dynamical charge density fluctuations (CDFs) can provide a dominant contribution even in the presence of nearly static charge density wave (CDW) correlations. Starting from a correlated Fermi-liquid description with Coulomb-frustrated charge ordering and electron–phonon coupling, we formulate a two-mode random-phase-approximation treatment in which a low-energy phonon channel involved in the charge-order instability is coupled, through the electronic polarization, to the higher-energy bond-stretching branch. The resulting off-diagonal phonon self-energy transfers the low-energy charge softening to the bond-stretching phonon. We then introduce an average self-energy description to account for the coexistence of CDW and CDF components. The model shows that, although a nearly static CDW component produces a stronger local softening, a broader CDF component can dominate the effective phonon self-energy because of its larger reciprocal-space volume. The analysis identifies two key parameters controlling the bond-stretching anomaly: the characteristic energy of charge correlations and the effective electron–phonon coupling.

Condens. Matter

5 August 2026

Representative diagrams of the Dyson series for the two-mode phonon model. Only the elementary self-energy insertions are shown: the diagonal channels 
  
    Σ
    11
  
 and 
  
    Σ
    22
  
 renormalize the low-energy and BS phonons, respectively, while the off-diagonal channel 
  
    
      Σ
      12
    
    =
    
      Σ
      21
    
  
 mixes the two modes through the electronic polarization bubble 
  
    Π
    
      e
      e
    
  
.

Organic semiconductors offer a potential class of materials for organic photovoltaic (OPV) applications due to their tunable optoelectronic properties and low-cost processing. A methodical DFT/TD-DFT study of a library of organic donor–π–acceptor (D–π–A) compounds based on triphenylamine donors, thiophene-based π-bridges, and benzothiadiazole/malononitrile acceptors is presented in this work, with the goal of rationalizing the structure–property relationships governing their photovoltaic behavior. CAM-B3LYP calculations were used to analyze the role of donor, bridge, and acceptor units in modulating frontier-orbital alignment, charge-transfer character, and optical absorption properties, as well as to evaluate the active-layer thickness in the estimation of the light-harvesting efficiency. The results, which are intended as internal comparative descriptors rather than predictive device efficiencies, reveal that the most pronounced bathochromic shifts and most favorable optical responses are not simply associated with the strongest donor or acceptor moieties, but rather arise from an optimal balance between frontier-orbital delocalization and charge-transfer character across the molecular framework. A preliminary assessment of photovoltaic descriptors suggests that the proposed computational workflow may provide useful guidelines for the descriptor-guided design and screening of next-generation organic photovoltaic materials.

Condens. Matter

31 July 2026

Sketch of the molecular structures of the donor groups with their name and acronym used for identification in parenthesis. The symbol (S) represents the binding site in the push–pull system.
  • Feature Paper
  • Article
  • Open Access

The theory of hole superconductivity has developed over more than three decades through a sequence of steps addressing distinct physical problems. This paper identifies and documents a recurring structural pattern in that development: ideas introduced to solve one problem were only later recognized as being required by independent physical constraints. By tracing a series of such delayed conceptual unifications, spanning pairing mechanism, charge expulsion, electrodynamics, spin structure, rotation, relativity, thermodynamics and momentum conservation, we highlight that the framework evolves by constraint tightening rather than by ad hoc embellishment. While this does not establish the correctness of the theory, it provides evidence that it is responding to real physical requirements uncovered progressively, in contrast to theories that accommodate discrepancies or new constraints primarily through auxiliary assumptions and ultimately fail.

Condens. Matter

20 July 2026

Schematic pictorial depiction of the principal elements of the theory of hole superconductivity.

Charge order driven by electron–phonon coupling is well understood at equilibrium but pump-probe experiments raise a new question: how does this order melt and recover after strong photoexcitation? A pump pulse promotes carriers across the charge-order gap and creates a nonequilibrium high-energy electronic population. In a closed system, the subsequent dynamics are constrained by energy conservation. In an ‘open system’—where the system is coupled to a thermal bath at some temperature Tbath—there are new fluctuation and dissipation processes at play. One can attempt a computational scheme that incorporates coupling of electrons to a laser pump, the coupling of system phonons to a thermal bath, and the Holstein interaction that couples electrons and phonons. We attempt an approximation where the pump-induced electronic excitations are modeled by a slowly time-varying ‘electron temperature’, Tel(t), indicative of a quasi-equilibrium electronic state. We solve the problem for different combinations of Tel and Tbath, probing the order parameter dynamics, the static properties and excitations in the long-time ‘quasi-steady state’, and establish a ‘phase diagram’ in terms of bath temperature and electron temperature.

Condens. Matter

17 July 2026

Schematic of two methods. Left: the response of a closed system (no thermal bath) to a pump pulse. The electrons ‘see’ the pump pulse and the phonon fluctuations, while the phonons see the fluctuating electron density. The system as a whole is energy conserving once the pump pulse passes. Right: the ‘two-temperature’ version of an open system. Here, the pump generates an effective electron temperature 
  
    
      T
      el
    
    
      (
      t
      )
    
  
, and electronic properties are computed as a thermal average at this temperature and in the background of instantaneous phonons. The phonons in turn see the instantaneous electron density. This scheme is valid provided 
  
    T
    el
  
 and the phonons vary on a timescale much greater than electron hopping.

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Condens. Matter - ISSN 2410-3896